diff --git a/Mathematics/4th/Real_and_functional_analysis/Real_and_functional_analysis.tex b/Mathematics/4th/Real_and_functional_analysis/Real_and_functional_analysis.tex
index dc87479..ec8ed6b 100644
--- a/Mathematics/4th/Real_and_functional_analysis/Real_and_functional_analysis.tex
+++ b/Mathematics/4th/Real_and_functional_analysis/Real_and_functional_analysis.tex
@@ -1172,7 +1172,10 @@
\end{enumerate}
\end{definition}
\begin{definition}
- Let $E$ be a normed vector space. The Banach space $E^*:=\mathcal{L}(E,\KK)$ is called \emph{dual space} of $E$.
+ Let $E$ be a normed vector space. The Banach space $E^*:=\mathcal{L}(E,\KK)$ is called \emph{dual space} of $E$. The \emph{bidual space} of $E$ is $E^{**}:=(E^*)^*$.
+ \end{definition}
+ \begin{definition}
+ Let $E$ be a normed vector space. We say that $E$ is \emph{reflexive} if $E=E^{**}$.
\end{definition}
\subsubsection{Compact operators}
\begin{definition}
@@ -1265,7 +1268,7 @@
\end{enumerate}
\end{definition}
\begin{theorem}[Hahn-Banach theorem]
- Let $E$ be a real vector space, $F\subseteq E$ be a subspace, $p:E\rightarrow\RR$ be a convex functional and $u\in F^*$. If $u(z)\leq p(z)$ $\forall z\in F$, then $\exists v\in E^*$ such that $v(z)=u(z)$ $\forall z\in F$ and $v(x)\leq p(x)$ $\forall x\in E$ ($v$ is called a \emph{prolongation} of $u$).
+ Let $E$ be a real vector space, $F\subseteq E$ be a subspace, $p:E\rightarrow\RR$ be a convex functional and $u\in F^*$. If $u(z)\leq p(z)$ $\forall z\in F$, then $\exists v\in E^*$ such that $v(z)=u(z)$ $\forall z\in F$ and $v(x)\leq p(x)$ $\forall x\in E$ ($v$ is called an \emph{extension} of $u$).
\end{theorem}
\begin{definition}[Seminorm]
Let $E$ be a vector space over $\KK$. A \emph{seminorm} $p:E\rightarrow[0,\infty)$ is a functional that satisfies:
@@ -1278,12 +1281,12 @@
Let $E$ be a vector space over $\KK$. A norm defined on $E$ is a seminorm.
\end{lemma}
\begin{theorem}[Hahn-Banach theorem]
- Let $E$ be a vector space over $\KK=\RR,\CC$, $F\subseteq E$ be a subspace, $p:E\rightarrow\RR$ be a seminorm and $u\in F^*$. If $\abs{u(z)}\leq p(z)$ $\forall z\in F$, then $\exists v\in E^*$ such that $v(z)=u(z)$ $\forall z\in F$ and $\abs{v(x)}\leq p(x)$ $\forall x\in E$. That is, $v$ prolongates $u$.
+ Let $E$ be a vector space over $\KK=\RR,\CC$, $F\subseteq E$ be a subspace, $p:E\rightarrow\RR$ be a seminorm and $u\in F^*$. If $\abs{u(z)}\leq p(z)$ $\forall z\in F$, then $\exists v\in E^*$ such that $v(z)=u(z)$ $\forall z\in F$ and $\abs{v(x)}\leq p(x)$ $\forall x\in E$. That is, $v$ extends $u$.
\end{theorem}
\begin{theorem}[Hahn-Banach theorem]
Let $E\ne\{0\}$ be a normed vector space.
\begin{enumerate}
- \item If $F\subseteq E$ is a subspace and $u\in F^*$, then $\exists v\in E^*$ such that prolongates $u$ and $\norm{v}=\norm{u}$.
+ \item If $F\subseteq E$ is a subspace and $u\in F^*$, then $\exists v\in E^*$ such that extends $u$ and $\norm{v}=\norm{u}$.
\item For all $a\in E$, $\exists v\in E^*$ such that $v(a)=\norm{a}$ and $\norm{v}=1$.
\item If $F\subseteq E$ is a closed subspace and $a\in E\setminus F$, then $\exists v\in E^*$ such that $v(a)=1$ and $v(F)=\{0\}$.
\end{enumerate}
@@ -1306,6 +1309,15 @@
\begin{proposition}
Let $E$, $F$ be normed vector spaces. The function $$\function{}{\mathcal{L}(E,F)}{\mathcal{L}(F^*,E^*)}{T}{T^*}$$ is linear, bijective and isometric. That is, $\norm{T}=\norm{T^*}$.
\end{proposition}
+ \begin{theorem}
+ Let $\Omega\subseteq \RR^n$ be a measurable set, $1\leq p\leq \infty$ and $q$ be the Hölder conjugate of $p$. Then:
+ \begin{itemize}
+ \item If $1
a})}}=0
+ $$
+ \end{definition}
+ \begin{proposition}
+ Let $(\Omega,\mathcal{F},\Prob)$ be a probability space and ${(X_n)}_{n\in\NN}$ be a family of uniformly integrable random variables such that $X_n\overset{\text{a.s.}}{\to} X$. Then, $X$ is integrable and $\Exp(X_n)\to \Exp(X)$.
+ \end{proposition}
+ \begin{theorem}
+ Let $(\Omega,\mathcal{F},\Prob)$ be a probability space and ${(M_n)}_{n\in\NN}$ be a martingale bounded in $L^p$, $1
Mathematics and Physics notes
- This website intends to summarize some notes about each important
subject in Mathematics and Physics degree at Autonomous University of Barcelona (UAB).
+ This website intends to summarize some notes about each important
subject in Mathematics and Physics degree at Autonomous University of Barcelona (UAB) and at Paris Dauphine - PSL University.
You can download the sections separately as you like or the whole file of Mathematics or Physics (better in order to avoid linking errors).
diff --git a/main_math.idx b/main_math.idx
index e55f700..31e0bbc 100644
--- a/main_math.idx
+++ b/main_math.idx
@@ -1,3055 +1,3096 @@
-\indexentry{Peano axioms|hyperpage}{5}
-\indexentry{Induction axiom|hyperpage}{5}
-\indexentry{Induction axiom|hyperpage}{5}
-\indexentry{set|hyperpage}{5}
-\indexentry{cardinal|hyperpage}{5}
-\indexentry{subset|hyperpage}{5}
-\indexentry{Axiom of extensionality|hyperpage}{5}
-\indexentry{equal|hyperpage}{5}
-\indexentry{power set|hyperpage}{5}
-\indexentry{empty set|hyperpage}{5}
-\indexentry{intersection|hyperpage}{5}
-\indexentry{union|hyperpage}{5}
-\indexentry{complement|hyperpage}{5}
-\indexentry{De Morgan's laws|hyperpage}{5}
-\indexentry{set difference|hyperpage}{5}
-\indexentry{predicate|hyperpage}{5}
-\indexentry{Cartesian product|hyperpage}{6}
-\indexentry{function|hyperpage}{6}
-\indexentry{composition|hyperpage}{6}
-\indexentry{image|hyperpage}{6}
-\indexentry{image|hyperpage}{6}
-\indexentry{preimage|hyperpage}{6}
-\indexentry{preimage|hyperpage}{6}
-\indexentry{injective|hyperpage}{6}
-\indexentry{surjective|hyperpage}{6}
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-\indexentry{invertible|hyperpage}{6}
-\indexentry{negation|hyperpage}{7}
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-\indexentry{$Q$ is true whenever $P$ is true|hyperpage}{7}
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-\indexentry{symmetric group|hyperpage}{7}
-\indexentry{order|hyperpage}{7}
-\indexentry{support|hyperpage}{7}
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-\indexentry{Orbit linear structure|hyperpage}{7}
-\indexentry{cycle|hyperpage}{7}
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-\indexentry{sign|hyperpage}{7}
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-\indexentry{poset|hyperpage}{8}
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-\indexentry{well-ordered set|hyperpage}{8}
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-\indexentry{Cantor's theorem|hyperpage}{8}
-\indexentry{characteristic function|hyperpage}{8}
-\indexentry{indicator function|hyperpage}{8}
-\indexentry{Binomial coefficient formulas|hyperpage}{8}
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-\indexentry{Combinations with repetition|hyperpage}{9}
-\indexentry{Variations without repetition|hyperpage}{9}
-\indexentry{Variacions with repetition|hyperpage}{9}
-\indexentry{multiple|hyperpage}{9}
-\indexentry{least common multiple|hyperpage}{9}
-\indexentry{greatest common divisor|hyperpage}{9}
-\indexentry{coprime|hyperpage}{9}
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-\indexentry{prime|hyperpage}{9}
-\indexentry{Bézout's theorem|hyperpage}{9}
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-\indexentry{Fundamental theorem of arithmetic|hyperpage}{9}
-\indexentry{Euclid's theorem|hyperpage}{9}
-\indexentry{Chinese remainder theorem|hyperpage}{10}
-\indexentry{Euler's totient function|hyperpage}{10}
-\indexentry{Euler's theorem|hyperpage}{10}
-\indexentry{Fermat's little theorem|hyperpage}{10}
-\indexentry{polynomial|hyperpage}{10}
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-\indexentry{coefficients|hyperpage}{10}
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-\indexentry{degree|hyperpage}{10}
-\indexentry{sum|hyperpage}{10}
-\indexentry{product|hyperpage}{10}
-\indexentry{Euclidian division|hyperpage}{10}
-\indexentry{monic|hyperpage}{10}
-\indexentry{Bézout's theorem|hyperpage}{10}
+\indexentry{Peano axioms|hyperpage}{6}
+\indexentry{Induction axiom|hyperpage}{6}
+\indexentry{Induction axiom|hyperpage}{6}
+\indexentry{set|hyperpage}{6}
+\indexentry{cardinal|hyperpage}{6}
+\indexentry{subset|hyperpage}{6}
+\indexentry{Axiom of extensionality|hyperpage}{6}
+\indexentry{equal|hyperpage}{6}
+\indexentry{power set|hyperpage}{6}
+\indexentry{empty set|hyperpage}{6}
+\indexentry{intersection|hyperpage}{6}
+\indexentry{union|hyperpage}{6}
+\indexentry{complement|hyperpage}{6}
+\indexentry{De Morgan's laws|hyperpage}{6}
+\indexentry{set difference|hyperpage}{6}
+\indexentry{predicate|hyperpage}{6}
+\indexentry{Cartesian product|hyperpage}{7}
+\indexentry{function|hyperpage}{7}
+\indexentry{composition|hyperpage}{7}
+\indexentry{image|hyperpage}{7}
+\indexentry{image|hyperpage}{7}
+\indexentry{preimage|hyperpage}{7}
+\indexentry{preimage|hyperpage}{7}
+\indexentry{injective|hyperpage}{7}
+\indexentry{surjective|hyperpage}{7}
+\indexentry{bijective|hyperpage}{7}
+\indexentry{inverse function|hyperpage}{7}
+\indexentry{invertible|hyperpage}{7}
+\indexentry{negation|hyperpage}{8}
+\indexentry{$P$ and $Q$ are both true|hyperpage}{8}
+\indexentry{either $P$ or $Q$ are true|hyperpage}{8}
+\indexentry{$Q$ is true whenever $P$ is true|hyperpage}{8}
+\indexentry{$P$ and $Q$ have the same truth-value|hyperpage}{8}
+\indexentry{symmetric group|hyperpage}{8}
+\indexentry{order|hyperpage}{8}
+\indexentry{support|hyperpage}{8}
+\indexentry{orbit|hyperpage}{8}
+\indexentry{Orbit structure|hyperpage}{8}
+\indexentry{Orbit linear structure|hyperpage}{8}
+\indexentry{cycle|hyperpage}{8}
+\indexentry{transposition|hyperpage}{8}
+\indexentry{sign|hyperpage}{8}
+\indexentry{equivalence relation|hyperpage}{8}
+\indexentry{equivalence class|hyperpage}{8}
+\indexentry{partial order relation|hyperpage}{9}
+\indexentry{partially ordered set|hyperpage}{9}
+\indexentry{poset|hyperpage}{9}
+\indexentry{minimal element|hyperpage}{9}
+\indexentry{least element|hyperpage}{9}
+\indexentry{maximal element|hyperpage}{9}
+\indexentry{total order relation|hyperpage}{9}
+\indexentry{well-order relation|hyperpage}{9}
+\indexentry{well-ordered set|hyperpage}{9}
+\indexentry{Cantor-Bernstein theorem|hyperpage}{9}
+\indexentry{Cantor's theorem|hyperpage}{9}
+\indexentry{characteristic function|hyperpage}{9}
+\indexentry{indicator function|hyperpage}{9}
+\indexentry{Binomial coefficient formulas|hyperpage}{9}
+\indexentry{Pigeonhole principle|hyperpage}{10}
+\indexentry{Combinations without repetition|hyperpage}{10}
+\indexentry{Combinations with repetition|hyperpage}{10}
+\indexentry{Variations without repetition|hyperpage}{10}
+\indexentry{Variacions with repetition|hyperpage}{10}
+\indexentry{multiple|hyperpage}{10}
+\indexentry{least common multiple|hyperpage}{10}
+\indexentry{greatest common divisor|hyperpage}{10}
\indexentry{coprime|hyperpage}{10}
\indexentry{relatively prime|hyperpage}{10}
+\indexentry{prime|hyperpage}{10}
+\indexentry{Bézout's theorem|hyperpage}{10}
\indexentry{Gau\ss ' theorem|hyperpage}{10}
-\indexentry{prime|hyperpage}{11}
-\indexentry{evaluation|hyperpage}{11}
-\indexentry{root|hyperpage}{11}
-\indexentry{Ruffini's rule|hyperpage}{11}
-\indexentry{irreducible|hyperpage}{11}
-\indexentry{D'Alembert theorem|hyperpage}{11}
-\indexentry{linear equation|hyperpage}{12}
-\indexentry{variables|hyperpage}{12}
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-\indexentry{constant term|hyperpage}{12}
-\indexentry{system of linear equations|hyperpage}{12}
-\indexentry{solution of a system of equations|hyperpage}{12}
-\indexentry{equivalent|hyperpage}{12}
-\indexentry{Matrix|hyperpage}{12}
-\indexentry{matrix|hyperpage}{12}
-\indexentry{sum|hyperpage}{12}
-\indexentry{product|hyperpage}{12}
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-\indexentry{product|hyperpage}{12}
-\indexentry{Properties of matrix product|hyperpage}{12}
-\indexentry{invertible|hyperpage}{13}
-\indexentry{idempotent|hyperpage}{13}
-\indexentry{nilpotent|hyperpage}{13}
-\indexentry{index|hyperpage}{13}
-\indexentry{$i$-th pivot|hyperpage}{13}
-\indexentry{Row echelon form|hyperpage}{13}
-\indexentry{row echelon form|hyperpage}{13}
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-\indexentry{reduced row echelon form|hyperpage}{13}
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-\indexentry{PAQ reduction theorem|hyperpage}{13}
-\indexentry{Rank|hyperpage}{13}
-\indexentry{rank|hyperpage}{13}
-\indexentry{Transposition|hyperpage}{13}
-\indexentry{transpose|hyperpage}{13}
-\indexentry{Rouché-Frobenius theorem|hyperpage}{13}
-\indexentry{determined and consistent|hyperpage}{13}
-\indexentry{indeterminate|hyperpage}{13}
-\indexentry{free variables|hyperpage}{13}
-\indexentry{inconsistent|hyperpage}{13}
-\indexentry{Determinant|hyperpage}{13}
-\indexentry{cofactor matrix|hyperpage}{14}
-\indexentry{adjugate matrix|hyperpage}{14}
-\indexentry{block matrix|hyperpage}{14}
-\indexentry{vector space|hyperpage}{14}
-\indexentry{vectors|hyperpage}{14}
-\indexentry{scalars|hyperpage}{14}
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-\indexentry{orthogonal complement|hyperpage}{21}
-\indexentry{radical|hyperpage}{21}
-\indexentry{nonsingular|hyperpage}{21}
+\indexentry{Prime number theorem|hyperpage}{10}
+\indexentry{Fundamental theorem of arithmetic|hyperpage}{10}
+\indexentry{Euclid's theorem|hyperpage}{10}
+\indexentry{Chinese remainder theorem|hyperpage}{11}
+\indexentry{Euler's totient function|hyperpage}{11}
+\indexentry{Euler's theorem|hyperpage}{11}
+\indexentry{Fermat's little theorem|hyperpage}{11}
+\indexentry{polynomial|hyperpage}{11}
+\indexentry{variable|hyperpage}{11}
+\indexentry{indeterminate|hyperpage}{11}
+\indexentry{coefficients|hyperpage}{11}
+\indexentry{constant term|hyperpage}{11}
+\indexentry{leading coefficient|hyperpage}{11}
+\indexentry{degree|hyperpage}{11}
+\indexentry{sum|hyperpage}{11}
+\indexentry{product|hyperpage}{11}
+\indexentry{Euclidian division|hyperpage}{11}
+\indexentry{monic|hyperpage}{11}
+\indexentry{Bézout's theorem|hyperpage}{11}
+\indexentry{coprime|hyperpage}{11}
+\indexentry{relatively prime|hyperpage}{11}
+\indexentry{Gau\ss ' theorem|hyperpage}{11}
+\indexentry{prime|hyperpage}{12}
+\indexentry{evaluation|hyperpage}{12}
+\indexentry{root|hyperpage}{12}
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+\indexentry{irreducible|hyperpage}{12}
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+\indexentry{variables|hyperpage}{13}
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+\indexentry{product|hyperpage}{13}
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+\indexentry{product|hyperpage}{13}
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+\indexentry{row echelon form|hyperpage}{14}
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+\indexentry{reduced row echelon form|hyperpage}{14}
+\indexentry{Gau\ss ' theorem|hyperpage}{14}
+\indexentry{PAQ reduction theorem|hyperpage}{14}
+\indexentry{Rank|hyperpage}{14}
+\indexentry{rank|hyperpage}{14}
+\indexentry{Transposition|hyperpage}{14}
+\indexentry{transpose|hyperpage}{14}
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+\indexentry{determined and consistent|hyperpage}{14}
+\indexentry{indeterminate|hyperpage}{14}
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+\indexentry{inconsistent|hyperpage}{14}
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+\indexentry{cofactor matrix|hyperpage}{15}
+\indexentry{adjugate matrix|hyperpage}{15}
+\indexentry{block matrix|hyperpage}{15}
+\indexentry{vector space|hyperpage}{15}
+\indexentry{vectors|hyperpage}{15}
+\indexentry{scalars|hyperpage}{15}
+\indexentry{vector subspace|hyperpage}{16}
+\indexentry{linear combination|hyperpage}{16}
+\indexentry{linear span|hyperpage}{16}
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+\indexentry{dimension|hyperpage}{16}
+\indexentry{coordinates|hyperpage}{16}
+\indexentry{sum|hyperpage}{16}
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+\indexentry{minor|hyperpage}{16}
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+\indexentry{equivalent|hyperpage}{17}
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+\indexentry{image|hyperpage}{17}
+\indexentry{kernel|hyperpage}{17}
+\indexentry{isomorphic|hyperpage}{17}
+\indexentry{Coordination theorem|hyperpage}{17}
+\indexentry{First isomorphism theorem|hyperpage}{18}
+\indexentry{Second isomorphism theorem|hyperpage}{18}
+\indexentry{Third isomorphism theorem|hyperpage}{18}
+\indexentry{matrix|hyperpage}{18}
+\indexentry{change-of-basis matrix|hyperpage}{18}
+\indexentry{Change of basis formula|hyperpage}{18}
+\indexentry{dual space|hyperpage}{19}
+\indexentry{Kronecker delta|hyperpage}{19}
+\indexentry{dual basis|hyperpage}{19}
+\indexentry{Dual map|hyperpage}{19}
+\indexentry{dual map|hyperpage}{19}
+\indexentry{Double dual space|hyperpage}{19}
+\indexentry{double dual space|hyperpage}{19}
+\indexentry{annihilator|hyperpage}{19}
+\indexentry{annihilator|hyperpage}{19}
+\indexentry{homothety|hyperpage}{19}
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+\indexentry{similar|hyperpage}{20}
+\indexentry{diagonal|hyperpage}{20}
+\indexentry{diagonalizable|hyperpage}{20}
+\indexentry{diagonalizable|hyperpage}{20}
+\indexentry{eigenvector|hyperpage}{20}
+\indexentry{eigenspace|hyperpage}{20}
+\indexentry{characteristic polynomial|hyperpage}{20}
+\indexentry{characteristic polynomial|hyperpage}{20}
+\indexentry{algebraic multiplicity|hyperpage}{20}
+\indexentry{geometric multiplicity|hyperpage}{20}
+\indexentry{Diagonalization theorem|hyperpage}{20}
+\indexentry{minimal polynomial|hyperpage}{20}
+\indexentry{Cayley-Hamilton theorem|hyperpage}{21}
+\indexentry{Cayley-Hamilton theorem|hyperpage}{21}
+\indexentry{algebraically closed field|hyperpage}{21}
+\indexentry{invariant subspace|hyperpage}{21}
+\indexentry{Jordan block|hyperpage}{21}
+\indexentry{Jordan matrix|hyperpage}{21}
+\indexentry{Jordan form|hyperpage}{21}
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+\indexentry{bilinear form|hyperpage}{22}
+\indexentry{symmetric|hyperpage}{22}
+\indexentry{matrix of the bilinear form|hyperpage}{22}
\indexentry{orthogonal|hyperpage}{22}
-\indexentry{orthogonal projection|hyperpage}{22}
-\indexentry{Gram-Schmidt process|hyperpage}{22}
-\indexentry{orthogonal geometry|hyperpage}{22}
-\indexentry{isometry|hyperpage}{22}
-\indexentry{isometric|hyperpage}{22}
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+\indexentry{class $\mathcal {C}^p$|hyperpage}{31}
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+\indexentry{partition|hyperpage}{32}
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+\indexentry{upper sum|hyperpage}{32}
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+\indexentry{lower integral|hyperpage}{32}
+\indexentry{upper integral|hyperpage}{32}
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+\indexentry{primitive function|hyperpage}{33}
+\indexentry{Integration by parts|hyperpage}{33}
+\indexentry{Integration by substitution|hyperpage}{33}
+\indexentry{Riemann sum|hyperpage}{34}
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+\indexentry{rectifiable|hyperpage}{34}
+\indexentry{length of the polygonal|hyperpage}{34}
+\indexentry{Surface of revolution|hyperpage}{34}
+\indexentry{Surface of revolution|hyperpage}{34}
+\indexentry{Volume of revolution|hyperpage}{34}
+\indexentry{Volume of revolution|hyperpage}{34}
+\indexentry{Center of masses|hyperpage}{35}
+\indexentry{center of masses|hyperpage}{35}
+\indexentry{Hermite reduction method|hyperpage}{35}
+\indexentry{Group|hyperpage}{37}
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+\indexentry{abelian|hyperpage}{37}
+\indexentry{Subgroup|hyperpage}{37}
+\indexentry{subgroup|hyperpage}{37}
+\indexentry{proper|hyperpage}{37}
+\indexentry{improper|hyperpage}{37}
+\indexentry{order|hyperpage}{37}
+\indexentry{subgroup generated|hyperpage}{37}
+\indexentry{cyclic group|hyperpage}{37}
+\indexentry{order|hyperpage}{37}
+\indexentry{Group morphism|hyperpage}{38}
+\indexentry{group morphism|hyperpage}{38}
+\indexentry{normal|hyperpage}{38}
+\indexentry{kernel|hyperpage}{38}
+\indexentry{image|hyperpage}{38}
+\indexentry{isomorphism|hyperpage}{38}
+\indexentry{isomorphic|hyperpage}{38}
+\indexentry{Classification of cyclic groups|hyperpage}{38}
+\indexentry{symmetric group|hyperpage}{38}
+\indexentry{Cayley's theorem|hyperpage}{39}
+\indexentry{right cosets|hyperpage}{39}
+\indexentry{left cosets|hyperpage}{39}
+\indexentry{set of right cosets|hyperpage}{39}
+\indexentry{set of left cosets|hyperpage}{39}
+\indexentry{Lagrange's theorem|hyperpage}{39}
+\indexentry{index|hyperpage}{39}
+\indexentry{Quotient group|hyperpage}{39}
+\indexentry{quotient group|hyperpage}{39}
+\indexentry{First isomorphism theorem|hyperpage}{39}
+\indexentry{products of group subsets|hyperpage}{40}
+\indexentry{Second isomorphism theorem|hyperpage}{40}
+\indexentry{Correspondence theorem|hyperpage}{40}
+\indexentry{Third isomorphism theorem|hyperpage}{40}
+\indexentry{(left) group action|hyperpage}{40}
+\indexentry{(left) $G$-set|hyperpage}{40}
+\indexentry{orbit|hyperpage}{40}
+\indexentry{stabilizer|hyperpage}{40}
+\indexentry{Orbit-stabilizer theorem|hyperpage}{40}
+\indexentry{Orbits formula|hyperpage}{40}
+\indexentry{Cauchy's theorem|hyperpage}{41}
+\indexentry{conjugation action|hyperpage}{41}
+\indexentry{Center of a group|hyperpage}{41}
+\indexentry{center|hyperpage}{41}
+\indexentry{normalizer|hyperpage}{41}
+\indexentry{First Sylow theorem|hyperpage}{41}
+\indexentry{$p$-group|hyperpage}{41}
+\indexentry{Sylow $p$-subgroup|hyperpage}{41}
+\indexentry{solvable|hyperpage}{41}
+\indexentry{Second Sylow theorem|hyperpage}{41}
+\indexentry{Third Sylow theorem|hyperpage}{41}
+\indexentry{alternating group|hyperpage}{42}
+\indexentry{dihedral group|hyperpage}{42}
+\indexentry{quaternion group|hyperpage}{42}
+\indexentry{dicyclic group|hyperpage}{42}
+\indexentry{Ring|hyperpage}{42}
+\indexentry{ring|hyperpage}{42}
+\indexentry{noncommutative ring|hyperpage}{42}
+\indexentry{Field|hyperpage}{42}
+\indexentry{field|hyperpage}{42}
+\indexentry{set of polynomials|hyperpage}{42}
+\indexentry{Boolean ring|hyperpage}{42}
+\indexentry{Subring|hyperpage}{42}
+\indexentry{subring|hyperpage}{42}
+\indexentry{Ring morphism|hyperpage}{43}
+\indexentry{ring morphism|hyperpage}{43}
+\indexentry{Ideal|hyperpage}{43}
+\indexentry{ideal|hyperpage}{43}
+\indexentry{Principal ideal|hyperpage}{43}
+\indexentry{principal ideal|hyperpage}{43}
+\indexentry{unit|hyperpage}{43}
+\indexentry{multiplicative group|hyperpage}{43}
+\indexentry{Noetherian|hyperpage}{43}
+\indexentry{Hilbert's basis theorem|hyperpage}{43}
+\indexentry{First isomorphism theorem|hyperpage}{44}
+\indexentry{Second isomorphism theorem|hyperpage}{44}
+\indexentry{Third isomorphism theorem|hyperpage}{44}
+\indexentry{Correspondence theorem|hyperpage}{44}
+\indexentry{integral domain|hyperpage}{44}
+\indexentry{zero divisor|hyperpage}{44}
+\indexentry{principal ideal domain|hyperpage}{44}
+\indexentry{PID|hyperpage}{44}
+\indexentry{prime|hyperpage}{44}
+\indexentry{maximal|hyperpage}{44}
+\indexentry{irreducible|hyperpage}{44}
+\indexentry{prime|hyperpage}{44}
+\indexentry{degree|hyperpage}{45}
+\indexentry{Universal property of polynomials|hyperpage}{45}
+\indexentry{Universal property of polynomials in several variables|hyperpage}{45}
+\indexentry{Fundamental theorem of algebra|hyperpage}{45}
+\indexentry{Hilbert's Nullstellensatz|hyperpage}{45}
+\indexentry{Eisenstein's criterion|hyperpage}{45}
+\indexentry{General Eisenstein's criterion|hyperpage}{45}
+\indexentry{associated|hyperpage}{45}
+\indexentry{unique factorization domain|hyperpage}{45}
+\indexentry{UFD|hyperpage}{45}
+\indexentry{greatest common divisor|hyperpage}{46}
+\indexentry{ascending chain condition on principal ideals|hyperpage}{46}
+\indexentry{ACCP|hyperpage}{46}
+\indexentry{field of fractions|hyperpage}{46}
+\indexentry{primitive polynomial|hyperpage}{47}
+\indexentry{Gau\ss ' lemma|hyperpage}{47}
+\indexentry{Eisenstein's criterion|hyperpage}{47}
+\indexentry{Gau\ss ian integers|hyperpage}{47}
+\indexentry{ordinary generating function|hyperpage}{48}
+\indexentry{Closed forms|hyperpage}{48}
+\indexentry{exponential generating function|hyperpage}{48}
+\indexentry{exponential series|hyperpage}{48}
+\indexentry{recurrence relation of order $k$|hyperpage}{48}
+\indexentry{recurrent|hyperpage}{48}
+\indexentry{initial values|hyperpage}{48}
+\indexentry{linear recurrence relation of order $k$|hyperpage}{48}
+\indexentry{homogeneous|hyperpage}{49}
+\indexentry{characteristic polynomial|hyperpage}{49}
+\indexentry{graph|hyperpage}{49}
+\indexentry{order|hyperpage}{49}
+\indexentry{size|hyperpage}{49}
+\indexentry{adjacent|hyperpage}{49}
+\indexentry{incident|hyperpage}{49}
+\indexentry{loop|hyperpage}{49}
+\indexentry{multiple edges|hyperpage}{49}
+\indexentry{finite|hyperpage}{49}
+\indexentry{simple|hyperpage}{49}
+\indexentry{complete graph|hyperpage}{49}
+\indexentry{degree of a vertex|hyperpage}{49}
+\indexentry{Handshaking lemma|hyperpage}{49}
+\indexentry{degree sequence|hyperpage}{49}
+\indexentry{regular|hyperpage}{49}
+\indexentry{induced subgraph|hyperpage}{49}
+\indexentry{walk|hyperpage}{49}
+\indexentry{closed|hyperpage}{49}
+\indexentry{trail|hyperpage}{49}
+\indexentry{path|hyperpage}{49}
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+\indexentry{cycle|hyperpage}{49}
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+\indexentry{connected|hyperpage}{50}
+\indexentry{bipartite|hyperpage}{50}
+\indexentry{bridge|hyperpage}{50}
+\indexentry{Eulerian trail|hyperpage}{50}
+\indexentry{Eulerian circuit|hyperpage}{50}
+\indexentry{Eulerian|hyperpage}{50}
+\indexentry{Euler theorem|hyperpage}{50}
+\indexentry{adjacency matrix|hyperpage}{50}
+\indexentry{tree|hyperpage}{50}
+\indexentry{leave|hyperpage}{50}
+\indexentry{generator tree|hyperpage}{50}
+\indexentry{traversable|hyperpage}{50}
+\indexentry{isomorphic|hyperpage}{50}
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+\indexentry{objective function|hyperpage}{51}
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+\indexentry{canonical form of a linear programming to maximize|hyperpage}{51}
+\indexentry{objective function|hyperpage}{51}
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+\indexentry{canonical form of a linear programming to minimize|hyperpage}{51}
+\indexentry{feasible region|hyperpage}{51}
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+\indexentry{polyhedron|hyperpage}{51}
+\indexentry{polytope|hyperpage}{51}
+\indexentry{standard form|hyperpage}{51}
+\indexentry{basic feasible solutions|hyperpage}{51}
+\indexentry{Simplex method: Phase I|hyperpage}{51}
+\indexentry{Simplex method: Phase II|hyperpage}{51}
+\indexentry{dual program|hyperpage}{51}
+\indexentry{primal|hyperpage}{51}
+\indexentry{Weak duality theorem|hyperpage}{51}
+\indexentry{linear programming to minimize|hyperpage}{51}
+\indexentry{Strong duality theorem|hyperpage}{52}
+\indexentry{Complementary property|hyperpage}{52}
+\indexentry{distance|hyperpage}{53}
+\indexentry{triangular inequality|hyperpage}{53}
+\indexentry{metric space|hyperpage}{53}
+\indexentry{norm|hyperpage}{53}
+\indexentry{triangular inequality|hyperpage}{53}
+\indexentry{normed vector space|hyperpage}{53}
+\indexentry{dot product|hyperpage}{53}
+\indexentry{Euclidean space|hyperpage}{53}
+\indexentry{Cauchy-Schwarz inequality|hyperpage}{53}
+\indexentry{Parallelogram law|hyperpage}{53}
+\indexentry{norm|hyperpage}{53}
+\indexentry{sphere|hyperpage}{54}
+\indexentry{open ball|hyperpage}{54}
+\indexentry{closed ball|hyperpage}{54}
+\indexentry{bounded set|hyperpage}{54}
+\indexentry{neighbourhood|hyperpage}{54}
+\indexentry{interior point|hyperpage}{54}
+\indexentry{interior|hyperpage}{54}
+\indexentry{exterior point|hyperpage}{54}
+\indexentry{exterior|hyperpage}{54}
+\indexentry{adherent point|hyperpage}{54}
+\indexentry{adherence|hyperpage}{54}
+\indexentry{accumulation point|hyperpage}{54}
+\indexentry{limit set|hyperpage}{54}
+\indexentry{isolated point|hyperpage}{54}
+\indexentry{boundary point|hyperpage}{54}
+\indexentry{boundary|hyperpage}{54}
+\indexentry{Bolzano-Weierstra\ss \ theorem|hyperpage}{54}
+\indexentry{open|hyperpage}{54}
+\indexentry{closed|hyperpage}{54}
+\indexentry{connected|hyperpage}{54}
+\indexentry{sequence|hyperpage}{54}
+\indexentry{convergent|hyperpage}{54}
+\indexentry{Cauchy sequence|hyperpage}{54}
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+\indexentry{compact|hyperpage}{54}
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+\indexentry{graph|hyperpage}{55}
+\indexentry{level set|hyperpage}{55}
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+\indexentry{uniformly continuous|hyperpage}{55}
+\indexentry{Heine's theorem|hyperpage}{55}
+\indexentry{Weierstra\ss ' theorem|hyperpage}{55}
+\indexentry{Intermediate value theorem|hyperpage}{55}
+\indexentry{Lipschitz continuous|hyperpage}{55}
+\indexentry{contraction|hyperpage}{55}
+\indexentry{modulus of continuity|hyperpage}{55}
+\indexentry{differentiable|hyperpage}{55}
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+\indexentry{Jacobian determinant|hyperpage}{55}
+\indexentry{gradient|hyperpage}{56}
+\indexentry{Chain rule|hyperpage}{56}
+\indexentry{class|hyperpage}{56}
+\indexentry{class|hyperpage}{56}
+\indexentry{Differentiability criterion|hyperpage}{56}
+\indexentry{Mean value theorem|hyperpage}{56}
+\indexentry{Mean value theorem for vector-valued functions|hyperpage}{56}
+\indexentry{partial derivative of order $k$|hyperpage}{56}
+\indexentry{Hessian matrix|hyperpage}{56}
+\indexentry{Schwarz's theorem|hyperpage}{57}
+\indexentry{Inverse function theorem|hyperpage}{57}
+\indexentry{diffeomorphism|hyperpage}{57}
+\indexentry{Implicit function theorem|hyperpage}{57}
+\indexentry{Taylor's theorem|hyperpage}{57}
+\indexentry{multi-index notation|hyperpage}{57}
+\indexentry{local maximum|hyperpage}{57}
+\indexentry{local minimum|hyperpage}{57}
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+\indexentry{global maximum|hyperpage}{57}
+\indexentry{global minimum|hyperpage}{57}
+\indexentry{critical point|hyperpage}{57}
+\indexentry{saddle point|hyperpage}{57}
+\indexentry{Sylvester's criterion|hyperpage}{58}
+\indexentry{Lagrange multipliers theorem|hyperpage}{58}
+\indexentry{rectangle|hyperpage}{58}
\indexentry{$n$-dimensional volume|hyperpage}{58}
-\indexentry{Cavalieri's principle|hyperpage}{58}
-\indexentry{Center of mass|hyperpage}{58}
-\indexentry{center of mass|hyperpage}{58}
-\indexentry{Moment of inertia|hyperpage}{58}
-\indexentry{moment of inertia|hyperpage}{58}
-\indexentry{integrable function|hyperpage}{58}
-\indexentry{Riemann-integrable function|hyperpage}{58}
-\indexentry{$y$-simple|hyperpage}{58}
-\indexentry{$yz$-simple|hyperpage}{58}
-\indexentry{$xz$-simple|hyperpage}{58}
-\indexentry{Change of variable theorem|hyperpage}{59}
-\indexentry{Integral in polar coordinates|hyperpage}{59}
-\indexentry{Integral in cylindrical coordinates|hyperpage}{59}
-\indexentry{Integral in spherical coordinates|hyperpage}{59}
-\indexentry{length of the polygonal|hyperpage}{59}
-\indexentry{arc length|hyperpage}{59}
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-\indexentry{reparametrization|hyperpage}{59}
-\indexentry{arc length parameter|hyperpage}{59}
-\indexentry{vector field|hyperpage}{59}
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-\indexentry{line integral|hyperpage}{60}
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-\indexentry{curl|hyperpage}{60}
-\indexentry{Laplacian|hyperpage}{60}
-\indexentry{parametrized surface|hyperpage}{60}
-\indexentry{surface integral|hyperpage}{60}
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+\indexentry{surface|hyperpage}{58}
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+\indexentry{Fubini's theorem for elementary regions|hyperpage}{59}
+\indexentry{$n$-dimensional volume|hyperpage}{59}
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+\indexentry{Center of mass|hyperpage}{59}
+\indexentry{center of mass|hyperpage}{59}
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+\indexentry{moment of inertia|hyperpage}{59}
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+\indexentry{$y$-simple|hyperpage}{59}
+\indexentry{$yz$-simple|hyperpage}{59}
+\indexentry{$xz$-simple|hyperpage}{59}
+\indexentry{Change of variable theorem|hyperpage}{60}
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+\indexentry{Integral in cylindrical coordinates|hyperpage}{60}
+\indexentry{Integral in spherical coordinates|hyperpage}{60}
+\indexentry{length of the polygonal|hyperpage}{60}
+\indexentry{arc length|hyperpage}{60}
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+\indexentry{arc length parameter|hyperpage}{60}
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+\indexentry{Laplacian|hyperpage}{61}
+\indexentry{parametrized surface|hyperpage}{61}
\indexentry{surface integral|hyperpage}{61}
-\indexentry{flux|hyperpage}{61}
-\indexentry{differential 1-form|hyperpage}{61}
-\indexentry{Green's theorem|hyperpage}{61}
-\indexentry{Divergence theorem on $\ensuremath {\mathbb {R}}^2$|hyperpage}{61}
-\indexentry{Stokes' theorem|hyperpage}{61}
-\indexentry{symmetric|hyperpage}{61}
-\indexentry{Divergence theorem on $\ensuremath {\mathbb {R}}^3$|hyperpage}{61}
-\indexentry{2-forms|hyperpage}{61}
-\indexentry{3-forms|hyperpage}{61}
-\indexentry{Euclid's axioms|hyperpage}{62}
-\indexentry{Playfair's axiom|hyperpage}{62}
-\indexentry{points|hyperpage}{62}
-\indexentry{lines|hyperpage}{62}
-\indexentry{incidence relation|hyperpage}{62}
-\indexentry{order relation|hyperpage}{62}
-\indexentry{congruence relation|hyperpage}{62}
-\indexentry{Incidence axioms|hyperpage}{62}
-\indexentry{Order axioms|hyperpage}{62}
-\indexentry{Pasch's axiom|hyperpage}{62}
-\indexentry{ray|hyperpage}{62}
-\indexentry{half-line|hyperpage}{62}
-\indexentry{half-plane|hyperpage}{62}
-\indexentry{angle|hyperpage}{62}
-\indexentry{Congruence axioms|hyperpage}{62}
-\indexentry{SAS criterion|hyperpage}{62}
-\indexentry{Continuity axioms|hyperpage}{62}
-\indexentry{Axiom of Archimedes|hyperpage}{62}
-\indexentry{Axiom of completeness|hyperpage}{62}
-\indexentry{RC|hyperpage}{63}
-\indexentry{CC|hyperpage}{63}
-\indexentry{Axiom of Parallels|hyperpage}{63}
-\indexentry{Hilbert plane|hyperpage}{63}
-\indexentry{Pythagorean plane|hyperpage}{63}
-\indexentry{Euclidean plane|hyperpage}{63}
-\indexentry{Cartesian geometry|hyperpage}{63}
-\indexentry{Absolute geometry|hyperpage}{63}
+\indexentry{surface integral|hyperpage}{62}
+\indexentry{flux|hyperpage}{62}
+\indexentry{differential 1-form|hyperpage}{62}
+\indexentry{Green's theorem|hyperpage}{62}
+\indexentry{Divergence theorem on $\ensuremath {\mathbb {R}}^2$|hyperpage}{62}
+\indexentry{Stokes' theorem|hyperpage}{62}
+\indexentry{symmetric|hyperpage}{62}
+\indexentry{Divergence theorem on $\ensuremath {\mathbb {R}}^3$|hyperpage}{62}
+\indexentry{2-forms|hyperpage}{62}
+\indexentry{3-forms|hyperpage}{62}
+\indexentry{Euclid's axioms|hyperpage}{63}
+\indexentry{Playfair's axiom|hyperpage}{63}
+\indexentry{points|hyperpage}{63}
+\indexentry{lines|hyperpage}{63}
+\indexentry{incidence relation|hyperpage}{63}
+\indexentry{order relation|hyperpage}{63}
+\indexentry{congruence relation|hyperpage}{63}
+\indexentry{Incidence axioms|hyperpage}{63}
+\indexentry{Order axioms|hyperpage}{63}
+\indexentry{Pasch's axiom|hyperpage}{63}
+\indexentry{ray|hyperpage}{63}
+\indexentry{half-line|hyperpage}{63}
+\indexentry{half-plane|hyperpage}{63}
+\indexentry{angle|hyperpage}{63}
+\indexentry{Congruence axioms|hyperpage}{63}
\indexentry{SAS criterion|hyperpage}{63}
-\indexentry{SSS criterion|hyperpage}{63}
-\indexentry{Exterior angle theorem|hyperpage}{63}
-\indexentry{ASA criterion|hyperpage}{63}
-\indexentry{SAA criterion|hyperpage}{63}
-\indexentry{Saccheri-Legendre theorem|hyperpage}{63}
-\indexentry{ordered field|hyperpage}{63}
-\indexentry{Pythagorean|hyperpage}{63}
-\indexentry{Archimedean|hyperpage}{63}
-\indexentry{Euclidean|hyperpage}{63}
-\indexentry{Hilbert field|hyperpage}{63}
-\indexentry{constructible field|hyperpage}{63}
-\indexentry{Hyperbolic geometry|hyperpage}{64}
-\indexentry{Hyperbolic geometry|hyperpage}{64}
-\indexentry{Non-Paschian geometry|hyperpage}{64}
-\indexentry{Non-Paschian geometry|hyperpage}{64}
-\indexentry{Construction of a non-Paschian geometry|hyperpage}{64}
-\indexentry{Non-SAS geometry|hyperpage}{65}
-\indexentry{Non-SAS geometry|hyperpage}{65}
-\indexentry{Construction of a non-SAS geometry|hyperpage}{65}
-\indexentry{Non-Archimedean geometry|hyperpage}{65}
-\indexentry{Non-Archimedean geometry|hyperpage}{65}
-\indexentry{axiomatic projective space|hyperpage}{65}
-\indexentry{Projective axiom|hyperpage}{65}
-\indexentry{projective subvariety|hyperpage}{65}
-\indexentry{collineation|hyperpage}{65}
-\indexentry{dimension|hyperpage}{65}
-\indexentry{projective plane|hyperpage}{65}
-\indexentry{Duality principle|hyperpage}{65}
-\indexentry{affine plane|hyperpage}{65}
-\indexentry{Passage from the projective plane to the affine plane|hyperpage}{65}
-\indexentry{Passage from the affine plane to the projective plane|hyperpage}{65}
-\indexentry{$n$-dimensional projective space|hyperpage}{66}
-\indexentry{homography|hyperpage}{66}
-\indexentry{semilinear isomorphism|hyperpage}{66}
-\indexentry{isomorphism between projective spaces|hyperpage}{66}
-\indexentry{$m$-dimensional projective subvariety|hyperpage}{66}
-\indexentry{line|hyperpage}{66}
-\indexentry{hyperplane|hyperpage}{66}
-\indexentry{homogeneous coordinates|hyperpage}{66}
-\indexentry{projective frame|hyperpage}{66}
-\indexentry{equation of the hyperplane|hyperpage}{66}
-\indexentry{Gra\ss mann formula|hyperpage}{66}
-\indexentry{configuration|hyperpage}{66}
-\indexentry{realizable|hyperpage}{66}
-\indexentry{theorem|hyperpage}{66}
-\indexentry{Fano configuration|hyperpage}{66}
-\indexentry{Pappus configuration|hyperpage}{67}
-\indexentry{in perspective with respect to a point|hyperpage}{67}
-\indexentry{centre of perspectivity|hyperpage}{67}
-\indexentry{in perspective with respect to a line|hyperpage}{67}
-\indexentry{axis of perspectivity|hyperpage}{67}
-\indexentry{Desargues' theorem|hyperpage}{67}
-\indexentry{Desargues configuration|hyperpage}{67}
-\indexentry{non-Desarguesian planes|hyperpage}{67}
-\indexentry{Coordination theorem|hyperpage}{67}
-\indexentry{Fundamental theorem of projective geometry|hyperpage}{67}
-\indexentry{Cross ratio|hyperpage}{68}
-\indexentry{cross ratio|hyperpage}{68}
-\indexentry{harmonic ratio|hyperpage}{68}
-\indexentry{cross ratio|hyperpage}{68}
-\indexentry{perspectivity|hyperpage}{68}
-\indexentry{projectivity|hyperpage}{68}
-\indexentry{Plücker coordinates|hyperpage}{68}
-\indexentry{affine space|hyperpage}{68}
-\indexentry{dimension|hyperpage}{68}
-\indexentry{affine combination|hyperpage}{68}
-\indexentry{affinely independents|hyperpage}{68}
-\indexentry{barycenter|hyperpage}{68}
-\indexentry{affine subvariety|hyperpage}{69}
-\indexentry{director subspace|hyperpage}{69}
-\indexentry{line|hyperpage}{69}
-\indexentry{hyperplane|hyperpage}{69}
-\indexentry{parallel|hyperpage}{69}
-\indexentry{sum|hyperpage}{69}
-\indexentry{Affine Gra\ss mann formulas|hyperpage}{69}
-\indexentry{origin|hyperpage}{69}
-\indexentry{affine coordinates|hyperpage}{69}
-\indexentry{homogenization|hyperpage}{69}
-\indexentry{dehomogenization|hyperpage}{69}
-\indexentry{parametric equations|hyperpage}{69}
-\indexentry{Cartesian equations|hyperpage}{69}
-\indexentry{affinity|hyperpage}{69}
-\indexentry{differential|hyperpage}{69}
-\indexentry{semiaffinity|hyperpage}{69}
-\indexentry{similar|hyperpage}{70}
-\indexentry{fixed point|hyperpage}{70}
-\indexentry{invariant under an affinity|hyperpage}{70}
-\indexentry{invariance level|hyperpage}{70}
-\indexentry{Translations|hyperpage}{70}
-\indexentry{translation|hyperpage}{70}
-\indexentry{Properties of translations|hyperpage}{70}
-\indexentry{Reflections|hyperpage}{70}
-\indexentry{reflection|hyperpage}{70}
-\indexentry{mirror of the reflection|hyperpage}{70}
-\indexentry{root of the reflection|hyperpage}{70}
-\indexentry{Properties of reflections|hyperpage}{70}
-\indexentry{Projections|hyperpage}{70}
-\indexentry{projection|hyperpage}{70}
-\indexentry{Properties of projections|hyperpage}{70}
-\indexentry{Homotheties|hyperpage}{71}
-\indexentry{homothety|hyperpage}{71}
-\indexentry{similitude ratio of the homothety|hyperpage}{71}
-\indexentry{Properties of homotheties|hyperpage}{71}
-\indexentry{glide reflection|hyperpage}{71}
-\indexentry{Simple ratio|hyperpage}{71}
-\indexentry{simple ratio|hyperpage}{71}
-\indexentry{Fundamental theorem of affine geometry|hyperpage}{71}
-\indexentry{Euclidean affine space|hyperpage}{71}
-\indexentry{distance between two points|hyperpage}{71}
-\indexentry{segment|hyperpage}{71}
-\indexentry{Triangular inequality|hyperpage}{71}
-\indexentry{Pythagorean theorem|hyperpage}{71}
-\indexentry{orthogonal|hyperpage}{71}
-\indexentry{distance between two affine subvarieties|hyperpage}{71}
-\indexentry{Euclidean motion|hyperpage}{72}
-\indexentry{Examples of Euclidean motions|hyperpage}{72}
-\indexentry{orthogonal reflections|hyperpage}{72}
-\indexentry{Glide orthogonal reflections|hyperpage}{72}
-\indexentry{Classification of isometries|hyperpage}{72}
-\indexentry{glide vector|hyperpage}{72}
-\indexentry{Classification of Euclidean motions|hyperpage}{72}
-\indexentry{quadric|hyperpage}{72}
-\indexentry{points of the quadric|hyperpage}{72}
-\indexentry{conic|hyperpage}{72}
-\indexentry{equivalent|hyperpage}{72}
-\indexentry{quadric|hyperpage}{72}
-\indexentry{points of the quadric|hyperpage}{72}
-\indexentry{equivalent|hyperpage}{72}
-\indexentry{Homogenization|hyperpage}{73}
-\indexentry{Dehomogenization|hyperpage}{73}
-\indexentry{anisotropic|hyperpage}{73}
-\indexentry{elliptic|hyperpage}{73}
-\indexentry{hyperbolic plane|hyperpage}{73}
-\indexentry{quadratic form|hyperpage}{73}
-\indexentry{non-degenerate|hyperpage}{73}
-\indexentry{quadratic space|hyperpage}{73}
-\indexentry{isometry|hyperpage}{73}
-\indexentry{totally isotropic|hyperpage}{73}
-\indexentry{rank|hyperpage}{73}
-\indexentry{Witt's theorem|hyperpage}{73}
-\indexentry{index|hyperpage}{73}
-\indexentry{Classification of quadratic forms in $\ensuremath {\mathbb {C}}$|hyperpage}{73}
-\indexentry{Classification of quadratic forms in $\ensuremath {\mathbb {F}}_q$|hyperpage}{73}
-\indexentry{Classification of quadratic forms in $\ensuremath {\mathbb {R}}$|hyperpage}{73}
-\indexentry{Classification of projective qua\-drics in $\ensuremath {\mathbb {C}}$|hyperpage}{73}
-\indexentry{Classification of projective qua\-drics in $\ensuremath {\mathbb {F}}_q$|hyperpage}{74}
-\indexentry{Classification of projective qua\-drics in $\ensuremath {\mathbb {R}}$|hyperpage}{74}
-\indexentry{Classification of affine quadrics|hyperpage}{74}
-\indexentry{numeric series|hyperpage}{75}
-\indexentry{general term of the series|hyperpage}{75}
-\indexentry{$N$-th partial sum of the series|hyperpage}{75}
-\indexentry{convergent|hyperpage}{75}
-\indexentry{sum of the series|hyperpage}{75}
-\indexentry{divergent|hyperpage}{75}
-\indexentry{Cauchy's test|hyperpage}{75}
-\indexentry{Linearity|hyperpage}{75}
-\indexentry{Associative property|hyperpage}{75}
-\indexentry{Comparison test|hyperpage}{75}
-\indexentry{Limit comparison test|hyperpage}{75}
-\indexentry{Root test|hyperpage}{75}
-\indexentry{Ratio test|hyperpage}{75}
-\indexentry{Raabe's test|hyperpage}{75}
-\indexentry{Condensation test|hyperpage}{75}
-\indexentry{Logarithmic test|hyperpage}{75}
-\indexentry{Integral test|hyperpage}{76}
-\indexentry{alternating series|hyperpage}{76}
-\indexentry{Leibnitz's test|hyperpage}{76}
-\indexentry{Abel's summation formula|hyperpage}{76}
-\indexentry{Dirichlet's test|hyperpage}{76}
-\indexentry{Abel's test|hyperpage}{76}
-\indexentry{absolutely convergent|hyperpage}{76}
-\indexentry{rearrangement of the sequence|hyperpage}{76}
-\indexentry{rearrangement of the series|hyperpage}{76}
-\indexentry{positive part|hyperpage}{76}
-\indexentry{negative part|hyperpage}{76}
-\indexentry{Riemann's theorem|hyperpage}{76}
-\indexentry{sequence of real functions|hyperpage}{76}
-\indexentry{converges pointwise|hyperpage}{76}
-\indexentry{converges uniformly|hyperpage}{76}
-\indexentry{Cauchy's test|hyperpage}{77}
-\indexentry{series of functions|hyperpage}{77}
-\indexentry{converges pointwise|hyperpage}{77}
-\indexentry{sum of the series in a pointwise sense|hyperpage}{77}
-\indexentry{converges uniformly|hyperpage}{77}
-\indexentry{sum of the series in an uniform sense|hyperpage}{77}
-\indexentry{Cauchy's test|hyperpage}{77}
-\indexentry{Weierstra\ss \ M-test|hyperpage}{77}
+\indexentry{Continuity axioms|hyperpage}{63}
+\indexentry{Axiom of Archimedes|hyperpage}{63}
+\indexentry{Axiom of completeness|hyperpage}{63}
+\indexentry{RC|hyperpage}{64}
+\indexentry{CC|hyperpage}{64}
+\indexentry{Axiom of Parallels|hyperpage}{64}
+\indexentry{Hilbert plane|hyperpage}{64}
+\indexentry{Pythagorean plane|hyperpage}{64}
+\indexentry{Euclidean plane|hyperpage}{64}
+\indexentry{Cartesian geometry|hyperpage}{64}
+\indexentry{Absolute geometry|hyperpage}{64}
+\indexentry{SAS criterion|hyperpage}{64}
+\indexentry{SSS criterion|hyperpage}{64}
+\indexentry{Exterior angle theorem|hyperpage}{64}
+\indexentry{ASA criterion|hyperpage}{64}
+\indexentry{SAA criterion|hyperpage}{64}
+\indexentry{Saccheri-Legendre theorem|hyperpage}{64}
+\indexentry{ordered field|hyperpage}{64}
+\indexentry{Pythagorean|hyperpage}{64}
+\indexentry{Archimedean|hyperpage}{64}
+\indexentry{Euclidean|hyperpage}{64}
+\indexentry{Hilbert field|hyperpage}{64}
+\indexentry{constructible field|hyperpage}{64}
+\indexentry{Hyperbolic geometry|hyperpage}{65}
+\indexentry{Hyperbolic geometry|hyperpage}{65}
+\indexentry{Non-Paschian geometry|hyperpage}{65}
+\indexentry{Non-Paschian geometry|hyperpage}{65}
+\indexentry{Construction of a non-Paschian geometry|hyperpage}{65}
+\indexentry{Non-SAS geometry|hyperpage}{66}
+\indexentry{Non-SAS geometry|hyperpage}{66}
+\indexentry{Construction of a non-SAS geometry|hyperpage}{66}
+\indexentry{Non-Archimedean geometry|hyperpage}{66}
+\indexentry{Non-Archimedean geometry|hyperpage}{66}
+\indexentry{axiomatic projective space|hyperpage}{66}
+\indexentry{Projective axiom|hyperpage}{66}
+\indexentry{projective subvariety|hyperpage}{66}
+\indexentry{collineation|hyperpage}{66}
+\indexentry{dimension|hyperpage}{66}
+\indexentry{projective plane|hyperpage}{66}
+\indexentry{Duality principle|hyperpage}{66}
+\indexentry{affine plane|hyperpage}{66}
+\indexentry{Passage from the projective plane to the affine plane|hyperpage}{66}
+\indexentry{Passage from the affine plane to the projective plane|hyperpage}{66}
+\indexentry{$n$-dimensional projective space|hyperpage}{67}
+\indexentry{homography|hyperpage}{67}
+\indexentry{semilinear isomorphism|hyperpage}{67}
+\indexentry{isomorphism between projective spaces|hyperpage}{67}
+\indexentry{$m$-dimensional projective subvariety|hyperpage}{67}
+\indexentry{line|hyperpage}{67}
+\indexentry{hyperplane|hyperpage}{67}
+\indexentry{homogeneous coordinates|hyperpage}{67}
+\indexentry{projective frame|hyperpage}{67}
+\indexentry{equation of the hyperplane|hyperpage}{67}
+\indexentry{Gra\ss mann formula|hyperpage}{67}
+\indexentry{configuration|hyperpage}{67}
+\indexentry{realizable|hyperpage}{67}
+\indexentry{theorem|hyperpage}{67}
+\indexentry{Fano configuration|hyperpage}{67}
+\indexentry{Pappus configuration|hyperpage}{68}
+\indexentry{in perspective with respect to a point|hyperpage}{68}
+\indexentry{centre of perspectivity|hyperpage}{68}
+\indexentry{in perspective with respect to a line|hyperpage}{68}
+\indexentry{axis of perspectivity|hyperpage}{68}
+\indexentry{Desargues' theorem|hyperpage}{68}
+\indexentry{Desargues configuration|hyperpage}{68}
+\indexentry{non-Desarguesian planes|hyperpage}{68}
+\indexentry{Coordination theorem|hyperpage}{68}
+\indexentry{Fundamental theorem of projective geometry|hyperpage}{68}
+\indexentry{Cross ratio|hyperpage}{69}
+\indexentry{cross ratio|hyperpage}{69}
+\indexentry{harmonic ratio|hyperpage}{69}
+\indexentry{cross ratio|hyperpage}{69}
+\indexentry{perspectivity|hyperpage}{69}
+\indexentry{projectivity|hyperpage}{69}
+\indexentry{Plücker coordinates|hyperpage}{69}
+\indexentry{affine space|hyperpage}{69}
+\indexentry{dimension|hyperpage}{69}
+\indexentry{affine combination|hyperpage}{69}
+\indexentry{affinely independents|hyperpage}{69}
+\indexentry{barycenter|hyperpage}{69}
+\indexentry{affine subvariety|hyperpage}{70}
+\indexentry{director subspace|hyperpage}{70}
+\indexentry{line|hyperpage}{70}
+\indexentry{hyperplane|hyperpage}{70}
+\indexentry{parallel|hyperpage}{70}
+\indexentry{sum|hyperpage}{70}
+\indexentry{Affine Gra\ss mann formulas|hyperpage}{70}
+\indexentry{origin|hyperpage}{70}
+\indexentry{affine coordinates|hyperpage}{70}
+\indexentry{homogenization|hyperpage}{70}
+\indexentry{dehomogenization|hyperpage}{70}
+\indexentry{parametric equations|hyperpage}{70}
+\indexentry{Cartesian equations|hyperpage}{70}
+\indexentry{affinity|hyperpage}{70}
+\indexentry{differential|hyperpage}{70}
+\indexentry{semiaffinity|hyperpage}{70}
+\indexentry{similar|hyperpage}{71}
+\indexentry{fixed point|hyperpage}{71}
+\indexentry{invariant under an affinity|hyperpage}{71}
+\indexentry{invariance level|hyperpage}{71}
+\indexentry{Translations|hyperpage}{71}
+\indexentry{translation|hyperpage}{71}
+\indexentry{Properties of translations|hyperpage}{71}
+\indexentry{Reflections|hyperpage}{71}
+\indexentry{reflection|hyperpage}{71}
+\indexentry{mirror of the reflection|hyperpage}{71}
+\indexentry{root of the reflection|hyperpage}{71}
+\indexentry{Properties of reflections|hyperpage}{71}
+\indexentry{Projections|hyperpage}{71}
+\indexentry{projection|hyperpage}{71}
+\indexentry{Properties of projections|hyperpage}{71}
+\indexentry{Homotheties|hyperpage}{72}
+\indexentry{homothety|hyperpage}{72}
+\indexentry{similitude ratio of the homothety|hyperpage}{72}
+\indexentry{Properties of homotheties|hyperpage}{72}
+\indexentry{glide reflection|hyperpage}{72}
+\indexentry{Simple ratio|hyperpage}{72}
+\indexentry{simple ratio|hyperpage}{72}
+\indexentry{Fundamental theorem of affine geometry|hyperpage}{72}
+\indexentry{Euclidean affine space|hyperpage}{72}
+\indexentry{distance between two points|hyperpage}{72}
+\indexentry{segment|hyperpage}{72}
+\indexentry{Triangular inequality|hyperpage}{72}
+\indexentry{Pythagorean theorem|hyperpage}{72}
+\indexentry{orthogonal|hyperpage}{72}
+\indexentry{distance between two affine subvarieties|hyperpage}{72}
+\indexentry{Euclidean motion|hyperpage}{73}
+\indexentry{Examples of Euclidean motions|hyperpage}{73}
+\indexentry{orthogonal reflections|hyperpage}{73}
+\indexentry{Glide orthogonal reflections|hyperpage}{73}
+\indexentry{Classification of isometries|hyperpage}{73}
+\indexentry{glide vector|hyperpage}{73}
+\indexentry{Classification of Euclidean motions|hyperpage}{73}
+\indexentry{quadric|hyperpage}{73}
+\indexentry{points of the quadric|hyperpage}{73}
+\indexentry{conic|hyperpage}{73}
+\indexentry{equivalent|hyperpage}{73}
+\indexentry{quadric|hyperpage}{73}
+\indexentry{points of the quadric|hyperpage}{73}
+\indexentry{equivalent|hyperpage}{73}
+\indexentry{Homogenization|hyperpage}{74}
+\indexentry{Dehomogenization|hyperpage}{74}
+\indexentry{anisotropic|hyperpage}{74}
+\indexentry{elliptic|hyperpage}{74}
+\indexentry{hyperbolic plane|hyperpage}{74}
+\indexentry{quadratic form|hyperpage}{74}
+\indexentry{non-degenerate|hyperpage}{74}
+\indexentry{quadratic space|hyperpage}{74}
+\indexentry{isometry|hyperpage}{74}
+\indexentry{totally isotropic|hyperpage}{74}
+\indexentry{rank|hyperpage}{74}
+\indexentry{Witt's theorem|hyperpage}{74}
+\indexentry{index|hyperpage}{74}
+\indexentry{Classification of quadratic forms in $\ensuremath {\mathbb {C}}$|hyperpage}{74}
+\indexentry{Classification of quadratic forms in $\ensuremath {\mathbb {F}}_q$|hyperpage}{74}
+\indexentry{Classification of quadratic forms in $\ensuremath {\mathbb {R}}$|hyperpage}{74}
+\indexentry{Classification of projective qua\-drics in $\ensuremath {\mathbb {C}}$|hyperpage}{74}
+\indexentry{Classification of projective qua\-drics in $\ensuremath {\mathbb {F}}_q$|hyperpage}{75}
+\indexentry{Classification of projective qua\-drics in $\ensuremath {\mathbb {R}}$|hyperpage}{75}
+\indexentry{Classification of affine quadrics|hyperpage}{75}
+\indexentry{numeric series|hyperpage}{76}
+\indexentry{general term of the series|hyperpage}{76}
+\indexentry{$N$-th partial sum of the series|hyperpage}{76}
+\indexentry{convergent|hyperpage}{76}
+\indexentry{sum of the series|hyperpage}{76}
+\indexentry{divergent|hyperpage}{76}
+\indexentry{Cauchy's test|hyperpage}{76}
+\indexentry{Linearity|hyperpage}{76}
+\indexentry{Associative property|hyperpage}{76}
+\indexentry{Comparison test|hyperpage}{76}
+\indexentry{Limit comparison test|hyperpage}{76}
+\indexentry{Root test|hyperpage}{76}
+\indexentry{Ratio test|hyperpage}{76}
+\indexentry{Raabe's test|hyperpage}{76}
+\indexentry{Condensation test|hyperpage}{76}
+\indexentry{Logarithmic test|hyperpage}{76}
+\indexentry{Integral test|hyperpage}{77}
+\indexentry{alternating series|hyperpage}{77}
+\indexentry{Leibnitz's test|hyperpage}{77}
+\indexentry{Abel's summation formula|hyperpage}{77}
\indexentry{Dirichlet's test|hyperpage}{77}
\indexentry{Abel's test|hyperpage}{77}
-\indexentry{power series|hyperpage}{77}
-\indexentry{radius of convergence of the power series|hyperpage}{78}
-\indexentry{Abel's theorem|hyperpage}{78}
-\indexentry{analytic|hyperpage}{78}
-\indexentry{compact support|hyperpage}{78}
-\indexentry{convolution|hyperpage}{78}
-\indexentry{kernel function|hyperpage}{78}
-\indexentry{approximation of identity|hyperpage}{78}
-\indexentry{Weierstra\ss \ approximation theorem|hyperpage}{78}
-\indexentry{locally integrable|hyperpage}{78}
-\indexentry{improper integral|hyperpage}{78}
-\indexentry{convergent|hyperpage}{78}
-\indexentry{support|hyperpage}{78}
-\indexentry{Cauchy's test|hyperpage}{79}
-\indexentry{Comparison test|hyperpage}{79}
-\indexentry{Integral test|hyperpage}{79}
-\indexentry{converges absolutely|hyperpage}{79}
-\indexentry{Dirichlet's test|hyperpage}{79}
-\indexentry{Abel's test|hyperpage}{79}
-\indexentry{Gamma function|hyperpage}{80}
-\indexentry{Stirling's formula|hyperpage}{80}
-\indexentry{$T$-periodic|hyperpage}{80}
-\indexentry{periodic with period $T$|hyperpage}{80}
-\indexentry{inner product|hyperpage}{81}
-\indexentry{distance|hyperpage}{81}
-\indexentry{Cauchy-Schwarz inequality|hyperpage}{81}
-\indexentry{Minkowski inequality|hyperpage}{81}
-\indexentry{orthogonal|hyperpage}{81}
-\indexentry{orthonormal|hyperpage}{81}
-\indexentry{orthonormal system|hyperpage}{81}
-\indexentry{linearly dependent|hyperpage}{81}
-\indexentry{linearly independent|hyperpage}{81}
-\indexentry{$n$-th Fourier coefficient|hyperpage}{82}
-\indexentry{Fourier series|hyperpage}{82}
-\indexentry{$N$-th partial sum of $Sf$|hyperpage}{82}
-\indexentry{even extension|hyperpage}{83}
-\indexentry{odd extension|hyperpage}{83}
-\indexentry{Dirichlet kernel|hyperpage}{83}
-\indexentry{Dirichlet kernel|hyperpage}{83}
-\indexentry{Riemann-Lebesgue lemma|hyperpage}{84}
-\indexentry{Dini's theorem|hyperpage}{84}
-\indexentry{Lipschitz's theorem|hyperpage}{84}
-\indexentry{Cesàro summable|hyperpage}{84}
-\indexentry{Fejér kernel|hyperpage}{84}
-\indexentry{Fejér kernel|hyperpage}{84}
-\indexentry{Fejér means|hyperpage}{85}
-\indexentry{Fejér's theorem|hyperpage}{85}
-\indexentry{Fejér's theorem|hyperpage}{85}
-\indexentry{converge in norm $L^p$|hyperpage}{86}
-\indexentry{Bessel's inequality|hyperpage}{86}
-\indexentry{Parseval's identity|hyperpage}{86}
-\indexentry{Wirtinger's inequality|hyperpage}{86}
+\indexentry{absolutely convergent|hyperpage}{77}
+\indexentry{rearrangement of the sequence|hyperpage}{77}
+\indexentry{rearrangement of the series|hyperpage}{77}
+\indexentry{positive part|hyperpage}{77}
+\indexentry{negative part|hyperpage}{77}
+\indexentry{Riemann's theorem|hyperpage}{77}
+\indexentry{sequence of real functions|hyperpage}{77}
+\indexentry{converges pointwise|hyperpage}{77}
+\indexentry{converges uniformly|hyperpage}{77}
+\indexentry{Cauchy's test|hyperpage}{78}
+\indexentry{series of functions|hyperpage}{78}
+\indexentry{converges pointwise|hyperpage}{78}
+\indexentry{sum of the series in a pointwise sense|hyperpage}{78}
+\indexentry{converges uniformly|hyperpage}{78}
+\indexentry{sum of the series in an uniform sense|hyperpage}{78}
+\indexentry{Cauchy's test|hyperpage}{78}
+\indexentry{Weierstra\ss \ M-test|hyperpage}{78}
+\indexentry{Dirichlet's test|hyperpage}{78}
+\indexentry{Abel's test|hyperpage}{78}
+\indexentry{power series|hyperpage}{78}
+\indexentry{radius of convergence of the power series|hyperpage}{79}
+\indexentry{Abel's theorem|hyperpage}{79}
+\indexentry{analytic|hyperpage}{79}
+\indexentry{compact support|hyperpage}{79}
+\indexentry{convolution|hyperpage}{79}
+\indexentry{kernel function|hyperpage}{79}
+\indexentry{approximation of identity|hyperpage}{79}
+\indexentry{Weierstra\ss \ approximation theorem|hyperpage}{79}
+\indexentry{locally integrable|hyperpage}{79}
+\indexentry{improper integral|hyperpage}{79}
+\indexentry{convergent|hyperpage}{79}
+\indexentry{support|hyperpage}{79}
+\indexentry{Cauchy's test|hyperpage}{80}
+\indexentry{Comparison test|hyperpage}{80}
+\indexentry{Integral test|hyperpage}{80}
+\indexentry{converges absolutely|hyperpage}{80}
+\indexentry{Dirichlet's test|hyperpage}{80}
+\indexentry{Abel's test|hyperpage}{80}
+\indexentry{Gamma function|hyperpage}{81}
+\indexentry{Stirling's formula|hyperpage}{81}
+\indexentry{$T$-periodic|hyperpage}{81}
+\indexentry{periodic with period $T$|hyperpage}{81}
+\indexentry{inner product|hyperpage}{82}
+\indexentry{distance|hyperpage}{82}
+\indexentry{Cauchy-Schwarz inequality|hyperpage}{82}
+\indexentry{Minkowski inequality|hyperpage}{82}
+\indexentry{orthogonal|hyperpage}{82}
+\indexentry{orthonormal|hyperpage}{82}
+\indexentry{orthonormal system|hyperpage}{82}
+\indexentry{linearly dependent|hyperpage}{82}
+\indexentry{linearly independent|hyperpage}{82}
+\indexentry{$n$-th Fourier coefficient|hyperpage}{83}
+\indexentry{Fourier series|hyperpage}{83}
+\indexentry{$N$-th partial sum of $Sf$|hyperpage}{83}
+\indexentry{even extension|hyperpage}{84}
+\indexentry{odd extension|hyperpage}{84}
+\indexentry{Dirichlet kernel|hyperpage}{84}
+\indexentry{Dirichlet kernel|hyperpage}{84}
+\indexentry{Riemann-Lebesgue lemma|hyperpage}{85}
+\indexentry{Dini's theorem|hyperpage}{85}
+\indexentry{Lipschitz's theorem|hyperpage}{85}
+\indexentry{Cesàro summable|hyperpage}{85}
+\indexentry{Fejér kernel|hyperpage}{85}
+\indexentry{Fejér kernel|hyperpage}{85}
+\indexentry{Fejér means|hyperpage}{86}
+\indexentry{Fejér's theorem|hyperpage}{86}
+\indexentry{Fejér's theorem|hyperpage}{86}
+\indexentry{converge in norm $L^p$|hyperpage}{87}
+\indexentry{Bessel's inequality|hyperpage}{87}
+\indexentry{Parseval's identity|hyperpage}{87}
\indexentry{Wirtinger's inequality|hyperpage}{87}
-\indexentry{Isoperimetric inequality|hyperpage}{87}
-\indexentry{Floating-point representation|hyperpage}{88}
-\indexentry{floating-point representation|hyperpage}{88}
-\indexentry{sign|hyperpage}{88}
-\indexentry{significant|hyperpage}{88}
-\indexentry{mantissa|hyperpage}{88}
-\indexentry{exponent|hyperpage}{88}
-\indexentry{normalized|hyperpage}{88}
-\indexentry{floating-point representation by truncation|hyperpage}{88}
-\indexentry{floating-point representation by rounding|hyperpage}{88}
-\indexentry{absolute error|hyperpage}{88}
-\indexentry{relative error|hyperpage}{88}
-\indexentry{has $t$ correct decimal digits|hyperpage}{88}
-\indexentry{has $u$ significant digits|hyperpage}{88}
-\indexentry{machine epsilon $\epsilon $|hyperpage}{88}
-\indexentry{Propagation of absolute errors|hyperpage}{88}
-\indexentry{absolute condition numbers|hyperpage}{88}
-\indexentry{Propagation of relative errors|hyperpage}{88}
-\indexentry{relative condition numbers|hyperpage}{89}
-\indexentry{numerically stable|hyperpage}{89}
-\indexentry{numerically unstable|hyperpage}{89}
-\indexentry{well-conditioned|hyperpage}{89}
-\indexentry{ill-conditioned|hyperpage}{89}
-\indexentry{zero|hyperpage}{89}
-\indexentry{solution|hyperpage}{89}
-\indexentry{zero of multiplicity $m\in \ensuremath {\mathbb {N}}$|hyperpage}{89}
-\indexentry{simple|hyperpage}{89}
-\indexentry{double|hyperpage}{89}
-\indexentry{triple|hyperpage}{89}
-\indexentry{Bisection method|hyperpage}{89}
-\indexentry{Regula falsi method|hyperpage}{89}
-\indexentry{Secant method|hyperpage}{89}
-\indexentry{Newton-Raphson method|hyperpage}{89}
-\indexentry{Newton-Raphson modified method|hyperpage}{89}
-\indexentry{Chebyshev method|hyperpage}{89}
-\indexentry{$n$-periodic|hyperpage}{89}
-\indexentry{contraction|hyperpage}{89}
-\indexentry{Fixed-point theorem|hyperpage}{89}
-\indexentry{attractor fixed point|hyperpage}{90}
-\indexentry{repulsor fixed point|hyperpage}{90}
-\indexentry{chaotic behavior|hyperpage}{90}
-\indexentry{Order of convergence|hyperpage}{90}
-\indexentry{order of convergence|hyperpage}{90}
-\indexentry{asymptotic error constant|hyperpage}{90}
-\indexentry{linear convergence|hyperpage}{90}
-\indexentry{quadratic convergence|hyperpage}{90}
-\indexentry{cubic convergence|hyperpage}{90}
-\indexentry{order of convergence at least $p$|hyperpage}{90}
-\indexentry{computational efficiency|hyperpage}{90}
-\indexentry{Aitken's $\Delta ^2$ method|hyperpage}{90}
-\indexentry{Aitken's $\Delta ^2$ method|hyperpage}{90}
-\indexentry{Steffensen's method|hyperpage}{91}
-\indexentry{Strum's sequence|hyperpage}{91}
-\indexentry{Sturm's sequence|hyperpage}{91}
-\indexentry{Sturm's theorem|hyperpage}{91}
-\indexentry{Budan-Fourier theorem|hyperpage}{91}
-\indexentry{Descartes' rule of signs|hyperpage}{91}
-\indexentry{Gershgorin circle theorem|hyperpage}{91}
-\indexentry{vector space of polynomials with real coefficients and degree less than or equal to $n$|hyperpage}{92}
-\indexentry{support points|hyperpage}{92}
-\indexentry{interpolation problem|hyperpage}{92}
-\indexentry{Lagrange's interpolation problem|hyperpage}{92}
-\indexentry{Lagrange basis polynomials|hyperpage}{92}
-\indexentry{Neville's algorithm|hyperpage}{92}
-\indexentry{divided difference|hyperpage}{92}
-\indexentry{Newton's divided differences\\method|hyperpage}{92}
-\indexentry{equally-spaced|hyperpage}{92}
-\indexentry{Hermite interpolation problem|hyperpage}{93}
-\indexentry{Spline|hyperpage}{93}
-\indexentry{spline|hyperpage}{93}
-\indexentry{cubic splines|hyperpage}{93}
-\indexentry{Natural cubic spline|hyperpage}{93}
-\indexentry{Cubic Hermite spline|hyperpage}{93}
-\indexentry{Cubic periodic spline|hyperpage}{93}
-\indexentry{seminorm|hyperpage}{93}
-\indexentry{Intermediate value theorem|hyperpage}{93}
-\indexentry{Forward and backward difference formula of order 1|hyperpage}{93}
-\indexentry{seminorm|hyperpage}{93}
-\indexentry{norm|hyperpage}{93}
-\indexentry{Symmetric difference formula of order 1|hyperpage}{94}
-\indexentry{Symmetric difference formula of order 2|hyperpage}{94}
-\indexentry{Richardson extrapolation|hyperpage}{94}
-\indexentry{quadrature formula|hyperpage}{94}
-\indexentry{degree of precision|hyperpage}{94}
-\indexentry{Mean value theorem for integrals|hyperpage}{94}
-\indexentry{Closed Newton-Cotes Formulas|hyperpage}{94}
-\indexentry{Trapezoidal rule|hyperpage}{94}
-\indexentry{Simpson's rule|hyperpage}{94}
-\indexentry{Composite Trapezoidal rule|hyperpage}{94}
-\indexentry{Composite Simpson's rule|hyperpage}{95}
-\indexentry{Bernoulli polynomials|hyperpage}{95}
-\indexentry{Bernoulli numbers|hyperpage}{95}
-\indexentry{Euler-Maclaurin formula|hyperpage}{95}
-\indexentry{Romberg method|hyperpage}{95}
-\indexentry{Orthogonal polynomials|hyperpage}{95}
-\indexentry{orthogonal with respect to the weight $\omega (x)$|hyperpage}{95}
-\indexentry{orthogonal basis|hyperpage}{95}
-\indexentry{Existence of orthogonal polynomials|hyperpage}{95}
-\indexentry{Chebyshev polynomials|hyperpage}{95}
-\indexentry{Chebyshev polynomials|hyperpage}{95}
-\indexentry{Laguerre polynomials|hyperpage}{95}
-\indexentry{Laguerre polynomials|hyperpage}{95}
-\indexentry{Legendre polynomials|hyperpage}{96}
-\indexentry{Legendre polynomials|hyperpage}{96}
-\indexentry{quadrature formula with weight $\omega (x)$|hyperpage}{96}
-\indexentry{upper triangular|hyperpage}{96}
-\indexentry{lower triangular|hyperpage}{96}
-\indexentry{triangular system|hyperpage}{96}
-\indexentry{matrix norm|hyperpage}{96}
-\indexentry{sub-multiplicativity|hyperpage}{96}
-\indexentry{compatible with|hyperpage}{96}
-\indexentry{subordinated matrix norm|hyperpage}{96}
-\indexentry{spectrum|hyperpage}{96}
-\indexentry{spectral radius|hyperpage}{97}
-\indexentry{Properties of matrix norms|hyperpage}{97}
-\indexentry{convergent|hyperpage}{97}
-\indexentry{condition number|hyperpage}{98}
-\indexentry{iteration matrix|hyperpage}{98}
-\indexentry{rate of convergence|hyperpage}{98}
-\indexentry{strictly diagonally dominant by rows|hyperpage}{98}
-\indexentry{strictly diagonally dominant by columns|hyperpage}{98}
-\indexentry{Jacobi method|hyperpage}{99}
-\indexentry{Jacobi method|hyperpage}{99}
-\indexentry{Gau\ss -Seidel method|hyperpage}{99}
-\indexentry{Gau\ss -Seidel method|hyperpage}{99}
-\indexentry{Over-relaxation methods|hyperpage}{99}
-\indexentry{relaxation factor|hyperpage}{99}
-\indexentry{Over-relaxation methods|hyperpage}{99}
-\indexentry{Successive over-relaxation \\method|hyperpage}{99}
-\indexentry{Successive over-relaxation method|hyperpage}{99}
-\indexentry{SOR|hyperpage}{99}
-\indexentry{dominant eigenvalue|hyperpage}{99}
-\indexentry{dominant eigenvector|hyperpage}{99}
-\indexentry{reducible|hyperpage}{99}
-\indexentry{irreducible|hyperpage}{99}
-\indexentry{Perron-Frobenius theorem|hyperpage}{100}
-\indexentry{Power method|hyperpage}{100}
-\indexentry{power method|hyperpage}{100}
-\indexentry{Normalized power method|hyperpage}{100}
-\indexentry{normalized power method|hyperpage}{100}
-\indexentry{Rayleigh quotient|hyperpage}{100}
-\indexentry{Rayleigh quotient|hyperpage}{100}
-\indexentry{Inverse power method|hyperpage}{100}
-\indexentry{inverse power method|hyperpage}{100}
-\indexentry{Gaussian elimination|hyperpage}{100}
-\indexentry{Partial pivoting|hyperpage}{101}
-\indexentry{Complete pivoting|hyperpage}{101}
-\indexentry{LU descompostion|hyperpage}{101}
-\indexentry{LU decomposition|hyperpage}{101}
-\indexentry{permutation matrix|hyperpage}{101}
-\indexentry{field of complex numbers|hyperpage}{103}
-\indexentry{complex conjugate|hyperpage}{103}
-\indexentry{conjugate|hyperpage}{103}
-\indexentry{real part|hyperpage}{103}
-\indexentry{imaginary part|hyperpage}{103}
-\indexentry{modulus|hyperpage}{103}
-\indexentry{argument|hyperpage}{103}
-\indexentry{multivalued function|hyperpage}{103}
-\indexentry{determination of the argument of $f$|hyperpage}{103}
-\indexentry{principal argument|hyperpage}{103}
-\indexentry{Cartesian form|hyperpage}{103}
-\indexentry{extended complex plane|hyperpage}{104}
-\indexentry{extended real numbers|hyperpage}{104}
-\indexentry{Stereographic projection|hyperpage}{104}
-\indexentry{stereographic projection|hyperpage}{104}
-\indexentry{sequence of complex numbers|hyperpage}{104}
-\indexentry{limit|hyperpage}{104}
-\indexentry{converges|hyperpage}{104}
-\indexentry{convergent|hyperpage}{104}
-\indexentry{divergent|hyperpage}{104}
-\indexentry{bounded|hyperpage}{104}
-\indexentry{Cauchy|hyperpage}{104}
-\indexentry{numeric series of complex numbers|hyperpage}{104}
-\indexentry{general term of the series|hyperpage}{104}
-\indexentry{$N$-th partial sum of the series|hyperpage}{104}
+\indexentry{Wirtinger's inequality|hyperpage}{88}
+\indexentry{Isoperimetric inequality|hyperpage}{88}
+\indexentry{Floating-point representation|hyperpage}{89}
+\indexentry{floating-point representation|hyperpage}{89}
+\indexentry{sign|hyperpage}{89}
+\indexentry{significant|hyperpage}{89}
+\indexentry{mantissa|hyperpage}{89}
+\indexentry{exponent|hyperpage}{89}
+\indexentry{normalized|hyperpage}{89}
+\indexentry{floating-point representation by truncation|hyperpage}{89}
+\indexentry{floating-point representation by rounding|hyperpage}{89}
+\indexentry{absolute error|hyperpage}{89}
+\indexentry{relative error|hyperpage}{89}
+\indexentry{has $t$ correct decimal digits|hyperpage}{89}
+\indexentry{has $u$ significant digits|hyperpage}{89}
+\indexentry{machine epsilon $\epsilon $|hyperpage}{89}
+\indexentry{Propagation of absolute errors|hyperpage}{89}
+\indexentry{absolute condition numbers|hyperpage}{89}
+\indexentry{Propagation of relative errors|hyperpage}{89}
+\indexentry{relative condition numbers|hyperpage}{90}
+\indexentry{numerically stable|hyperpage}{90}
+\indexentry{numerically unstable|hyperpage}{90}
+\indexentry{well-conditioned|hyperpage}{90}
+\indexentry{ill-conditioned|hyperpage}{90}
+\indexentry{zero|hyperpage}{90}
+\indexentry{solution|hyperpage}{90}
+\indexentry{zero of multiplicity $m\in \ensuremath {\mathbb {N}}$|hyperpage}{90}
+\indexentry{simple|hyperpage}{90}
+\indexentry{double|hyperpage}{90}
+\indexentry{triple|hyperpage}{90}
+\indexentry{Bisection method|hyperpage}{90}
+\indexentry{Regula falsi method|hyperpage}{90}
+\indexentry{Secant method|hyperpage}{90}
+\indexentry{Newton-Raphson method|hyperpage}{90}
+\indexentry{Newton-Raphson modified method|hyperpage}{90}
+\indexentry{Chebyshev method|hyperpage}{90}
+\indexentry{$n$-periodic|hyperpage}{90}
+\indexentry{contraction|hyperpage}{90}
+\indexentry{Fixed-point theorem|hyperpage}{90}
+\indexentry{attractor fixed point|hyperpage}{91}
+\indexentry{repulsor fixed point|hyperpage}{91}
+\indexentry{chaotic behavior|hyperpage}{91}
+\indexentry{Order of convergence|hyperpage}{91}
+\indexentry{order of convergence|hyperpage}{91}
+\indexentry{asymptotic error constant|hyperpage}{91}
+\indexentry{linear convergence|hyperpage}{91}
+\indexentry{quadratic convergence|hyperpage}{91}
+\indexentry{cubic convergence|hyperpage}{91}
+\indexentry{order of convergence at least $p$|hyperpage}{91}
+\indexentry{computational efficiency|hyperpage}{91}
+\indexentry{Aitken's $\Delta ^2$ method|hyperpage}{91}
+\indexentry{Aitken's $\Delta ^2$ method|hyperpage}{91}
+\indexentry{Steffensen's method|hyperpage}{92}
+\indexentry{Strum's sequence|hyperpage}{92}
+\indexentry{Sturm's sequence|hyperpage}{92}
+\indexentry{Sturm's theorem|hyperpage}{92}
+\indexentry{Budan-Fourier theorem|hyperpage}{92}
+\indexentry{Descartes' rule of signs|hyperpage}{92}
+\indexentry{Gershgorin circle theorem|hyperpage}{92}
+\indexentry{vector space of polynomials with real coefficients and degree less than or equal to $n$|hyperpage}{93}
+\indexentry{support points|hyperpage}{93}
+\indexentry{interpolation problem|hyperpage}{93}
+\indexentry{Lagrange's interpolation problem|hyperpage}{93}
+\indexentry{Lagrange basis polynomials|hyperpage}{93}
+\indexentry{Neville's algorithm|hyperpage}{93}
+\indexentry{divided difference|hyperpage}{93}
+\indexentry{Newton's divided differences\\method|hyperpage}{93}
+\indexentry{equally-spaced|hyperpage}{93}
+\indexentry{Hermite interpolation problem|hyperpage}{94}
+\indexentry{Spline|hyperpage}{94}
+\indexentry{spline|hyperpage}{94}
+\indexentry{cubic splines|hyperpage}{94}
+\indexentry{Natural cubic spline|hyperpage}{94}
+\indexentry{Cubic Hermite spline|hyperpage}{94}
+\indexentry{Cubic periodic spline|hyperpage}{94}
+\indexentry{seminorm|hyperpage}{94}
+\indexentry{Intermediate value theorem|hyperpage}{94}
+\indexentry{Forward and backward difference formula of order 1|hyperpage}{94}
+\indexentry{seminorm|hyperpage}{94}
+\indexentry{norm|hyperpage}{94}
+\indexentry{Symmetric difference formula of order 1|hyperpage}{95}
+\indexentry{Symmetric difference formula of order 2|hyperpage}{95}
+\indexentry{Richardson extrapolation|hyperpage}{95}
+\indexentry{quadrature formula|hyperpage}{95}
+\indexentry{degree of precision|hyperpage}{95}
+\indexentry{Mean value theorem for integrals|hyperpage}{95}
+\indexentry{Closed Newton-Cotes Formulas|hyperpage}{95}
+\indexentry{Trapezoidal rule|hyperpage}{95}
+\indexentry{Simpson's rule|hyperpage}{95}
+\indexentry{Composite Trapezoidal rule|hyperpage}{95}
+\indexentry{Composite Simpson's rule|hyperpage}{96}
+\indexentry{Bernoulli polynomials|hyperpage}{96}
+\indexentry{Bernoulli numbers|hyperpage}{96}
+\indexentry{Euler-Maclaurin formula|hyperpage}{96}
+\indexentry{Romberg method|hyperpage}{96}
+\indexentry{Orthogonal polynomials|hyperpage}{96}
+\indexentry{orthogonal with respect to the weight $\omega (x)$|hyperpage}{96}
+\indexentry{orthogonal basis|hyperpage}{96}
+\indexentry{Existence of orthogonal polynomials|hyperpage}{96}
+\indexentry{Chebyshev polynomials|hyperpage}{96}
+\indexentry{Chebyshev polynomials|hyperpage}{96}
+\indexentry{Laguerre polynomials|hyperpage}{96}
+\indexentry{Laguerre polynomials|hyperpage}{96}
+\indexentry{Legendre polynomials|hyperpage}{97}
+\indexentry{Legendre polynomials|hyperpage}{97}
+\indexentry{quadrature formula with weight $\omega (x)$|hyperpage}{97}
+\indexentry{upper triangular|hyperpage}{97}
+\indexentry{lower triangular|hyperpage}{97}
+\indexentry{triangular system|hyperpage}{97}
+\indexentry{matrix norm|hyperpage}{97}
+\indexentry{sub-multiplicativity|hyperpage}{97}
+\indexentry{compatible with|hyperpage}{97}
+\indexentry{subordinated matrix norm|hyperpage}{97}
+\indexentry{spectrum|hyperpage}{97}
+\indexentry{spectral radius|hyperpage}{98}
+\indexentry{Properties of matrix norms|hyperpage}{98}
+\indexentry{convergent|hyperpage}{98}
+\indexentry{condition number|hyperpage}{99}
+\indexentry{iteration matrix|hyperpage}{99}
+\indexentry{rate of convergence|hyperpage}{99}
+\indexentry{strictly diagonally dominant by rows|hyperpage}{99}
+\indexentry{strictly diagonally dominant by columns|hyperpage}{99}
+\indexentry{Jacobi method|hyperpage}{100}
+\indexentry{Jacobi method|hyperpage}{100}
+\indexentry{Gau\ss -Seidel method|hyperpage}{100}
+\indexentry{Gau\ss -Seidel method|hyperpage}{100}
+\indexentry{Over-relaxation methods|hyperpage}{100}
+\indexentry{relaxation factor|hyperpage}{100}
+\indexentry{Over-relaxation methods|hyperpage}{100}
+\indexentry{Successive over-relaxation \\method|hyperpage}{100}
+\indexentry{Successive over-relaxation method|hyperpage}{100}
+\indexentry{SOR|hyperpage}{100}
+\indexentry{dominant eigenvalue|hyperpage}{100}
+\indexentry{dominant eigenvector|hyperpage}{100}
+\indexentry{reducible|hyperpage}{100}
+\indexentry{irreducible|hyperpage}{100}
+\indexentry{Perron-Frobenius theorem|hyperpage}{101}
+\indexentry{Power method|hyperpage}{101}
+\indexentry{power method|hyperpage}{101}
+\indexentry{Normalized power method|hyperpage}{101}
+\indexentry{normalized power method|hyperpage}{101}
+\indexentry{Rayleigh quotient|hyperpage}{101}
+\indexentry{Rayleigh quotient|hyperpage}{101}
+\indexentry{Inverse power method|hyperpage}{101}
+\indexentry{inverse power method|hyperpage}{101}
+\indexentry{Gaussian elimination|hyperpage}{101}
+\indexentry{Partial pivoting|hyperpage}{102}
+\indexentry{Complete pivoting|hyperpage}{102}
+\indexentry{LU descompostion|hyperpage}{102}
+\indexentry{LU decomposition|hyperpage}{102}
+\indexentry{permutation matrix|hyperpage}{102}
+\indexentry{field of complex numbers|hyperpage}{104}
+\indexentry{complex conjugate|hyperpage}{104}
+\indexentry{conjugate|hyperpage}{104}
+\indexentry{real part|hyperpage}{104}
+\indexentry{imaginary part|hyperpage}{104}
+\indexentry{modulus|hyperpage}{104}
+\indexentry{argument|hyperpage}{104}
+\indexentry{multivalued function|hyperpage}{104}
+\indexentry{determination of the argument of $f$|hyperpage}{104}
+\indexentry{principal argument|hyperpage}{104}
+\indexentry{Cartesian form|hyperpage}{104}
+\indexentry{extended complex plane|hyperpage}{105}
+\indexentry{extended real numbers|hyperpage}{105}
+\indexentry{Stereographic projection|hyperpage}{105}
+\indexentry{stereographic projection|hyperpage}{105}
+\indexentry{sequence of complex numbers|hyperpage}{105}
+\indexentry{limit|hyperpage}{105}
+\indexentry{converges|hyperpage}{105}
\indexentry{convergent|hyperpage}{105}
-\indexentry{sum of the series|hyperpage}{105}
\indexentry{divergent|hyperpage}{105}
-\indexentry{reordering|hyperpage}{105}
-\indexentry{Abel's summation formula|hyperpage}{105}
-\indexentry{absolutely convergent|hyperpage}{105}
-\indexentry{Cauchy product|hyperpage}{105}
-\indexentry{product|hyperpage}{105}
-\indexentry{complex function|hyperpage}{105}
-\indexentry{continuous|hyperpage}{105}
-\indexentry{sequence of complex functions|hyperpage}{105}
-\indexentry{converges pointwise|hyperpage}{105}
-\indexentry{converges uniformly|hyperpage}{105}
-\indexentry{Cauchy's test|hyperpage}{106}
-\indexentry{series of functions|hyperpage}{106}
+\indexentry{bounded|hyperpage}{105}
+\indexentry{Cauchy|hyperpage}{105}
+\indexentry{numeric series of complex numbers|hyperpage}{105}
+\indexentry{general term of the series|hyperpage}{105}
+\indexentry{$N$-th partial sum of the series|hyperpage}{105}
+\indexentry{convergent|hyperpage}{106}
+\indexentry{sum of the series|hyperpage}{106}
+\indexentry{divergent|hyperpage}{106}
+\indexentry{reordering|hyperpage}{106}
+\indexentry{Abel's summation formula|hyperpage}{106}
+\indexentry{absolutely convergent|hyperpage}{106}
+\indexentry{Cauchy product|hyperpage}{106}
+\indexentry{product|hyperpage}{106}
+\indexentry{complex function|hyperpage}{106}
+\indexentry{continuous|hyperpage}{106}
+\indexentry{sequence of complex functions|hyperpage}{106}
\indexentry{converges pointwise|hyperpage}{106}
-\indexentry{sum of the series in a pointwise sense|hyperpage}{106}
\indexentry{converges uniformly|hyperpage}{106}
-\indexentry{sum of the series in an uniform sense|hyperpage}{106}
-\indexentry{Cauchy's test|hyperpage}{106}
-\indexentry{Weierstra\ss \ M-test|hyperpage}{106}
-\indexentry{Dirichlet's test|hyperpage}{106}
-\indexentry{Abel's test|hyperpage}{106}
-\indexentry{Dedekind's test|hyperpage}{106}
-\indexentry{Du Bois-Reymond's test|hyperpage}{106}
-\indexentry{complex power series|hyperpage}{106}
-\indexentry{Cauchy-Hadamard theorem|hyperpage}{106}
-\indexentry{radius of convergence|hyperpage}{107}
-\indexentry{Abel's theorem|hyperpage}{107}
-\indexentry{cone|hyperpage}{107}
-\indexentry{Abel's theorem|hyperpage}{107}
-\indexentry{complex exponential function|hyperpage}{107}
-\indexentry{Euler's formula|hyperpage}{107}
-\indexentry{Polar form|hyperpage}{107}
-\indexentry{polar form|hyperpage}{107}
-\indexentry{De Moivre's formula|hyperpage}{107}
-\indexentry{complex natural logarithm|hyperpage}{107}
-\indexentry{principal value|hyperpage}{107}
-\indexentry{complex sine|hyperpage}{107}
-\indexentry{complex cosine|hyperpage}{107}
-\indexentry{complex tangent|hyperpage}{108}
-\indexentry{complex secant|hyperpage}{108}
-\indexentry{complex cosecant|hyperpage}{108}
-\indexentry{complex cotangent|hyperpage}{108}
-\indexentry{complex hyperbolic sine|hyperpage}{108}
-\indexentry{complex hyperbolic cosine|hyperpage}{108}
-\indexentry{complex hyperbolic tangent|hyperpage}{108}
-\indexentry{complex hyperbolic secant|hyperpage}{108}
-\indexentry{complex hyperbolic cosecant|hyperpage}{108}
-\indexentry{complex hyperbolic cotangent|hyperpage}{108}
-\indexentry{$\ensuremath {\mathbb {C}}$-differentiable|hyperpage}{108}
-\indexentry{derivative of $f$ at $z_0$|hyperpage}{108}
-\indexentry{Chain rule|hyperpage}{108}
-\indexentry{holomorphic|hyperpage}{108}
-\indexentry{entire function|hyperpage}{108}
-\indexentry{determination|hyperpage}{109}
-\indexentry{determination of the logarithm|hyperpage}{109}
-\indexentry{determination|hyperpage}{109}
-\indexentry{associated multivalued function|hyperpage}{109}
-\indexentry{$\ensuremath {\mathbb {R}}$-differentiable|hyperpage}{109}
-\indexentry{differential|hyperpage}{109}
-\indexentry{Cauchy-Riemann theorem|hyperpage}{110}
-\indexentry{Cauchy-Riemann equations|hyperpage}{110}
-\indexentry{Wirtinger operators|hyperpage}{110}
-\indexentry{integral|hyperpage}{110}
-\indexentry{line integral|hyperpage}{111}
-\indexentry{Goursat's theorem|hyperpage}{111}
-\indexentry{Local Cauchy's integral theorem|hyperpage}{111}
-\indexentry{Fresnel integrals|hyperpage}{112}
-\indexentry{index|hyperpage}{112}
-\indexentry{winding number|hyperpage}{112}
-\indexentry{Local Cauchy's integral formula|hyperpage}{112}
-\indexentry{analytic|hyperpage}{112}
-\indexentry{Local Cauchy's integral formula for derivatives|hyperpage}{112}
-\indexentry{Cauchy's inequality|hyperpage}{113}
-\indexentry{Liouville's theorem|hyperpage}{113}
-\indexentry{Fundamental theorem of algebra|hyperpage}{113}
-\indexentry{Cardano-Vieta's formulas|hyperpage}{113}
-\indexentry{Morera's theorem|hyperpage}{113}
-\indexentry{Weierstra\ss ' theorem|hyperpage}{113}
-\indexentry{multiplicity|hyperpage}{113}
-\indexentry{Analytic continuation theorem|hyperpage}{113}
-\indexentry{Maximum modulus principle|hyperpage}{113}
-\indexentry{Minimum modulus principle|hyperpage}{113}
-\indexentry{harmonic|hyperpage}{114}
-\indexentry{domain|hyperpage}{114}
-\indexentry{region|hyperpage}{114}
-\indexentry{star domain|hyperpage}{114}
-\indexentry{convex|hyperpage}{114}
-\indexentry{Mean value property|hyperpage}{114}
-\indexentry{chain of paths|hyperpage}{114}
-\indexentry{image|hyperpage}{114}
-\indexentry{cycle|hyperpage}{114}
-\indexentry{index|hyperpage}{114}
-\indexentry{homologous to zero|hyperpage}{114}
-\indexentry{General Cauchy's integral formula|hyperpage}{114}
-\indexentry{Cauchy's integral theorem|hyperpage}{115}
-\indexentry{General Cauchy's integral formula for derivatives|hyperpage}{115}
-\indexentry{Local behaviour of a holomorphic function|hyperpage}{115}
-\indexentry{Open mapping theorem|hyperpage}{115}
-\indexentry{simply connected|hyperpage}{115}
-\indexentry{simply connected|hyperpage}{115}
-\indexentry{isolated singularity|hyperpage}{115}
-\indexentry{Removable singularity|hyperpage}{115}
-\indexentry{removable singularity|hyperpage}{115}
-\indexentry{Riemann's theorem on removable singularities|hyperpage}{115}
-\indexentry{pole|hyperpage}{115}
-\indexentry{Pole|hyperpage}{115}
-\indexentry{order|hyperpage}{115}
-\indexentry{simple|hyperpage}{115}
-\indexentry{residue|hyperpage}{115}
-\indexentry{Essential singularity|hyperpage}{116}
-\indexentry{essential singularity|hyperpage}{116}
-\indexentry{convergent|hyperpage}{116}
-\indexentry{absolutely convergent|hyperpage}{116}
-\indexentry{uniformly convergent|hyperpage}{116}
-\indexentry{Laurent series theorem|hyperpage}{116}
-\indexentry{Laurent series|hyperpage}{116}
-\indexentry{Partial fraction decomposition theorem|hyperpage}{116}
-\indexentry{Residues theorem|hyperpage}{116}
-\indexentry{Calculation of integrals|hyperpage}{116}
-\indexentry{Casorati-Weierstra\ss \ theorem|hyperpage}{117}
-\indexentry{Little Picard's theorem|hyperpage}{117}
-\indexentry{Great Picard's theorem|hyperpage}{117}
-\indexentry{meromorphic|hyperpage}{117}
-\indexentry{Argument principle|hyperpage}{117}
-\indexentry{Generalized argument principle|hyperpage}{117}
-\indexentry{Rouché's theorem|hyperpage}{118}
-\indexentry{Binomial theorem|hyperpage}{118}
-\indexentry{Hurwitz's theorem|hyperpage}{118}
-\indexentry{conformal|hyperpage}{118}
-\indexentry{conformal|hyperpage}{118}
-\indexentry{conformal representation|hyperpage}{118}
-\indexentry{Möbius transformations|hyperpage}{118}
-\indexentry{Möbius transformation|hyperpage}{118}
-\indexentry{translation|hyperpage}{118}
-\indexentry{rotation|hyperpage}{118}
-\indexentry{dilatation|hyperpage}{118}
-\indexentry{inversion|hyperpage}{118}
-\indexentry{cross ratio|hyperpage}{119}
-\indexentry{circle|hyperpage}{119}
-\indexentry{orientation|hyperpage}{119}
-\indexentry{Right side|hyperpage}{119}
-\indexentry{Left side|hyperpage}{119}
-\indexentry{Center|hyperpage}{119}
-\indexentry{Orientation principle|hyperpage}{119}
-\indexentry{reflection|hyperpage}{119}
-\indexentry{Symmetry principle|hyperpage}{119}
-\indexentry{Schwarz lemma|hyperpage}{119}
-\indexentry{Schwarz-Pick lemma|hyperpage}{120}
-\indexentry{surjective|hyperpage}{120}
-\indexentry{relatively compact|hyperpage}{120}
-\indexentry{normal|hyperpage}{120}
-\indexentry{equicontinuous|hyperpage}{120}
-\indexentry{Arzelà-Ascoli theorem|hyperpage}{120}
-\indexentry{locally bounded|hyperpage}{120}
-\indexentry{bounded by compact sets|hyperpage}{120}
-\indexentry{Montel's theorem|hyperpage}{120}
-\indexentry{Riemann conformal representation theorem|hyperpage}{120}
-\indexentry{ordinary differential equation|hyperpage}{121}
-\indexentry{ode|hyperpage}{121}
-\indexentry{implicit form|hyperpage}{121}
-\indexentry{independent variable|hyperpage}{121}
-\indexentry{explicit form|hyperpage}{121}
-\indexentry{solution of the ode|hyperpage}{121}
-\indexentry{general solution of the ode|hyperpage}{121}
-\indexentry{system of ordinary differential equations|hyperpage}{121}
-\indexentry{differential system|hyperpage}{121}
-\indexentry{autonomous|hyperpage}{121}
-\indexentry{non-autonomous|hyperpage}{121}
-\indexentry{linear|hyperpage}{121}
-\indexentry{homogeneous|hyperpage}{121}
-\indexentry{constant coefficients|hyperpage}{121}
-\indexentry{Initial value problem|hyperpage}{121}
-\indexentry{initial value problem|hyperpage}{121}
-\indexentry{ivp|hyperpage}{121}
-\indexentry{Cauchy problem|hyperpage}{121}
-\indexentry{initial conditions|hyperpage}{121}
-\indexentry{Separation of variables|hyperpage}{122}
-\indexentry{Variation of constants|hyperpage}{122}
-\indexentry{Characteristic equation|hyperpage}{122}
-\indexentry{characteristic equation|hyperpage}{122}
-\indexentry{Reducible linear ode of second order|hyperpage}{122}
-\indexentry{Bernoulli differential equation|hyperpage}{122}
-\indexentry{Bernoulli differential equation|hyperpage}{122}
-\indexentry{Riccati differential equation|hyperpage}{122}
-\indexentry{Riccati differential equation|hyperpage}{122}
-\indexentry{Integrating factor|hyperpage}{123}
-\indexentry{integrating factor|hyperpage}{123}
-\indexentry{Lipschitz continuous with respect to the second variable|hyperpage}{123}
-\indexentry{locally Lipschitz continuous with respect to the second variable|hyperpage}{123}
-\indexentry{operator|hyperpage}{123}
-\indexentry{Banach fixed-point theorem|hyperpage}{124}
-\indexentry{Picard theorem|hyperpage}{124}
-\indexentry{Picard iteration process|hyperpage}{124}
-\indexentry{pointwise bounded|hyperpage}{124}
-\indexentry{uniformly bounded|hyperpage}{124}
-\indexentry{equicontinuous at a point|hyperpage}{124}
-\indexentry{pointwise equicontinuous|hyperpage}{124}
-\indexentry{uniformly equicontinuous|hyperpage}{124}
-\indexentry{Arzelà-Ascoli theorem|hyperpage}{124}
-\indexentry{Peano theorem|hyperpage}{124}
-\indexentry{extension|hyperpage}{125}
-\indexentry{maximal element|hyperpage}{125}
-\indexentry{maximal|hyperpage}{125}
-\indexentry{chain|hyperpage}{125}
-\indexentry{upper bound|hyperpage}{125}
-\indexentry{greatest element|hyperpage}{125}
-\indexentry{Zorn's lemma|hyperpage}{125}
-\indexentry{Wintner lemma|hyperpage}{125}
-\indexentry{tends to the boundary|hyperpage}{125}
-\indexentry{system of linear differential equations|hyperpage}{125}
-\indexentry{homogeneous|hyperpage}{125}
-\indexentry{constant coefficients|hyperpage}{125}
-\indexentry{flow of the linear ode|hyperpage}{125}
-\indexentry{matrix solution|hyperpage}{126}
-\indexentry{fundamental matrix solution|hyperpage}{126}
-\indexentry{Liouville's formula|hyperpage}{126}
-\indexentry{matrix exponential|hyperpage}{126}
-\indexentry{generalized eigenvector|hyperpage}{127}
-\indexentry{generalized eigenspace|hyperpage}{127}
-\indexentry{flow|hyperpage}{127}
-\indexentry{Grönwall's lemma|hyperpage}{128}
-\indexentry{Dependence on $\boldsymbol {\mathrm {x}}_0$|hyperpage}{128}
-\indexentry{variational equations|hyperpage}{128}
-\indexentry{Dependence on $t_0$|hyperpage}{128}
-\indexentry{Dependence on $\boldsymbol {\mathrm {\lambda }}$|hyperpage}{128}
-\indexentry{dynamical system|hyperpage}{129}
-\indexentry{discrete|hyperpage}{129}
-\indexentry{continuous|hyperpage}{129}
-\indexentry{semidynamical system|hyperpage}{129}
-\indexentry{orbit|hyperpage}{129}
-\indexentry{positive semi-orbit|hyperpage}{129}
-\indexentry{negative semi-orbit|hyperpage}{129}
-\indexentry{phase portrait|hyperpage}{129}
-\indexentry{phase space|hyperpage}{129}
-\indexentry{equivalent|hyperpage}{129}
-\indexentry{critical point|hyperpage}{130}
-\indexentry{singular point|hyperpage}{130}
-\indexentry{non-singular|hyperpage}{130}
-\indexentry{regular|hyperpage}{130}
-\indexentry{periodic|hyperpage}{130}
-\indexentry{$\alpha $-limit point|hyperpage}{130}
-\indexentry{$\alpha $-limit set|hyperpage}{130}
-\indexentry{$\omega $-limit point|hyperpage}{130}
-\indexentry{$\omega $-limit point|hyperpage}{130}
-\indexentry{$\omega $-limit set|hyperpage}{130}
-\indexentry{$\omega $-limit point|hyperpage}{130}
-\indexentry{invariant|hyperpage}{130}
-\indexentry{positively invariant|hyperpage}{130}
-\indexentry{negatively invariant|hyperpage}{130}
-\indexentry{positively stable|hyperpage}{130}
-\indexentry{negatively stable|hyperpage}{130}
-\indexentry{attracting|hyperpage}{130}
-\indexentry{repelling|hyperpage}{130}
-\indexentry{asymptotically stable|hyperpage}{130}
-\indexentry{center|hyperpage}{130}
-\indexentry{basin|hyperpage}{130}
-\indexentry{equivalent dynamical systems|hyperpage}{130}
-\indexentry{topologically equivalent|hyperpage}{130}
-\indexentry{equivalence|hyperpage}{130}
-\indexentry{conjugate dynamical systems|hyperpage}{130}
-\indexentry{topologically conjugate|hyperpage}{131}
-\indexentry{conjugacy|hyperpage}{131}
-\indexentry{flow|hyperpage}{131}
-\indexentry{equivalent|hyperpage}{131}
-\indexentry{locally topologically equivalent|hyperpage}{131}
-\indexentry{local equivalence|hyperpage}{131}
-\indexentry{conjugate|hyperpage}{131}
-\indexentry{locally topologically conjugate|hyperpage}{131}
-\indexentry{local conjugacy|hyperpage}{131}
-\indexentry{local transversal section|hyperpage}{131}
-\indexentry{transversal section|hyperpage}{131}
-\indexentry{Flow box theorem|hyperpage}{131}
-\indexentry{local transversal section|hyperpage}{131}
-\indexentry{stable node|hyperpage}{132}
-\indexentry{stable degenerated node|hyperpage}{132}
-\indexentry{stable star|hyperpage}{132}
-\indexentry{unstable node|hyperpage}{132}
-\indexentry{unstable degenerated node|hyperpage}{132}
-\indexentry{unstable star|hyperpage}{132}
-\indexentry{saddle point|hyperpage}{132}
-\indexentry{stable focus|hyperpage}{132}
-\indexentry{sink|hyperpage}{132}
-\indexentry{unstable focus|hyperpage}{132}
-\indexentry{source|hyperpage}{132}
-\indexentry{center|hyperpage}{132}
-\indexentry{saddle separatrices|hyperpage}{132}
-\indexentry{homoclinic orbit|hyperpage}{132}
-\indexentry{heteroclinic orbit|hyperpage}{132}
-\indexentry{elliptic sector|hyperpage}{132}
-\indexentry{hyperbolic sector|hyperpage}{132}
-\indexentry{attracting parabolic sector|hyperpage}{132}
-\indexentry{repelling parabolic sector|hyperpage}{132}
-\indexentry{sectorial decomposition|hyperpage}{132}
-\indexentry{first integral|hyperpage}{133}
-\indexentry{functionally independent|hyperpage}{133}
-\indexentry{independent|hyperpage}{133}
-\indexentry{Hamiltonian system|hyperpage}{133}
-\indexentry{Hamiltonian|hyperpage}{133}
-\indexentry{hyperbolic critical point|hyperpage}{133}
-\indexentry{Hartman-Grobman theorem|hyperpage}{133}
-\indexentry{hyperbolic matrix|hyperpage}{133}
-\indexentry{stability number|hyperpage}{133}
-\indexentry{polynomial system|hyperpage}{134}
-\indexentry{polynomial vector field|hyperpage}{134}
-\indexentry{degree|hyperpage}{134}
-\indexentry{algebraic curve|hyperpage}{134}
-\indexentry{invariant algebraic curve|hyperpage}{134}
-\indexentry{cofactor|hyperpage}{135}
-\indexentry{Poincaré map|hyperpage}{135}
-\indexentry{Poincaré map|hyperpage}{135}
-\indexentry{limit cycle|hyperpage}{135}
-\indexentry{stable|hyperpage}{135}
-\indexentry{unstable|hyperpage}{135}
-\indexentry{semi-stable|hyperpage}{135}
-\indexentry{hyperbolic periodic orbit|hyperpage}{135}
-\indexentry{Poincaré-Bendixson theorem|hyperpage}{135}
-\indexentry{Poincaré-Bendixson theorem|hyperpage}{135}
-\indexentry{Lyapunov stable|hyperpage}{136}
-\indexentry{Lyapunov function|hyperpage}{136}
-\indexentry{strict Lyapunov function|hyperpage}{136}
-\indexentry{Lyapunov's theorem|hyperpage}{136}
-\indexentry{Bendixson's theorem|hyperpage}{136}
-\indexentry{Bendixson-Dulac theorem|hyperpage}{136}
-\indexentry{Generalized Bendixson-Dulac theorem|hyperpage}{136}
-\indexentry{Poincaré compactification|hyperpage}{137}
-\indexentry{Poincaré disk|hyperpage}{137}
-\indexentry{integrating factor|hyperpage}{137}
-\indexentry{exponential factor|hyperpage}{137}
-\indexentry{Darboux theorem|hyperpage}{137}
-\indexentry{index|hyperpage}{137}
-\indexentry{homotopic|hyperpage}{138}
-\indexentry{homotopy|hyperpage}{138}
-\indexentry{contractible|hyperpage}{138}
+\indexentry{Cauchy's test|hyperpage}{107}
+\indexentry{series of functions|hyperpage}{107}
+\indexentry{converges pointwise|hyperpage}{107}
+\indexentry{sum of the series in a pointwise sense|hyperpage}{107}
+\indexentry{converges uniformly|hyperpage}{107}
+\indexentry{sum of the series in an uniform sense|hyperpage}{107}
+\indexentry{Cauchy's test|hyperpage}{107}
+\indexentry{Weierstra\ss \ M-test|hyperpage}{107}
+\indexentry{Dirichlet's test|hyperpage}{107}
+\indexentry{Abel's test|hyperpage}{107}
+\indexentry{Dedekind's test|hyperpage}{107}
+\indexentry{Du Bois-Reymond's test|hyperpage}{107}
+\indexentry{complex power series|hyperpage}{107}
+\indexentry{Cauchy-Hadamard theorem|hyperpage}{107}
+\indexentry{radius of convergence|hyperpage}{108}
+\indexentry{Abel's theorem|hyperpage}{108}
+\indexentry{cone|hyperpage}{108}
+\indexentry{Abel's theorem|hyperpage}{108}
+\indexentry{complex exponential function|hyperpage}{108}
+\indexentry{Euler's formula|hyperpage}{108}
+\indexentry{Polar form|hyperpage}{108}
+\indexentry{polar form|hyperpage}{108}
+\indexentry{De Moivre's formula|hyperpage}{108}
+\indexentry{complex natural logarithm|hyperpage}{108}
+\indexentry{principal value|hyperpage}{108}
+\indexentry{complex sine|hyperpage}{108}
+\indexentry{complex cosine|hyperpage}{108}
+\indexentry{complex tangent|hyperpage}{109}
+\indexentry{complex secant|hyperpage}{109}
+\indexentry{complex cosecant|hyperpage}{109}
+\indexentry{complex cotangent|hyperpage}{109}
+\indexentry{complex hyperbolic sine|hyperpage}{109}
+\indexentry{complex hyperbolic cosine|hyperpage}{109}
+\indexentry{complex hyperbolic tangent|hyperpage}{109}
+\indexentry{complex hyperbolic secant|hyperpage}{109}
+\indexentry{complex hyperbolic cosecant|hyperpage}{109}
+\indexentry{complex hyperbolic cotangent|hyperpage}{109}
+\indexentry{$\ensuremath {\mathbb {C}}$-differentiable|hyperpage}{109}
+\indexentry{derivative of $f$ at $z_0$|hyperpage}{109}
+\indexentry{Chain rule|hyperpage}{109}
+\indexentry{holomorphic|hyperpage}{109}
+\indexentry{entire function|hyperpage}{109}
+\indexentry{determination|hyperpage}{110}
+\indexentry{determination of the logarithm|hyperpage}{110}
+\indexentry{determination|hyperpage}{110}
+\indexentry{associated multivalued function|hyperpage}{110}
+\indexentry{$\ensuremath {\mathbb {R}}$-differentiable|hyperpage}{110}
+\indexentry{differential|hyperpage}{110}
+\indexentry{Cauchy-Riemann theorem|hyperpage}{111}
+\indexentry{Cauchy-Riemann equations|hyperpage}{111}
+\indexentry{Wirtinger operators|hyperpage}{111}
+\indexentry{integral|hyperpage}{111}
+\indexentry{line integral|hyperpage}{112}
+\indexentry{Goursat's theorem|hyperpage}{112}
+\indexentry{Local Cauchy's integral theorem|hyperpage}{112}
+\indexentry{Fresnel integrals|hyperpage}{113}
+\indexentry{index|hyperpage}{113}
+\indexentry{winding number|hyperpage}{113}
+\indexentry{Local Cauchy's integral formula|hyperpage}{113}
+\indexentry{analytic|hyperpage}{113}
+\indexentry{Local Cauchy's integral formula for derivatives|hyperpage}{113}
+\indexentry{Cauchy's inequality|hyperpage}{114}
+\indexentry{Liouville's theorem|hyperpage}{114}
+\indexentry{Fundamental theorem of algebra|hyperpage}{114}
+\indexentry{Cardano-Vieta's formulas|hyperpage}{114}
+\indexentry{Morera's theorem|hyperpage}{114}
+\indexentry{Weierstra\ss ' theorem|hyperpage}{114}
+\indexentry{multiplicity|hyperpage}{114}
+\indexentry{Analytic continuation theorem|hyperpage}{114}
+\indexentry{Maximum modulus principle|hyperpage}{114}
+\indexentry{Minimum modulus principle|hyperpage}{114}
+\indexentry{harmonic|hyperpage}{115}
+\indexentry{domain|hyperpage}{115}
+\indexentry{region|hyperpage}{115}
+\indexentry{star domain|hyperpage}{115}
+\indexentry{convex|hyperpage}{115}
+\indexentry{Mean value property|hyperpage}{115}
+\indexentry{chain of paths|hyperpage}{115}
+\indexentry{image|hyperpage}{115}
+\indexentry{cycle|hyperpage}{115}
+\indexentry{index|hyperpage}{115}
+\indexentry{homologous to zero|hyperpage}{115}
+\indexentry{General Cauchy's integral formula|hyperpage}{115}
+\indexentry{Cauchy's integral theorem|hyperpage}{116}
+\indexentry{General Cauchy's integral formula for derivatives|hyperpage}{116}
+\indexentry{Local behaviour of a holomorphic function|hyperpage}{116}
+\indexentry{Open mapping theorem|hyperpage}{116}
+\indexentry{simply connected|hyperpage}{116}
+\indexentry{simply connected|hyperpage}{116}
+\indexentry{isolated singularity|hyperpage}{116}
+\indexentry{Removable singularity|hyperpage}{116}
+\indexentry{removable singularity|hyperpage}{116}
+\indexentry{Riemann's theorem on removable singularities|hyperpage}{116}
+\indexentry{pole|hyperpage}{116}
+\indexentry{Pole|hyperpage}{116}
+\indexentry{order|hyperpage}{116}
+\indexentry{simple|hyperpage}{116}
+\indexentry{residue|hyperpage}{116}
+\indexentry{Essential singularity|hyperpage}{117}
+\indexentry{essential singularity|hyperpage}{117}
+\indexentry{convergent|hyperpage}{117}
+\indexentry{absolutely convergent|hyperpage}{117}
+\indexentry{uniformly convergent|hyperpage}{117}
+\indexentry{Laurent series theorem|hyperpage}{117}
+\indexentry{Laurent series|hyperpage}{117}
+\indexentry{Partial fraction decomposition theorem|hyperpage}{117}
+\indexentry{Residues theorem|hyperpage}{117}
+\indexentry{Calculation of integrals|hyperpage}{117}
+\indexentry{Casorati-Weierstra\ss \ theorem|hyperpage}{118}
+\indexentry{Little Picard's theorem|hyperpage}{118}
+\indexentry{Great Picard's theorem|hyperpage}{118}
+\indexentry{meromorphic|hyperpage}{118}
+\indexentry{Argument principle|hyperpage}{118}
+\indexentry{Generalized argument principle|hyperpage}{118}
+\indexentry{Rouché's theorem|hyperpage}{119}
+\indexentry{Binomial theorem|hyperpage}{119}
+\indexentry{Hurwitz's theorem|hyperpage}{119}
+\indexentry{conformal|hyperpage}{119}
+\indexentry{conformal|hyperpage}{119}
+\indexentry{conformal representation|hyperpage}{119}
+\indexentry{Möbius transformations|hyperpage}{119}
+\indexentry{Möbius transformation|hyperpage}{119}
+\indexentry{translation|hyperpage}{119}
+\indexentry{rotation|hyperpage}{119}
+\indexentry{dilatation|hyperpage}{119}
+\indexentry{inversion|hyperpage}{119}
+\indexentry{cross ratio|hyperpage}{120}
+\indexentry{circle|hyperpage}{120}
+\indexentry{orientation|hyperpage}{120}
+\indexentry{Right side|hyperpage}{120}
+\indexentry{Left side|hyperpage}{120}
+\indexentry{Center|hyperpage}{120}
+\indexentry{Orientation principle|hyperpage}{120}
+\indexentry{reflection|hyperpage}{120}
+\indexentry{Symmetry principle|hyperpage}{120}
+\indexentry{Schwarz lemma|hyperpage}{120}
+\indexentry{Schwarz-Pick lemma|hyperpage}{121}
+\indexentry{surjective|hyperpage}{121}
+\indexentry{relatively compact|hyperpage}{121}
+\indexentry{normal|hyperpage}{121}
+\indexentry{equicontinuous|hyperpage}{121}
+\indexentry{Arzelà-Ascoli theorem|hyperpage}{121}
+\indexentry{locally bounded|hyperpage}{121}
+\indexentry{bounded by compact sets|hyperpage}{121}
+\indexentry{Montel's theorem|hyperpage}{121}
+\indexentry{Riemann conformal representation theorem|hyperpage}{121}
+\indexentry{ordinary differential equation|hyperpage}{122}
+\indexentry{ode|hyperpage}{122}
+\indexentry{implicit form|hyperpage}{122}
+\indexentry{independent variable|hyperpage}{122}
+\indexentry{explicit form|hyperpage}{122}
+\indexentry{solution of the ode|hyperpage}{122}
+\indexentry{general solution of the ode|hyperpage}{122}
+\indexentry{system of ordinary differential equations|hyperpage}{122}
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+\indexentry{autonomous|hyperpage}{122}
+\indexentry{non-autonomous|hyperpage}{122}
+\indexentry{linear|hyperpage}{122}
+\indexentry{homogeneous|hyperpage}{122}
+\indexentry{constant coefficients|hyperpage}{122}
+\indexentry{Initial value problem|hyperpage}{122}
+\indexentry{initial value problem|hyperpage}{122}
+\indexentry{ivp|hyperpage}{122}
+\indexentry{Cauchy problem|hyperpage}{122}
+\indexentry{initial conditions|hyperpage}{122}
+\indexentry{Separation of variables|hyperpage}{123}
+\indexentry{Variation of constants|hyperpage}{123}
+\indexentry{Characteristic equation|hyperpage}{123}
+\indexentry{characteristic equation|hyperpage}{123}
+\indexentry{Reducible linear ode of second order|hyperpage}{123}
+\indexentry{Bernoulli differential equation|hyperpage}{123}
+\indexentry{Bernoulli differential equation|hyperpage}{123}
+\indexentry{Riccati differential equation|hyperpage}{123}
+\indexentry{Riccati differential equation|hyperpage}{123}
+\indexentry{Integrating factor|hyperpage}{124}
+\indexentry{integrating factor|hyperpage}{124}
+\indexentry{Lipschitz continuous with respect to the second variable|hyperpage}{124}
+\indexentry{locally Lipschitz continuous with respect to the second variable|hyperpage}{124}
+\indexentry{operator|hyperpage}{124}
+\indexentry{Banach fixed-point theorem|hyperpage}{125}
+\indexentry{Picard theorem|hyperpage}{125}
+\indexentry{Picard iteration process|hyperpage}{125}
+\indexentry{pointwise bounded|hyperpage}{125}
+\indexentry{uniformly bounded|hyperpage}{125}
+\indexentry{equicontinuous at a point|hyperpage}{125}
+\indexentry{pointwise equicontinuous|hyperpage}{125}
+\indexentry{uniformly equicontinuous|hyperpage}{125}
+\indexentry{Arzelà-Ascoli theorem|hyperpage}{125}
+\indexentry{Peano theorem|hyperpage}{125}
+\indexentry{extension|hyperpage}{126}
+\indexentry{maximal element|hyperpage}{126}
+\indexentry{maximal|hyperpage}{126}
+\indexentry{chain|hyperpage}{126}
+\indexentry{upper bound|hyperpage}{126}
+\indexentry{greatest element|hyperpage}{126}
+\indexentry{Zorn's lemma|hyperpage}{126}
+\indexentry{Wintner lemma|hyperpage}{126}
+\indexentry{tends to the boundary|hyperpage}{126}
+\indexentry{system of linear differential equations|hyperpage}{126}
+\indexentry{homogeneous|hyperpage}{126}
+\indexentry{constant coefficients|hyperpage}{126}
+\indexentry{flow of the linear ode|hyperpage}{126}
+\indexentry{matrix solution|hyperpage}{127}
+\indexentry{fundamental matrix solution|hyperpage}{127}
+\indexentry{Liouville's formula|hyperpage}{127}
+\indexentry{matrix exponential|hyperpage}{127}
+\indexentry{generalized eigenvector|hyperpage}{128}
+\indexentry{generalized eigenspace|hyperpage}{128}
+\indexentry{flow|hyperpage}{128}
+\indexentry{Grönwall's lemma|hyperpage}{129}
+\indexentry{Dependence on $\boldsymbol {\mathrm {x}}_0$|hyperpage}{129}
+\indexentry{variational equations|hyperpage}{129}
+\indexentry{Dependence on $t_0$|hyperpage}{129}
+\indexentry{Dependence on $\boldsymbol {\mathrm {\lambda }}$|hyperpage}{129}
+\indexentry{dynamical system|hyperpage}{130}
+\indexentry{discrete|hyperpage}{130}
+\indexentry{continuous|hyperpage}{130}
+\indexentry{semidynamical system|hyperpage}{130}
+\indexentry{orbit|hyperpage}{130}
+\indexentry{positive semi-orbit|hyperpage}{130}
+\indexentry{negative semi-orbit|hyperpage}{130}
+\indexentry{phase portrait|hyperpage}{130}
+\indexentry{phase space|hyperpage}{130}
+\indexentry{equivalent|hyperpage}{130}
+\indexentry{critical point|hyperpage}{131}
+\indexentry{singular point|hyperpage}{131}
+\indexentry{non-singular|hyperpage}{131}
+\indexentry{regular|hyperpage}{131}
+\indexentry{periodic|hyperpage}{131}
+\indexentry{$\alpha $-limit point|hyperpage}{131}
+\indexentry{$\alpha $-limit set|hyperpage}{131}
+\indexentry{$\omega $-limit point|hyperpage}{131}
+\indexentry{$\omega $-limit point|hyperpage}{131}
+\indexentry{$\omega $-limit set|hyperpage}{131}
+\indexentry{$\omega $-limit point|hyperpage}{131}
+\indexentry{invariant|hyperpage}{131}
+\indexentry{positively invariant|hyperpage}{131}
+\indexentry{negatively invariant|hyperpage}{131}
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+\indexentry{negatively stable|hyperpage}{131}
+\indexentry{attracting|hyperpage}{131}
+\indexentry{repelling|hyperpage}{131}
+\indexentry{asymptotically stable|hyperpage}{131}
+\indexentry{center|hyperpage}{131}
+\indexentry{basin|hyperpage}{131}
+\indexentry{equivalent dynamical systems|hyperpage}{131}
+\indexentry{topologically equivalent|hyperpage}{131}
+\indexentry{equivalence|hyperpage}{131}
+\indexentry{conjugate dynamical systems|hyperpage}{131}
+\indexentry{topologically conjugate|hyperpage}{132}
+\indexentry{conjugacy|hyperpage}{132}
+\indexentry{flow|hyperpage}{132}
+\indexentry{equivalent|hyperpage}{132}
+\indexentry{locally topologically equivalent|hyperpage}{132}
+\indexentry{local equivalence|hyperpage}{132}
+\indexentry{conjugate|hyperpage}{132}
+\indexentry{locally topologically conjugate|hyperpage}{132}
+\indexentry{local conjugacy|hyperpage}{132}
+\indexentry{local transversal section|hyperpage}{132}
+\indexentry{transversal section|hyperpage}{132}
+\indexentry{Flow box theorem|hyperpage}{132}
+\indexentry{local transversal section|hyperpage}{132}
+\indexentry{stable node|hyperpage}{133}
+\indexentry{stable degenerated node|hyperpage}{133}
+\indexentry{stable star|hyperpage}{133}
+\indexentry{unstable node|hyperpage}{133}
+\indexentry{unstable degenerated node|hyperpage}{133}
+\indexentry{unstable star|hyperpage}{133}
+\indexentry{saddle point|hyperpage}{133}
+\indexentry{stable focus|hyperpage}{133}
+\indexentry{sink|hyperpage}{133}
+\indexentry{unstable focus|hyperpage}{133}
+\indexentry{source|hyperpage}{133}
+\indexentry{center|hyperpage}{133}
+\indexentry{saddle separatrices|hyperpage}{133}
+\indexentry{homoclinic orbit|hyperpage}{133}
+\indexentry{heteroclinic orbit|hyperpage}{133}
+\indexentry{elliptic sector|hyperpage}{133}
+\indexentry{hyperbolic sector|hyperpage}{133}
+\indexentry{attracting parabolic sector|hyperpage}{133}
+\indexentry{repelling parabolic sector|hyperpage}{133}
+\indexentry{sectorial decomposition|hyperpage}{133}
+\indexentry{first integral|hyperpage}{134}
+\indexentry{functionally independent|hyperpage}{134}
+\indexentry{independent|hyperpage}{134}
+\indexentry{Hamiltonian system|hyperpage}{134}
+\indexentry{Hamiltonian|hyperpage}{134}
+\indexentry{hyperbolic critical point|hyperpage}{134}
+\indexentry{Hartman-Grobman theorem|hyperpage}{134}
+\indexentry{hyperbolic matrix|hyperpage}{134}
+\indexentry{stability number|hyperpage}{134}
+\indexentry{polynomial system|hyperpage}{135}
+\indexentry{polynomial vector field|hyperpage}{135}
+\indexentry{degree|hyperpage}{135}
+\indexentry{algebraic curve|hyperpage}{135}
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+\indexentry{Poincaré map|hyperpage}{136}
+\indexentry{Poincaré map|hyperpage}{136}
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+\indexentry{stable|hyperpage}{136}
+\indexentry{unstable|hyperpage}{136}
+\indexentry{semi-stable|hyperpage}{136}
+\indexentry{hyperbolic periodic orbit|hyperpage}{136}
+\indexentry{Poincaré-Bendixson theorem|hyperpage}{136}
+\indexentry{Poincaré-Bendixson theorem|hyperpage}{136}
+\indexentry{Lyapunov stable|hyperpage}{137}
+\indexentry{Lyapunov function|hyperpage}{137}
+\indexentry{strict Lyapunov function|hyperpage}{137}
+\indexentry{Lyapunov's theorem|hyperpage}{137}
+\indexentry{Bendixson's theorem|hyperpage}{137}
+\indexentry{Bendixson-Dulac theorem|hyperpage}{137}
+\indexentry{Generalized Bendixson-Dulac theorem|hyperpage}{137}
+\indexentry{Poincaré compactification|hyperpage}{138}
+\indexentry{Poincaré disk|hyperpage}{138}
+\indexentry{integrating factor|hyperpage}{138}
+\indexentry{exponential factor|hyperpage}{138}
+\indexentry{Darboux theorem|hyperpage}{138}
\indexentry{index|hyperpage}{138}
-\indexentry{index|hyperpage}{138}
-\indexentry{tangent vector field|hyperpage}{138}
-\indexentry{Poincaré-Hopf theorem|hyperpage}{138}
-\indexentry{Poincaré-Hopf theorem on $S^2$|hyperpage}{138}
-\indexentry{Poincaré index formula|hyperpage}{138}
-\indexentry{partial differential equation|hyperpage}{138}
-\indexentry{pde|hyperpage}{138}
-\indexentry{solution|hyperpage}{138}
-\indexentry{quasilinear pde|hyperpage}{139}
-\indexentry{Heat equation|hyperpage}{139}
-\indexentry{heat equation|hyperpage}{139}
-\indexentry{Wave equation|hyperpage}{139}
-\indexentry{wave equation|hyperpage}{139}
-\indexentry{D'Alembert formula|hyperpage}{139}
-\indexentry{Laplace equation|hyperpage}{139}
-\indexentry{Laplace equation|hyperpage}{139}
-\indexentry{Dirichlet problem|hyperpage}{139}
-\indexentry{local diffeomorphism|hyperpage}{140}
-\indexentry{parametrization|hyperpage}{140}
-\indexentry{trace|hyperpage}{140}
-\indexentry{tangent vector|hyperpage}{140}
-\indexentry{regular|hyperpage}{140}
-\indexentry{tangent line|hyperpage}{140}
-\indexentry{plane curve|hyperpage}{140}
-\indexentry{reparametrization|hyperpage}{140}
-\indexentry{change of parameter|hyperpage}{140}
-\indexentry{positive|hyperpage}{140}
-\indexentry{negative|hyperpage}{140}
-\indexentry{length of the polygonal|hyperpage}{140}
-\indexentry{rectifiable|hyperpage}{140}
-\indexentry{length|hyperpage}{140}
-\indexentry{unit-speed parametrization|hyperpage}{140}
-\indexentry{arc-length parameter|hyperpage}{140}
-\indexentry{arc-length function|hyperpage}{141}
-\indexentry{same orientation|hyperpage}{141}
-\indexentry{opposite orientations|hyperpage}{141}
-\indexentry{orientation|hyperpage}{141}
-\indexentry{oriented vector space|hyperpage}{141}
-\indexentry{unoriented vector space|hyperpage}{141}
-\indexentry{positive basis|hyperpage}{141}
-\indexentry{negative basis|hyperpage}{141}
-\indexentry{orientation-preserving|hyperpage}{141}
-\indexentry{positively oriented|hyperpage}{141}
-\indexentry{negatively-oriented|hyperpage}{141}
-\indexentry{determinant|hyperpage}{141}
-\indexentry{cross product|hyperpage}{141}
-\indexentry{Jacobi identity|hyperpage}{141}
-\indexentry{curvature|hyperpage}{142}
-\indexentry{unit normal vector|hyperpage}{142}
-\indexentry{binormal vector|hyperpage}{142}
-\indexentry{Frenet-Serret frame|hyperpage}{142}
-\indexentry{TNB frame|hyperpage}{142}
-\indexentry{torsion|hyperpage}{142}
-\indexentry{Frenet-Serret formulas|hyperpage}{142}
-\indexentry{Osculating plane|hyperpage}{142}
-\indexentry{Normal plane|hyperpage}{142}
-\indexentry{Rectifying plane|hyperpage}{142}
-\indexentry{General Frenet-Serret formulas|hyperpage}{142}
-\indexentry{contact|hyperpage}{143}
-\indexentry{contact|hyperpage}{143}
-\indexentry{tangent line|hyperpage}{143}
-\indexentry{osculating circle|hyperpage}{143}
-\indexentry{radius of curvature|hyperpage}{143}
-\indexentry{osculating sphere|hyperpage}{143}
-\indexentry{envelope|hyperpage}{143}
-\indexentry{evolute|hyperpage}{143}
-\indexentry{involute|hyperpage}{143}
-\indexentry{signed curvature|hyperpage}{144}
-\indexentry{local canonical form|hyperpage}{144}
-\indexentry{dextrorotation|hyperpage}{144}
-\indexentry{levorotation|hyperpage}{144}
-\indexentry{orthogonal group|hyperpage}{144}
-\indexentry{special orthogonal group|hyperpage}{144}
-\indexentry{Fundamental theorem of curves|hyperpage}{145}
-\indexentry{support|hyperpage}{145}
-\indexentry{Immersion|hyperpage}{145}
-\indexentry{immersion|hyperpage}{145}
-\indexentry{immersion|hyperpage}{145}
-\indexentry{Submersion|hyperpage}{145}
-\indexentry{submersion|hyperpage}{145}
-\indexentry{submersion|hyperpage}{145}
-\indexentry{Local structure of immersions|hyperpage}{145}
-\indexentry{Local structure of submersions|hyperpage}{145}
-\indexentry{submanifold|hyperpage}{145}
-\indexentry{parametrization|hyperpage}{146}
-\indexentry{coordinate chart|hyperpage}{146}
-\indexentry{regular surface|hyperpage}{146}
-\indexentry{surface|hyperpage}{146}
-\indexentry{surface of revolution|hyperpage}{146}
-\indexentry{generatrix|hyperpage}{146}
-\indexentry{differentiable|hyperpage}{146}
-\indexentry{differentiable|hyperpage}{146}
-\indexentry{tangent vector|hyperpage}{146}
-\indexentry{tangent space|hyperpage}{146}
-\indexentry{tangent plane|hyperpage}{146}
-\indexentry{tangent function|hyperpage}{147}
-\indexentry{differential|hyperpage}{147}
-\indexentry{Inverse function theorem for surfaces|hyperpage}{147}
-\indexentry{first fundamental form|hyperpage}{147}
-\indexentry{orthogonal|hyperpage}{147}
-\indexentry{orthogonal coordinates|hyperpage}{147}
-\indexentry{regular domain|hyperpage}{147}
-\indexentry{domain|hyperpage}{147}
-\indexentry{region|hyperpage}{147}
-\indexentry{integral of $f$ over the region $R$|hyperpage}{147}
-\indexentry{local isometry|hyperpage}{147}
-\indexentry{isometry|hyperpage}{147}
-\indexentry{conformal|hyperpage}{148}
-\indexentry{angle-preserving|hyperpage}{148}
-\indexentry{conformal|hyperpage}{148}
-\indexentry{orientable|hyperpage}{148}
-\indexentry{normal unit field|hyperpage}{148}
-\indexentry{Gau\ss \ map|hyperpage}{148}
-\indexentry{orientation|hyperpage}{148}
-\indexentry{compatible|hyperpage}{148}
-\indexentry{Weingarten endomorphsim|hyperpage}{148}
-\indexentry{principal directons|hyperpage}{148}
-\indexentry{principal curvatures|hyperpage}{148}
-\indexentry{umbilic point|hyperpage}{148}
-\indexentry{Gau\ss \ curvature|hyperpage}{148}
-\indexentry{mean curvature|hyperpage}{148}
-\indexentry{minimal surface|hyperpage}{148}
-\indexentry{second fundamental form|hyperpage}{149}
-\indexentry{normal curvature|hyperpage}{149}
-\indexentry{Meusnier's theorem|hyperpage}{149}
-\indexentry{normal curvature|hyperpage}{149}
-\indexentry{asymptotic direction|hyperpage}{149}
-\indexentry{line of curvature|hyperpage}{149}
-\indexentry{asymptotic line|hyperpage}{149}
-\indexentry{Olinde Rodrigues' theorem|hyperpage}{149}
-\indexentry{Euler's formula|hyperpage}{149}
-\indexentry{elliptic point|hyperpage}{149}
-\indexentry{hyperbolic point|hyperpage}{149}
-\indexentry{parabolic point|hyperpage}{149}
-\indexentry{plane point|hyperpage}{149}
-\indexentry{ruled surface|hyperpage}{150}
-\indexentry{developable|hyperpage}{150}
-\indexentry{regression axis|hyperpage}{150}
-\indexentry{Christoffel symbols|hyperpage}{150}
-\indexentry{Gau\ss \ equations|hyperpage}{151}
-\indexentry{Codazzi-Mainardi equations|hyperpage}{151}
-\indexentry{Gau\ss ' Theorema Egregium|hyperpage}{151}
-\indexentry{Bonnet's theorem|hyperpage}{151}
-\indexentry{vector field|hyperpage}{151}
-\indexentry{differentiable|hyperpage}{151}
-\indexentry{differentiable|hyperpage}{151}
-\indexentry{covariant derivative|hyperpage}{151}
-\indexentry{vector field|hyperpage}{151}
-\indexentry{differentiable|hyperpage}{151}
-\indexentry{parallel|hyperpage}{151}
-\indexentry{parallel transport|hyperpage}{151}
-\indexentry{geodesic|hyperpage}{152}
-\indexentry{algebraic value|hyperpage}{152}
-\indexentry{geodesic curvature|hyperpage}{152}
-\indexentry{Liouville's formula|hyperpage}{152}
-\indexentry{vector field|hyperpage}{153}
-\indexentry{differentiable|hyperpage}{153}
-\indexentry{differentiable|hyperpage}{153}
-\indexentry{integral curve|hyperpage}{153}
-\indexentry{first integral|hyperpage}{153}
-\indexentry{vector field|hyperpage}{153}
-\indexentry{differentiable|hyperpage}{153}
-\indexentry{tangent|hyperpage}{153}
-\indexentry{multilinear map|hyperpage}{154}
-\indexentry{$k$-linear map|hyperpage}{154}
-\indexentry{degree|hyperpage}{154}
-\indexentry{alternating|hyperpage}{154}
-\indexentry{multilinear forms|hyperpage}{154}
-\indexentry{exterior product|hyperpage}{154}
-\indexentry{differential $k$-form|hyperpage}{154}
-\indexentry{differential|hyperpage}{154}
-\indexentry{pull-back|hyperpage}{155}
-\indexentry{pull-back|hyperpage}{155}
-\indexentry{interior product|hyperpage}{155}
-\indexentry{volume element|hyperpage}{155}
-\indexentry{exterior differential|hyperpage}{155}
-\indexentry{closed|hyperpage}{155}
-\indexentry{exact|hyperpage}{155}
-\indexentry{tangent vector|hyperpage}{155}
-\indexentry{tangent space|hyperpage}{155}
-\indexentry{vector field|hyperpage}{155}
-\indexentry{differentiable|hyperpage}{155}
-\indexentry{differentiable|hyperpage}{155}
-\indexentry{tangent|hyperpage}{155}
-\indexentry{differential $\ell $-form|hyperpage}{155}
+\indexentry{homotopic|hyperpage}{139}
+\indexentry{homotopy|hyperpage}{139}
+\indexentry{contractible|hyperpage}{139}
+\indexentry{index|hyperpage}{139}
+\indexentry{index|hyperpage}{139}
+\indexentry{tangent vector field|hyperpage}{139}
+\indexentry{Poincaré-Hopf theorem|hyperpage}{139}
+\indexentry{Poincaré-Hopf theorem on $S^2$|hyperpage}{139}
+\indexentry{Poincaré index formula|hyperpage}{139}
+\indexentry{partial differential equation|hyperpage}{139}
+\indexentry{pde|hyperpage}{139}
+\indexentry{solution|hyperpage}{139}
+\indexentry{quasilinear pde|hyperpage}{140}
+\indexentry{Heat equation|hyperpage}{140}
+\indexentry{heat equation|hyperpage}{140}
+\indexentry{Wave equation|hyperpage}{140}
+\indexentry{wave equation|hyperpage}{140}
+\indexentry{D'Alembert formula|hyperpage}{140}
+\indexentry{Laplace equation|hyperpage}{140}
+\indexentry{Laplace equation|hyperpage}{140}
+\indexentry{Dirichlet problem|hyperpage}{140}
+\indexentry{local diffeomorphism|hyperpage}{141}
+\indexentry{parametrization|hyperpage}{141}
+\indexentry{trace|hyperpage}{141}
+\indexentry{tangent vector|hyperpage}{141}
+\indexentry{regular|hyperpage}{141}
+\indexentry{tangent line|hyperpage}{141}
+\indexentry{plane curve|hyperpage}{141}
+\indexentry{reparametrization|hyperpage}{141}
+\indexentry{change of parameter|hyperpage}{141}
+\indexentry{positive|hyperpage}{141}
+\indexentry{negative|hyperpage}{141}
+\indexentry{length of the polygonal|hyperpage}{141}
+\indexentry{rectifiable|hyperpage}{141}
+\indexentry{length|hyperpage}{141}
+\indexentry{unit-speed parametrization|hyperpage}{141}
+\indexentry{arc-length parameter|hyperpage}{141}
+\indexentry{arc-length function|hyperpage}{142}
+\indexentry{same orientation|hyperpage}{142}
+\indexentry{opposite orientations|hyperpage}{142}
+\indexentry{orientation|hyperpage}{142}
+\indexentry{oriented vector space|hyperpage}{142}
+\indexentry{unoriented vector space|hyperpage}{142}
+\indexentry{positive basis|hyperpage}{142}
+\indexentry{negative basis|hyperpage}{142}
+\indexentry{orientation-preserving|hyperpage}{142}
+\indexentry{positively oriented|hyperpage}{142}
+\indexentry{negatively-oriented|hyperpage}{142}
+\indexentry{determinant|hyperpage}{142}
+\indexentry{cross product|hyperpage}{142}
+\indexentry{Jacobi identity|hyperpage}{142}
+\indexentry{curvature|hyperpage}{143}
+\indexentry{unit normal vector|hyperpage}{143}
+\indexentry{binormal vector|hyperpage}{143}
+\indexentry{Frenet-Serret frame|hyperpage}{143}
+\indexentry{TNB frame|hyperpage}{143}
+\indexentry{torsion|hyperpage}{143}
+\indexentry{Frenet-Serret formulas|hyperpage}{143}
+\indexentry{Osculating plane|hyperpage}{143}
+\indexentry{Normal plane|hyperpage}{143}
+\indexentry{Rectifying plane|hyperpage}{143}
+\indexentry{General Frenet-Serret formulas|hyperpage}{143}
+\indexentry{contact|hyperpage}{144}
+\indexentry{contact|hyperpage}{144}
+\indexentry{tangent line|hyperpage}{144}
+\indexentry{osculating circle|hyperpage}{144}
+\indexentry{radius of curvature|hyperpage}{144}
+\indexentry{osculating sphere|hyperpage}{144}
+\indexentry{envelope|hyperpage}{144}
+\indexentry{evolute|hyperpage}{144}
+\indexentry{involute|hyperpage}{144}
+\indexentry{signed curvature|hyperpage}{145}
+\indexentry{local canonical form|hyperpage}{145}
+\indexentry{dextrorotation|hyperpage}{145}
+\indexentry{levorotation|hyperpage}{145}
+\indexentry{orthogonal group|hyperpage}{145}
+\indexentry{special orthogonal group|hyperpage}{145}
+\indexentry{Fundamental theorem of curves|hyperpage}{146}
+\indexentry{support|hyperpage}{146}
+\indexentry{Immersion|hyperpage}{146}
+\indexentry{immersion|hyperpage}{146}
+\indexentry{immersion|hyperpage}{146}
+\indexentry{Submersion|hyperpage}{146}
+\indexentry{submersion|hyperpage}{146}
+\indexentry{submersion|hyperpage}{146}
+\indexentry{Local structure of immersions|hyperpage}{146}
+\indexentry{Local structure of submersions|hyperpage}{146}
+\indexentry{submanifold|hyperpage}{146}
+\indexentry{parametrization|hyperpage}{147}
+\indexentry{coordinate chart|hyperpage}{147}
+\indexentry{regular surface|hyperpage}{147}
+\indexentry{surface|hyperpage}{147}
+\indexentry{surface of revolution|hyperpage}{147}
+\indexentry{generatrix|hyperpage}{147}
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+\indexentry{differentiable|hyperpage}{147}
+\indexentry{tangent vector|hyperpage}{147}
+\indexentry{tangent space|hyperpage}{147}
+\indexentry{tangent plane|hyperpage}{147}
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+\indexentry{differential|hyperpage}{148}
+\indexentry{Inverse function theorem for surfaces|hyperpage}{148}
+\indexentry{first fundamental form|hyperpage}{148}
+\indexentry{orthogonal|hyperpage}{148}
+\indexentry{orthogonal coordinates|hyperpage}{148}
+\indexentry{regular domain|hyperpage}{148}
+\indexentry{domain|hyperpage}{148}
+\indexentry{region|hyperpage}{148}
+\indexentry{integral of $f$ over the region $R$|hyperpage}{148}
+\indexentry{local isometry|hyperpage}{148}
+\indexentry{isometry|hyperpage}{148}
+\indexentry{conformal|hyperpage}{149}
+\indexentry{angle-preserving|hyperpage}{149}
+\indexentry{conformal|hyperpage}{149}
+\indexentry{orientable|hyperpage}{149}
+\indexentry{normal unit field|hyperpage}{149}
+\indexentry{Gau\ss \ map|hyperpage}{149}
+\indexentry{orientation|hyperpage}{149}
+\indexentry{compatible|hyperpage}{149}
+\indexentry{Weingarten endomorphsim|hyperpage}{149}
+\indexentry{principal directons|hyperpage}{149}
+\indexentry{principal curvatures|hyperpage}{149}
+\indexentry{umbilic point|hyperpage}{149}
+\indexentry{Gau\ss \ curvature|hyperpage}{149}
+\indexentry{mean curvature|hyperpage}{149}
+\indexentry{minimal surface|hyperpage}{149}
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+\indexentry{normal curvature|hyperpage}{150}
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+\indexentry{normal curvature|hyperpage}{150}
+\indexentry{asymptotic direction|hyperpage}{150}
+\indexentry{line of curvature|hyperpage}{150}
+\indexentry{asymptotic line|hyperpage}{150}
+\indexentry{Olinde Rodrigues' theorem|hyperpage}{150}
+\indexentry{Euler's formula|hyperpage}{150}
+\indexentry{elliptic point|hyperpage}{150}
+\indexentry{hyperbolic point|hyperpage}{150}
+\indexentry{parabolic point|hyperpage}{150}
+\indexentry{plane point|hyperpage}{150}
+\indexentry{ruled surface|hyperpage}{151}
+\indexentry{developable|hyperpage}{151}
+\indexentry{regression axis|hyperpage}{151}
+\indexentry{Christoffel symbols|hyperpage}{151}
+\indexentry{Gau\ss \ equations|hyperpage}{152}
+\indexentry{Codazzi-Mainardi equations|hyperpage}{152}
+\indexentry{Gau\ss ' Theorema Egregium|hyperpage}{152}
+\indexentry{Bonnet's theorem|hyperpage}{152}
+\indexentry{vector field|hyperpage}{152}
+\indexentry{differentiable|hyperpage}{152}
+\indexentry{differentiable|hyperpage}{152}
+\indexentry{covariant derivative|hyperpage}{152}
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+\indexentry{differentiable|hyperpage}{154}
+\indexentry{integral curve|hyperpage}{154}
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\indexentry{exterior differential|hyperpage}{156}
-\indexentry{differentiable|hyperpage}{156}
-\indexentry{differential|hyperpage}{156}
-\indexentry{submanifold with boundary|hyperpage}{156}
-\indexentry{interior point|hyperpage}{156}
-\indexentry{boundary|hyperpage}{156}
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+\indexentry{exact|hyperpage}{156}
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\indexentry{tangent space|hyperpage}{156}
-\indexentry{set of interior vectors|hyperpage}{156}
-\indexentry{exterior vectors|hyperpage}{156}
-\indexentry{orientable|hyperpage}{157}
-\indexentry{compatible|hyperpage}{157}
-\indexentry{volume element|hyperpage}{157}
-\indexentry{unit normal exterior vector field|hyperpage}{157}
-\indexentry{positive|hyperpage}{157}
-\indexentry{orientation induced by $M$|hyperpage}{157}
-\indexentry{integral|hyperpage}{157}
-\indexentry{integral|hyperpage}{157}
-\indexentry{integral|hyperpage}{157}
-\indexentry{partition of unity|hyperpage}{157}
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+\indexentry{orientation induced by $M$|hyperpage}{158}
+\indexentry{integral|hyperpage}{158}
+\indexentry{integral|hyperpage}{158}
\indexentry{integral|hyperpage}{158}
-\indexentry{Change of variables|hyperpage}{158}
-\indexentry{Stokes theorem|hyperpage}{158}
-\indexentry{Green's formula|hyperpage}{158}
-\indexentry{line intergal|hyperpage}{158}
-\indexentry{circulation|hyperpage}{158}
-\indexentry{surface intergal|hyperpage}{158}
-\indexentry{flux|hyperpage}{158}
-\indexentry{Curl theorem|hyperpage}{158}
-\indexentry{Divergence theorem on $\ensuremath {\mathbb {R}}^3$|hyperpage}{159}
-\indexentry{Divergence theorem|hyperpage}{159}
-\indexentry{simple region|hyperpage}{159}
-\indexentry{edges|hyperpage}{159}
-\indexentry{vertices|hyperpage}{159}
-\indexentry{exterior angle|hyperpage}{159}
-\indexentry{Local Gau\ss -Bonnet theorem|hyperpage}{159}
-\indexentry{triangle|hyperpage}{159}
-\indexentry{regular region|hyperpage}{159}
-\indexentry{Global Gau\ss -Bonnet theorem|hyperpage}{159}
-\indexentry{singular point|hyperpage}{159}
-\indexentry{isolated singular point|hyperpage}{159}
-\indexentry{isolated singularity|hyperpage}{159}
-\indexentry{index|hyperpage}{159}
-\indexentry{Poincaré-Hopf theorem|hyperpage}{160}
-\indexentry{quadratic polynomial|hyperpage}{161}
-\indexentry{cubic polynomial|hyperpage}{161}
-\indexentry{quartic polynomial|hyperpage}{161}
-\indexentry{depressed equation|hyperpage}{161}
-\indexentry{field morphism|hyperpage}{161}
-\indexentry{characteristic|hyperpage}{161}
-\indexentry{polynomial ring|hyperpage}{161}
-\indexentry{Universal property of polynomials in several variables|hyperpage}{161}
-\indexentry{evaluation|hyperpage}{161}
-\indexentry{Universal property of the field of fractions|hyperpage}{162}
-\indexentry{field of fractions|hyperpage}{162}
-\indexentry{field of rational functions|hyperpage}{162}
-\indexentry{subring generated|hyperpage}{162}
-\indexentry{subfield generated|hyperpage}{162}
-\indexentry{Symmetric polynomials|hyperpage}{162}
-\indexentry{symmetric polynomial|hyperpage}{162}
-\indexentry{elementary symmetric polynomials|hyperpage}{162}
-\indexentry{lexicographic order|hyperpage}{162}
-\indexentry{lexicographic degree|hyperpage}{162}
-\indexentry{Waring's method|hyperpage}{163}
-\indexentry{Fundamental theorem of symmetric polynomials|hyperpage}{163}
-\indexentry{$n$-th cyclotomic polynomial|hyperpage}{163}
-\indexentry{field extension|hyperpage}{163}
-\indexentry{degree|hyperpage}{163}
-\indexentry{finite|hyperpage}{163}
-\indexentry{infinite|hyperpage}{163}
-\indexentry{Kronecker's lemma|hyperpage}{163}
-\indexentry{algebraic|hyperpage}{163}
-\indexentry{irreducible polynomial|hyperpage}{163}
-\indexentry{transcendental|hyperpage}{163}
-\indexentry{simple|hyperpage}{163}
-\indexentry{primitive element|hyperpage}{163}
-\indexentry{Steinitz's theorem|hyperpage}{163}
-\indexentry{Tower formula|hyperpage}{164}
-\indexentry{tower of fields|hyperpage}{164}
-\indexentry{finitely generated|hyperpage}{164}
-\indexentry{compositum|hyperpage}{164}
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+\indexentry{integral|hyperpage}{159}
+\indexentry{Change of variables|hyperpage}{159}
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+\indexentry{Green's formula|hyperpage}{159}
+\indexentry{line intergal|hyperpage}{159}
+\indexentry{circulation|hyperpage}{159}
+\indexentry{surface intergal|hyperpage}{159}
+\indexentry{flux|hyperpage}{159}
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+\indexentry{Divergence theorem|hyperpage}{160}
+\indexentry{simple region|hyperpage}{160}
+\indexentry{edges|hyperpage}{160}
+\indexentry{vertices|hyperpage}{160}
+\indexentry{exterior angle|hyperpage}{160}
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+\indexentry{triangle|hyperpage}{160}
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+\indexentry{Global Gau\ss -Bonnet theorem|hyperpage}{160}
+\indexentry{singular point|hyperpage}{160}
+\indexentry{isolated singular point|hyperpage}{160}
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+\indexentry{evaluation|hyperpage}{162}
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+\indexentry{field of fractions|hyperpage}{163}
+\indexentry{field of rational functions|hyperpage}{163}
+\indexentry{subring generated|hyperpage}{163}
+\indexentry{subfield generated|hyperpage}{163}
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+\indexentry{symmetric polynomial|hyperpage}{163}
+\indexentry{elementary symmetric polynomials|hyperpage}{163}
+\indexentry{lexicographic order|hyperpage}{163}
+\indexentry{lexicographic degree|hyperpage}{163}
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+\indexentry{Fundamental theorem of symmetric polynomials|hyperpage}{164}
+\indexentry{$n$-th cyclotomic polynomial|hyperpage}{164}
+\indexentry{field extension|hyperpage}{164}
+\indexentry{degree|hyperpage}{164}
+\indexentry{finite|hyperpage}{164}
+\indexentry{infinite|hyperpage}{164}
+\indexentry{Kronecker's lemma|hyperpage}{164}
\indexentry{algebraic|hyperpage}{164}
-\indexentry{purely transcendental|hyperpage}{164}
-\indexentry{morphism of field extensions|hyperpage}{164}
-\indexentry{$K$-field morphism|hyperpage}{164}
-\indexentry{Galois group|hyperpage}{165}
-\indexentry{Finite field|hyperpage}{165}
-\indexentry{finite field|hyperpage}{165}
-\indexentry{Frobenius endomorphism|hyperpage}{165}
-\indexentry{Perfect fields|hyperpage}{165}
-\indexentry{perfect|hyperpage}{165}
-\indexentry{splits into linear factors|hyperpage}{166}
-\indexentry{Kronecker's theorem|hyperpage}{166}
-\indexentry{Splitting field|hyperpage}{166}
-\indexentry{splitting field|hyperpage}{166}
-\indexentry{Existence of the splitting field|hyperpage}{166}
-\indexentry{Unicity of the splitting field|hyperpage}{166}
-\indexentry{normal|hyperpage}{166}
-\indexentry{normal closure|hyperpage}{166}
-\indexentry{Formal derivative|hyperpage}{166}
-\indexentry{formal derivative|hyperpage}{166}
-\indexentry{separable|hyperpage}{167}
-\indexentry{Separable extension|hyperpage}{167}
-\indexentry{separable|hyperpage}{167}
-\indexentry{separable|hyperpage}{167}
-\indexentry{Separability theorem|hyperpage}{167}
-\indexentry{purely inseparable|hyperpage}{167}
-\indexentry{Primitive element theorem|hyperpage}{167}
-\indexentry{Galois extension|hyperpage}{167}
-\indexentry{Galois|hyperpage}{167}
-\indexentry{fixed field|hyperpage}{167}
-\indexentry{Artin's lemma|hyperpage}{168}
-\indexentry{Fundamental theorem of Galois theory|hyperpage}{168}
-\indexentry{lattice of subgroups|hyperpage}{168}
-\indexentry{transitive|hyperpage}{168}
-\indexentry{discriminant|hyperpage}{168}
-\indexentry{algebraically closed|hyperpage}{169}
-\indexentry{Fundamental theorem of algebra|hyperpage}{169}
-\indexentry{algebraic closure|hyperpage}{169}
-\indexentry{solvable|hyperpage}{169}
-\indexentry{simple|hyperpage}{169}
-\indexentry{radical|hyperpage}{169}
-\indexentry{cyclotomic|hyperpage}{169}
-\indexentry{radical tower|hyperpage}{169}
-\indexentry{solvable by radicals|hyperpage}{169}
-\indexentry{solvable by radicals|hyperpage}{169}
-\indexentry{$n$-th root of unity|hyperpage}{169}
-\indexentry{$n$-th primitive root of unity|hyperpage}{169}
-\indexentry{abelian|hyperpage}{169}
-\indexentry{cyclic|hyperpage}{169}
-\indexentry{Dedekind's lemma|hyperpage}{169}
-\indexentry{$F$-linearly independent|hyperpage}{169}
-\indexentry{Abel-Ruffini theorem|hyperpage}{170}
-\indexentry{Nart-Vila theorem|hyperpage}{170}
-\indexentry{Algebra|hyperpage}{171}
-\indexentry{algebra|hyperpage}{171}
-\indexentry{$\sigma $-algebra|hyperpage}{171}
-\indexentry{$\sigma $-algebra|hyperpage}{171}
-\indexentry{trivial $\sigma $-algebra|hyperpage}{171}
-\indexentry{discrete $\sigma $-algebra|hyperpage}{171}
-\indexentry{$\sigma $-algebra generated|hyperpage}{171}
-\indexentry{$\sigma $-algebra generated|hyperpage}{171}
-\indexentry{Borel $\sigma $-algebra|hyperpage}{171}
-\indexentry{Sample space|hyperpage}{172}
-\indexentry{sample space|hyperpage}{172}
-\indexentry{Kolmogorov axioms|hyperpage}{172}
-\indexentry{probability|hyperpage}{172}
-\indexentry{$\sigma $-additivity|hyperpage}{172}
-\indexentry{event|hyperpage}{172}
-\indexentry{probability space|hyperpage}{172}
-\indexentry{Finite subadditivity|hyperpage}{172}
-\indexentry{Continuity from below|hyperpage}{172}
-\indexentry{Continuity from above|hyperpage}{172}
-\indexentry{Countable subadditivity|hyperpage}{172}
-\indexentry{conditional probability|hyperpage}{173}
-\indexentry{Compound probability formula|hyperpage}{173}
-\indexentry{Generalized compound probability formula|hyperpage}{173}
-\indexentry{partition|hyperpage}{173}
-\indexentry{Law of total probability|hyperpage}{173}
-\indexentry{Bayes' formula|hyperpage}{173}
-\indexentry{independent events|hyperpage}{173}
-\indexentry{independent events|hyperpage}{173}
-\indexentry{independent events|hyperpage}{173}
-\indexentry{null set|hyperpage}{173}
-\indexentry{set of zero-content|hyperpage}{173}
-\indexentry{measure|hyperpage}{173}
-\indexentry{measurable space|hyperpage}{174}
-\indexentry{$\sigma $-algebra of all Lebesgue measurable sets in $\ensuremath {\mathbb {R}}^n$|hyperpage}{174}
-\indexentry{Lebesgue measure|hyperpage}{174}
-\indexentry{volume|hyperpage}{174}
-\indexentry{measurable|hyperpage}{174}
-\indexentry{Lebesgue integral|hyperpage}{174}
-\indexentry{Lebesgue integrable|hyperpage}{174}
-\indexentry{Tonelli's theorem|hyperpage}{174}
-\indexentry{Fubini's theorem|hyperpage}{174}
-\indexentry{real random variable|hyperpage}{174}
-\indexentry{random variable|hyperpage}{174}
-\indexentry{distribution|hyperpage}{175}
-\indexentry{equal in distribution|hyperpage}{175}
-\indexentry{equal almost surely|hyperpage}{175}
-\indexentry{Cumulative distribution function|hyperpage}{175}
-\indexentry{cumulative distribution function|hyperpage}{175}
-\indexentry{cdf|hyperpage}{175}
-\indexentry{càdlàg|hyperpage}{175}
-\indexentry{discrete|hyperpage}{175}
-\indexentry{support|hyperpage}{175}
-\indexentry{Probability mass function|hyperpage}{175}
-\indexentry{probability mass function|hyperpage}{175}
-\indexentry{pmf|hyperpage}{175}
-\indexentry{distribution functions|hyperpage}{175}
-\indexentry{Degenerated distribution|hyperpage}{176}
-\indexentry{degenerated distribution|hyperpage}{176}
-\indexentry{Bernoulli distribution|hyperpage}{176}
-\indexentry{Bernoulli distribution|hyperpage}{176}
-\indexentry{Discrete uniform distribution|hyperpage}{176}
-\indexentry{discrete uniform distribution|hyperpage}{176}
-\indexentry{equiprobable space|hyperpage}{176}
-\indexentry{Binomial distribution|hyperpage}{176}
-\indexentry{binomial distribution|hyperpage}{176}
-\indexentry{Poisson distribution|hyperpage}{176}
-\indexentry{Poisson distribution|hyperpage}{176}
-\indexentry{Geometric distribution|hyperpage}{176}
-\indexentry{geometric distribution|hyperpage}{176}
-\indexentry{Discrete memorylessness property|hyperpage}{176}
-\indexentry{memoryless|hyperpage}{176}
-\indexentry{Hypergeometric distribution|hyperpage}{176}
-\indexentry{hypergeometric distribution|hyperpage}{176}
-\indexentry{success|hyperpage}{176}
-\indexentry{true|hyperpage}{176}
-\indexentry{failure|hyperpage}{176}
-\indexentry{false|hyperpage}{176}
-\indexentry{Negative binomial distribution|hyperpage}{177}
-\indexentry{negative binomial distribution|hyperpage}{177}
-\indexentry{absolutely continuous|hyperpage}{177}
-\indexentry{probability density function|hyperpage}{177}
-\indexentry{pdf|hyperpage}{177}
-\indexentry{density function|hyperpage}{177}
-\indexentry{Continuous uniform distribution|hyperpage}{177}
-\indexentry{continuous uniform distribution|hyperpage}{177}
-\indexentry{Exponential distribution|hyperpage}{177}
-\indexentry{exponential distribution|hyperpage}{177}
-\indexentry{Continuous memorylessness property|hyperpage}{177}
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+\indexentry{transcendental|hyperpage}{164}
+\indexentry{simple|hyperpage}{164}
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+\indexentry{Tower formula|hyperpage}{165}
+\indexentry{tower of fields|hyperpage}{165}
+\indexentry{finitely generated|hyperpage}{165}
+\indexentry{compositum|hyperpage}{165}
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+\indexentry{purely transcendental|hyperpage}{165}
+\indexentry{morphism of field extensions|hyperpage}{165}
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+\indexentry{Finite field|hyperpage}{166}
+\indexentry{finite field|hyperpage}{166}
+\indexentry{Frobenius endomorphism|hyperpage}{166}
+\indexentry{Perfect fields|hyperpage}{166}
+\indexentry{perfect|hyperpage}{166}
+\indexentry{splits into linear factors|hyperpage}{167}
+\indexentry{Kronecker's theorem|hyperpage}{167}
+\indexentry{Splitting field|hyperpage}{167}
+\indexentry{splitting field|hyperpage}{167}
+\indexentry{Existence of the splitting field|hyperpage}{167}
+\indexentry{Unicity of the splitting field|hyperpage}{167}
+\indexentry{normal|hyperpage}{167}
+\indexentry{normal closure|hyperpage}{167}
+\indexentry{Formal derivative|hyperpage}{167}
+\indexentry{formal derivative|hyperpage}{167}
+\indexentry{separable|hyperpage}{168}
+\indexentry{Separable extension|hyperpage}{168}
+\indexentry{separable|hyperpage}{168}
+\indexentry{separable|hyperpage}{168}
+\indexentry{Separability theorem|hyperpage}{168}
+\indexentry{purely inseparable|hyperpage}{168}
+\indexentry{Primitive element theorem|hyperpage}{168}
+\indexentry{Galois extension|hyperpage}{168}
+\indexentry{Galois|hyperpage}{168}
+\indexentry{fixed field|hyperpage}{168}
+\indexentry{Artin's lemma|hyperpage}{169}
+\indexentry{Fundamental theorem of Galois theory|hyperpage}{169}
+\indexentry{lattice of subgroups|hyperpage}{169}
+\indexentry{transitive|hyperpage}{169}
+\indexentry{discriminant|hyperpage}{169}
+\indexentry{algebraically closed|hyperpage}{170}
+\indexentry{Fundamental theorem of algebra|hyperpage}{170}
+\indexentry{algebraic closure|hyperpage}{170}
+\indexentry{solvable|hyperpage}{170}
+\indexentry{simple|hyperpage}{170}
+\indexentry{radical|hyperpage}{170}
+\indexentry{cyclotomic|hyperpage}{170}
+\indexentry{radical tower|hyperpage}{170}
+\indexentry{solvable by radicals|hyperpage}{170}
+\indexentry{solvable by radicals|hyperpage}{170}
+\indexentry{$n$-th root of unity|hyperpage}{170}
+\indexentry{$n$-th primitive root of unity|hyperpage}{170}
+\indexentry{abelian|hyperpage}{170}
+\indexentry{cyclic|hyperpage}{170}
+\indexentry{Dedekind's lemma|hyperpage}{170}
+\indexentry{$F$-linearly independent|hyperpage}{170}
+\indexentry{Abel-Ruffini theorem|hyperpage}{171}
+\indexentry{Nart-Vila theorem|hyperpage}{171}
+\indexentry{Algebra|hyperpage}{172}
+\indexentry{algebra|hyperpage}{172}
+\indexentry{$\sigma $-algebra|hyperpage}{172}
+\indexentry{$\sigma $-algebra|hyperpage}{172}
+\indexentry{trivial $\sigma $-algebra|hyperpage}{172}
+\indexentry{discrete $\sigma $-algebra|hyperpage}{172}
+\indexentry{$\sigma $-algebra generated|hyperpage}{172}
+\indexentry{$\sigma $-algebra generated|hyperpage}{172}
+\indexentry{Borel $\sigma $-algebra|hyperpage}{172}
+\indexentry{Sample space|hyperpage}{173}
+\indexentry{sample space|hyperpage}{173}
+\indexentry{Kolmogorov axioms|hyperpage}{173}
+\indexentry{probability|hyperpage}{173}
+\indexentry{$\sigma $-additivity|hyperpage}{173}
+\indexentry{event|hyperpage}{173}
+\indexentry{probability space|hyperpage}{173}
+\indexentry{Finite subadditivity|hyperpage}{173}
+\indexentry{Continuity from below|hyperpage}{173}
+\indexentry{Continuity from above|hyperpage}{173}
+\indexentry{Countable subadditivity|hyperpage}{173}
+\indexentry{conditional probability|hyperpage}{174}
+\indexentry{Compound probability formula|hyperpage}{174}
+\indexentry{Generalized compound probability formula|hyperpage}{174}
+\indexentry{partition|hyperpage}{174}
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+\indexentry{Bayes' formula|hyperpage}{174}
+\indexentry{independent events|hyperpage}{174}
+\indexentry{independent events|hyperpage}{174}
+\indexentry{independent events|hyperpage}{174}
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+\indexentry{set of zero-content|hyperpage}{174}
+\indexentry{measure|hyperpage}{174}
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+\indexentry{$\sigma $-algebra of all Lebesgue measurable sets in $\ensuremath {\mathbb {R}}^n$|hyperpage}{175}
+\indexentry{Lebesgue measure|hyperpage}{175}
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+\indexentry{Lebesgue integral|hyperpage}{175}
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+\indexentry{cdf|hyperpage}{176}
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+\indexentry{probability mass function|hyperpage}{176}
+\indexentry{pmf|hyperpage}{176}
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+\indexentry{Degenerated distribution|hyperpage}{177}
+\indexentry{degenerated distribution|hyperpage}{177}
+\indexentry{Bernoulli distribution|hyperpage}{177}
+\indexentry{Bernoulli distribution|hyperpage}{177}
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+\indexentry{discrete uniform distribution|hyperpage}{177}
+\indexentry{equiprobable space|hyperpage}{177}
+\indexentry{Binomial distribution|hyperpage}{177}
+\indexentry{binomial distribution|hyperpage}{177}
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+\indexentry{Geometric distribution|hyperpage}{177}
+\indexentry{geometric distribution|hyperpage}{177}
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\indexentry{memoryless|hyperpage}{177}
-\indexentry{Standard normal distribution|hyperpage}{177}
-\indexentry{standard normal distribution|hyperpage}{177}
-\indexentry{Normal distribution|hyperpage}{177}
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-\indexentry{mean|hyperpage}{177}
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-\indexentry{rate|hyperpage}{178}
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-\indexentry{discrete|hyperpage}{179}
-\indexentry{support|hyperpage}{179}
-\indexentry{Joint probability mass function|hyperpage}{179}
-\indexentry{joint probability mass function|hyperpage}{179}
-\indexentry{joint pmf|hyperpage}{179}
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-\indexentry{marginal probability mass functions|hyperpage}{179}
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-\indexentry{joint pdf|hyperpage}{179}
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-\indexentry{marginal probability density functions|hyperpage}{179}
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-\indexentry{multivariate normal distribution|hyperpage}{179}
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-\indexentry{independent and identically distributed|hyperpage}{180}
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-\indexentry{integrable|hyperpage}{181}
-\indexentry{expectation|hyperpage}{181}
-\indexentry{not integrable|hyperpage}{181}
-\indexentry{Expectation|hyperpage}{182}
+\indexentry{Hypergeometric distribution|hyperpage}{177}
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+\indexentry{Negative binomial distribution|hyperpage}{178}
+\indexentry{negative binomial distribution|hyperpage}{178}
+\indexentry{absolutely continuous|hyperpage}{178}
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+\indexentry{continuous uniform distribution|hyperpage}{178}
+\indexentry{Exponential distribution|hyperpage}{178}
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+\indexentry{memoryless|hyperpage}{178}
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+\indexentry{Normal distribution|hyperpage}{178}
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-\indexentry{Dominated convergence theorem|hyperpage}{183}
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\indexentry{expectation|hyperpage}{183}
-\indexentry{Moment|hyperpage}{184}
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-\indexentry{Cauchy-Schwarz inequality|hyperpage}{184}
-\indexentry{Variance|hyperpage}{184}
-\indexentry{variance|hyperpage}{184}
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-\indexentry{standard error|hyperpage}{184}
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-\indexentry{Pearson correlation coefficient|hyperpage}{184}
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-\indexentry{conditional expectation|hyperpage}{185}
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+\indexentry{standard error|hyperpage}{185}
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+\indexentry{Pearson correlation coefficient|hyperpage}{185}
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-\indexentry{Cauchy in $p$-th mean|hyperpage}{188}
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-\indexentry{Skorokhod's representation theorem|hyperpage}{189}
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-\indexentry{Weak law|hyperpage}{189}
-\indexentry{Weak law|hyperpage}{189}
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-\indexentry{Strong law|hyperpage}{189}
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-\indexentry{normal|hyperpage}{189}
-\indexentry{Borel's theorem|hyperpage}{189}
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-\indexentry{realization|hyperpage}{192}
-\indexentry{identifiable|hyperpage}{192}
-\indexentry{parametric|hyperpage}{192}
-\indexentry{Statistic|hyperpage}{192}
-\indexentry{statistic|hyperpage}{192}
-\indexentry{dimension|hyperpage}{192}
+\indexentry{conditional expectation|hyperpage}{186}
+\indexentry{Law of total expectation|hyperpage}{187}
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+\indexentry{Second Borel-Cantelli lemma|hyperpage}{189}
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+\indexentry{Cauchy in $p$-th mean|hyperpage}{189}
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+\indexentry{Strong law|hyperpage}{191}
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\indexentry{sample mean|hyperpage}{192}
-\indexentry{sample variance|hyperpage}{192}
-\indexentry{corrected sample variance|hyperpage}{192}
-\indexentry{estimator|hyperpage}{192}
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-\indexentry{biased estimator|hyperpage}{192}
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-\indexentry{MVUE|hyperpage}{193}
-\indexentry{sufficient|hyperpage}{193}
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-\indexentry{Likelihood|hyperpage}{194}
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-\indexentry{likelihood function|hyperpage}{194}
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-\indexentry{MLE|hyperpage}{194}
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-\indexentry{regular|hyperpage}{194}
-\indexentry{observed information|hyperpage}{194}
-\indexentry{Fisher information|hyperpage}{194}
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+\indexentry{sample space|hyperpage}{193}
+\indexentry{parameter space|hyperpage}{193}
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+\indexentry{simple random sample|hyperpage}{193}
+\indexentry{realization|hyperpage}{193}
+\indexentry{identifiable|hyperpage}{193}
+\indexentry{parametric|hyperpage}{193}
+\indexentry{Statistic|hyperpage}{193}
+\indexentry{statistic|hyperpage}{193}
+\indexentry{dimension|hyperpage}{193}
+\indexentry{sample mean|hyperpage}{193}
+\indexentry{sample variance|hyperpage}{193}
+\indexentry{corrected sample variance|hyperpage}{193}
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+\indexentry{Bias|hyperpage}{193}
+\indexentry{bias|hyperpage}{193}
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+\indexentry{biased estimator|hyperpage}{193}
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+\indexentry{asymptotically unbiased estimator|hyperpage}{194}
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+\indexentry{Method of moments|hyperpage}{194}
+\indexentry{Likelihood|hyperpage}{195}
+\indexentry{likelihood function|hyperpage}{195}
+\indexentry{likelihood function|hyperpage}{195}
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+\indexentry{MLE|hyperpage}{195}
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\indexentry{regular|hyperpage}{195}
-\indexentry{Cramér-Rao bound|hyperpage}{195}
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-\indexentry{Quantile|hyperpage}{195}
-\indexentry{multivariate normal distribution|hyperpage}{195}
-\indexentry{mean vector|hyperpage}{195}
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-\indexentry{Intervals for $\mu $ and $\sigma ^2$|hyperpage}{197}
-\indexentry{Independent samples with known variances|hyperpage}{197}
-\indexentry{Independent samples with unknown equal variances|hyperpage}{197}
-\indexentry{Independent samples with unknown variances|hyperpage}{197}
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-\indexentry{hypothesis|hyperpage}{198}
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-\indexentry{simple|hyperpage}{198}
-\indexentry{Hypothesis test|hyperpage}{198}
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-\indexentry{error of type II|hyperpage}{198}
-\indexentry{power|hyperpage}{198}
-\indexentry{size|hyperpage}{198}
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+\indexentry{Quantile|hyperpage}{196}
+\indexentry{multivariate normal distribution|hyperpage}{196}
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+\indexentry{confidence intervals|hyperpage}{198}
\indexentry{significance level|hyperpage}{198}
-\indexentry{power function|hyperpage}{198}
-\indexentry{test statistic|hyperpage}{198}
-\indexentry{$p$-value|hyperpage}{198}
-\indexentry{one-sided right tail test|hyperpage}{198}
-\indexentry{one-sided left tail test|hyperpage}{198}
-\indexentry{two-sided test|hyperpage}{199}
-\indexentry{uniformly most powerful|hyperpage}{199}
-\indexentry{UMP|hyperpage}{199}
-\indexentry{test|hyperpage}{199}
-\indexentry{Neymann-Pearson test|hyperpage}{199}
-\indexentry{Neyman-Pearson test|hyperpage}{199}
-\indexentry{Neyman-Pearson lemma|hyperpage}{199}
-\indexentry{Likelihood-ratio test|hyperpage}{199}
-\indexentry{likelihood ratio test|hyperpage}{199}
-\indexentry{LRT|hyperpage}{199}
-\indexentry{Asymptotic behaviour of the LRT|hyperpage}{199}
-\indexentry{LRT test statistic|hyperpage}{199}
-\indexentry{Goodness of fit|hyperpage}{199}
-\indexentry{Test of homogenity|hyperpage}{200}
-\indexentry{Test of independence|hyperpage}{200}
-\indexentry{$t$-test|hyperpage}{200}
-\indexentry{$t$-test|hyperpage}{200}
-\indexentry{Wald test|hyperpage}{200}
-\indexentry{Wald test|hyperpage}{200}
-\indexentry{contrast matrix|hyperpage}{200}
-\indexentry{Score test|hyperpage}{201}
-\indexentry{score test|hyperpage}{201}
-\indexentry{Non-parametric bootstrap|hyperpage}{201}
-\indexentry{empirical distribution|hyperpage}{201}
-\indexentry{bootstrap distribution|hyperpage}{201}
-\indexentry{Parametric bootstrap|hyperpage}{201}
-\indexentry{parametric bootstrap distribution|hyperpage}{201}
-\indexentry{Normal confidence interval|hyperpage}{201}
-\indexentry{normal confidence interval|hyperpage}{201}
-\indexentry{Basic bootstrap confidence interval|hyperpage}{201}
-\indexentry{basic bootstrap confidence interval|hyperpage}{201}
-\indexentry{Bootstrap-t confidence interval|hyperpage}{201}
-\indexentry{bootstrap-t confidence interval|hyperpage}{201}
-\indexentry{Percentile confidence interval|hyperpage}{201}
-\indexentry{percentile confidence interval|hyperpage}{201}
-\indexentry{prior distribution|hyperpage}{201}
-\indexentry{prior|hyperpage}{201}
-\indexentry{posterior distribution|hyperpage}{201}
-\indexentry{posterior|hyperpage}{201}
-\indexentry{conjugate|hyperpage}{201}
-\indexentry{Bayesian point estimates|hyperpage}{202}
-\indexentry{posterior mean|hyperpage}{202}
-\indexentry{posterior mode|hyperpage}{202}
-\indexentry{posterior median|hyperpage}{202}
-\indexentry{flat|hyperpage}{202}
-\indexentry{improper|hyperpage}{202}
-\indexentry{Jeffrey's prior|hyperpage}{202}
-\indexentry{Jeffrey's prior|hyperpage}{202}
-\indexentry{loss function|hyperpage}{202}
-\indexentry{Quadratic loss function|hyperpage}{202}
-\indexentry{Linear loss function|hyperpage}{202}
-\indexentry{Zero-one loss function|hyperpage}{202}
-\indexentry{Bayes estimate|hyperpage}{202}
-\indexentry{credible region|hyperpage}{202}
-\indexentry{credible interval|hyperpage}{202}
-\indexentry{highest posterior density|hyperpage}{203}
-\indexentry{region|hyperpage}{203}
-\indexentry{Q-Q plots|hyperpage}{203}
-\indexentry{Quantile-Quantile plot|hyperpage}{203}
-\indexentry{Q-Q plots|hyperpage}{203}
-\indexentry{theoretical quantiles|hyperpage}{203}
-\indexentry{sample quantiles|hyperpage}{203}
-\indexentry{Normal Q-Q plots|hyperpage}{203}
-\indexentry{distance|hyperpage}{204}
-\indexentry{metric|hyperpage}{204}
-\indexentry{triangular inequality|hyperpage}{204}
-\indexentry{metric space|hyperpage}{204}
-\indexentry{Euclidean metric|hyperpage}{204}
-\indexentry{Taxicab metric|hyperpage}{204}
-\indexentry{Maximum metric|hyperpage}{204}
-\indexentry{discrete metric|hyperpage}{204}
-\indexentry{ball|hyperpage}{204}
-\indexentry{open|hyperpage}{204}
-\indexentry{Topological space|hyperpage}{204}
-\indexentry{topology|hyperpage}{204}
-\indexentry{topological space|hyperpage}{204}
-\indexentry{points|hyperpage}{204}
-\indexentry{open sets|hyperpage}{204}
-\indexentry{finer|hyperpage}{204}
-\indexentry{Topology induced from the metric|hyperpage}{204}
-\indexentry{Trivial topology|hyperpage}{205}
-\indexentry{Discrete topology|hyperpage}{205}
-\indexentry{Cofinite topology|hyperpage}{205}
-\indexentry{Cocountable topology|hyperpage}{205}
-\indexentry{Particular point topology|hyperpage}{205}
-\indexentry{Excluded point topology|hyperpage}{205}
-\indexentry{Sierpiński topology|hyperpage}{205}
-\indexentry{closed|hyperpage}{205}
-\indexentry{clopen|hyperpage}{205}
-\indexentry{basis|hyperpage}{205}
-\indexentry{topology generated|hyperpage}{205}
-\indexentry{lower limit topology|hyperpage}{205}
-\indexentry{digital topology|hyperpage}{205}
-\indexentry{subbasis|hyperpage}{205}
-\indexentry{Interior|hyperpage}{205}
-\indexentry{interior|hyperpage}{205}
-\indexentry{Closure|hyperpage}{205}
-\indexentry{closure|hyperpage}{205}
-\indexentry{dense|hyperpage}{206}
-\indexentry{Boundary|hyperpage}{206}
-\indexentry{boundary|hyperpage}{206}
-\indexentry{neighbourhood|hyperpage}{206}
-\indexentry{interior point|hyperpage}{206}
-\indexentry{adherent point|hyperpage}{206}
-\indexentry{Kuratowski's problem|hyperpage}{206}
-\indexentry{separated|hyperpage}{206}
-\indexentry{separated by closed neighbourhoods|hyperpage}{206}
-\indexentry{Continuous function|hyperpage}{207}
-\indexentry{homeomorphism|hyperpage}{207}
-\indexentry{homeomorphic|hyperpage}{207}
-\indexentry{Open function|hyperpage}{207}
-\indexentry{open|hyperpage}{207}
-\indexentry{Closed function|hyperpage}{207}
-\indexentry{closed|hyperpage}{207}
-\indexentry{topological subspace|hyperpage}{207}
-\indexentry{subspace topology|hyperpage}{207}
-\indexentry{Cantor set|hyperpage}{208}
-\indexentry{product topology|hyperpage}{208}
-\indexentry{box topology|hyperpage}{208}
-\indexentry{infinite product topology|hyperpage}{208}
-\indexentry{$n-1$-th sphere|hyperpage}{209}
-\indexentry{$n$-th ball|hyperpage}{209}
-\indexentry{Torus|hyperpage}{209}
-\indexentry{torus|hyperpage}{209}
-\indexentry{quotient topology|hyperpage}{209}
-\indexentry{quotient map|hyperpage}{209}
-\indexentry{quotient space|hyperpage}{209}
-\indexentry{quotient space of collapsing a set to a point|hyperpage}{210}
-\indexentry{action|hyperpage}{210}
-\indexentry{$(G,\cdot )$-space|hyperpage}{210}
-\indexentry{Möbius band|hyperpage}{210}
-\indexentry{Klein bottle|hyperpage}{210}
-\indexentry{$T_0$ space|hyperpage}{211}
-\indexentry{Kolmogorov|hyperpage}{211}
-\indexentry{$T_1$ space|hyperpage}{211}
-\indexentry{Fréchet|hyperpage}{211}
-\indexentry{$T_2$ space|hyperpage}{211}
-\indexentry{Hausdorff|hyperpage}{211}
-\indexentry{$T_{2\frac {1}{2}}$ space|hyperpage}{211}
-\indexentry{regular|hyperpage}{211}
-\indexentry{$T_3$ space|hyperpage}{211}
-\indexentry{normal|hyperpage}{211}
-\indexentry{$T_4$ space|hyperpage}{211}
-\indexentry{Urysohn's lemma|hyperpage}{211}
-\indexentry{Tietze extension theorem|hyperpage}{211}
-\indexentry{metrizable|hyperpage}{211}
-\indexentry{Urysohn's metrization theorem|hyperpage}{211}
-\indexentry{topological property|hyperpage}{212}
-\indexentry{Cover|hyperpage}{212}
-\indexentry{cover|hyperpage}{212}
-\indexentry{finite|hyperpage}{212}
-\indexentry{countable|hyperpage}{212}
-\indexentry{open cover|hyperpage}{212}
-\indexentry{cover|hyperpage}{212}
-\indexentry{subcover|hyperpage}{212}
-\indexentry{Compact space|hyperpage}{212}
-\indexentry{compact|hyperpage}{212}
-\indexentry{compactness|hyperpage}{212}
-\indexentry{compact subset|hyperpage}{212}
-\indexentry{Tychonoff's theorem|hyperpage}{212}
-\indexentry{Axiom of choice|hyperpage}{212}
-\indexentry{Kelley's theorem|hyperpage}{212}
-\indexentry{topological embedding|hyperpage}{213}
-\indexentry{One-point compactification|hyperpage}{213}
-\indexentry{one-point compactification|hyperpage}{213}
-\indexentry{locally|hyperpage}{213}
-\indexentry{locally compact|hyperpage}{213}
-\indexentry{Heine-Borel theorem|hyperpage}{213}
-\indexentry{Heine-Borel theorem|hyperpage}{213}
-\indexentry{Weierstra\ss ' theorem|hyperpage}{213}
-\indexentry{Connected space|hyperpage}{213}
-\indexentry{connected|hyperpage}{213}
-\indexentry{disconnected|hyperpage}{213}
-\indexentry{connected subset|hyperpage}{213}
-\indexentry{totally disconnected|hyperpage}{214}
-\indexentry{Intermediate value theorem|hyperpage}{214}
-\indexentry{Bolzano's theorem|hyperpage}{214}
-\indexentry{Brouwer's fixed-point theorem|hyperpage}{214}
-\indexentry{Borsuk-Ulam theorem|hyperpage}{214}
-\indexentry{connected components|hyperpage}{214}
-\indexentry{locally connected|hyperpage}{214}
-\indexentry{path|hyperpage}{214}
-\indexentry{initial point|hyperpage}{214}
-\indexentry{terminal point|hyperpage}{214}
-\indexentry{path from $x$ to $y$|hyperpage}{214}
-\indexentry{loop|hyperpage}{214}
-\indexentry{path-connected|hyperpage}{214}
+\indexentry{pivot|hyperpage}{198}
+\indexentry{Interval for $\mu $ with $\sigma $ known|hyperpage}{198}
+\indexentry{Intervals for $\mu $ and $\sigma ^2$|hyperpage}{198}
+\indexentry{Independent samples with known variances|hyperpage}{198}
+\indexentry{Independent samples with unknown equal variances|hyperpage}{198}
+\indexentry{Independent samples with unknown variances|hyperpage}{198}
+\indexentry{Related samples with unknown variances|hyperpage}{199}
+\indexentry{hypothesis|hyperpage}{199}
+\indexentry{null hypothesis|hyperpage}{199}
+\indexentry{alternative hypothesis|hyperpage}{199}
+\indexentry{simple|hyperpage}{199}
+\indexentry{Hypothesis test|hyperpage}{199}
+\indexentry{hypothesis test|hyperpage}{199}
+\indexentry{acceptation region|hyperpage}{199}
+\indexentry{critical region|hyperpage}{199}
+\indexentry{error of type I|hyperpage}{199}
+\indexentry{error of type II|hyperpage}{199}
+\indexentry{power|hyperpage}{199}
+\indexentry{size|hyperpage}{199}
+\indexentry{significance level|hyperpage}{199}
+\indexentry{power function|hyperpage}{199}
+\indexentry{test statistic|hyperpage}{199}
+\indexentry{$p$-value|hyperpage}{199}
+\indexentry{one-sided right tail test|hyperpage}{199}
+\indexentry{one-sided left tail test|hyperpage}{199}
+\indexentry{two-sided test|hyperpage}{200}
+\indexentry{uniformly most powerful|hyperpage}{200}
+\indexentry{UMP|hyperpage}{200}
+\indexentry{test|hyperpage}{200}
+\indexentry{Neymann-Pearson test|hyperpage}{200}
+\indexentry{Neyman-Pearson test|hyperpage}{200}
+\indexentry{Neyman-Pearson lemma|hyperpage}{200}
+\indexentry{Likelihood-ratio test|hyperpage}{200}
+\indexentry{likelihood ratio test|hyperpage}{200}
+\indexentry{LRT|hyperpage}{200}
+\indexentry{Asymptotic behaviour of the LRT|hyperpage}{200}
+\indexentry{LRT test statistic|hyperpage}{200}
+\indexentry{Goodness of fit|hyperpage}{200}
+\indexentry{Test of homogenity|hyperpage}{201}
+\indexentry{Test of independence|hyperpage}{201}
+\indexentry{$t$-test|hyperpage}{201}
+\indexentry{$t$-test|hyperpage}{201}
+\indexentry{Wald test|hyperpage}{201}
+\indexentry{Wald test|hyperpage}{201}
+\indexentry{contrast matrix|hyperpage}{201}
+\indexentry{Score test|hyperpage}{202}
+\indexentry{score test|hyperpage}{202}
+\indexentry{Non-parametric bootstrap|hyperpage}{202}
+\indexentry{empirical distribution|hyperpage}{202}
+\indexentry{bootstrap distribution|hyperpage}{202}
+\indexentry{Parametric bootstrap|hyperpage}{202}
+\indexentry{parametric bootstrap distribution|hyperpage}{202}
+\indexentry{Normal confidence interval|hyperpage}{202}
+\indexentry{normal confidence interval|hyperpage}{202}
+\indexentry{Basic bootstrap confidence interval|hyperpage}{202}
+\indexentry{basic bootstrap confidence interval|hyperpage}{202}
+\indexentry{Bootstrap-t confidence interval|hyperpage}{202}
+\indexentry{bootstrap-t confidence interval|hyperpage}{202}
+\indexentry{Percentile confidence interval|hyperpage}{202}
+\indexentry{percentile confidence interval|hyperpage}{202}
+\indexentry{prior distribution|hyperpage}{202}
+\indexentry{prior|hyperpage}{202}
+\indexentry{posterior distribution|hyperpage}{202}
+\indexentry{posterior|hyperpage}{202}
+\indexentry{conjugate|hyperpage}{202}
+\indexentry{Bayesian point estimates|hyperpage}{203}
+\indexentry{posterior mean|hyperpage}{203}
+\indexentry{posterior mode|hyperpage}{203}
+\indexentry{posterior median|hyperpage}{203}
+\indexentry{flat|hyperpage}{203}
+\indexentry{improper|hyperpage}{203}
+\indexentry{Jeffrey's prior|hyperpage}{203}
+\indexentry{Jeffrey's prior|hyperpage}{203}
+\indexentry{loss function|hyperpage}{203}
+\indexentry{Quadratic loss function|hyperpage}{203}
+\indexentry{Linear loss function|hyperpage}{203}
+\indexentry{Zero-one loss function|hyperpage}{203}
+\indexentry{Bayes estimate|hyperpage}{203}
+\indexentry{credible region|hyperpage}{203}
+\indexentry{credible interval|hyperpage}{203}
+\indexentry{highest posterior density|hyperpage}{204}
+\indexentry{region|hyperpage}{204}
+\indexentry{Q-Q plots|hyperpage}{204}
+\indexentry{Quantile-Quantile plot|hyperpage}{204}
+\indexentry{Q-Q plots|hyperpage}{204}
+\indexentry{theoretical quantiles|hyperpage}{204}
+\indexentry{sample quantiles|hyperpage}{204}
+\indexentry{Normal Q-Q plots|hyperpage}{204}
+\indexentry{distance|hyperpage}{205}
+\indexentry{metric|hyperpage}{205}
+\indexentry{triangular inequality|hyperpage}{205}
+\indexentry{metric space|hyperpage}{205}
+\indexentry{Euclidean metric|hyperpage}{205}
+\indexentry{Taxicab metric|hyperpage}{205}
+\indexentry{Maximum metric|hyperpage}{205}
+\indexentry{discrete metric|hyperpage}{205}
+\indexentry{ball|hyperpage}{205}
+\indexentry{open|hyperpage}{205}
+\indexentry{Topological space|hyperpage}{205}
+\indexentry{topology|hyperpage}{205}
+\indexentry{topological space|hyperpage}{205}
+\indexentry{points|hyperpage}{205}
+\indexentry{open sets|hyperpage}{205}
+\indexentry{finer|hyperpage}{205}
+\indexentry{Topology induced from the metric|hyperpage}{205}
+\indexentry{Trivial topology|hyperpage}{206}
+\indexentry{Discrete topology|hyperpage}{206}
+\indexentry{Cofinite topology|hyperpage}{206}
+\indexentry{Cocountable topology|hyperpage}{206}
+\indexentry{Particular point topology|hyperpage}{206}
+\indexentry{Excluded point topology|hyperpage}{206}
+\indexentry{Sierpiński topology|hyperpage}{206}
+\indexentry{closed|hyperpage}{206}
+\indexentry{clopen|hyperpage}{206}
+\indexentry{basis|hyperpage}{206}
+\indexentry{topology generated|hyperpage}{206}
+\indexentry{lower limit topology|hyperpage}{206}
+\indexentry{digital topology|hyperpage}{206}
+\indexentry{subbasis|hyperpage}{206}
+\indexentry{Interior|hyperpage}{206}
+\indexentry{interior|hyperpage}{206}
+\indexentry{Closure|hyperpage}{206}
+\indexentry{closure|hyperpage}{206}
+\indexentry{dense|hyperpage}{207}
+\indexentry{Boundary|hyperpage}{207}
+\indexentry{boundary|hyperpage}{207}
+\indexentry{neighbourhood|hyperpage}{207}
+\indexentry{interior point|hyperpage}{207}
+\indexentry{adherent point|hyperpage}{207}
+\indexentry{Kuratowski's problem|hyperpage}{207}
+\indexentry{separated|hyperpage}{207}
+\indexentry{separated by closed neighbourhoods|hyperpage}{207}
+\indexentry{Continuous function|hyperpage}{208}
+\indexentry{homeomorphism|hyperpage}{208}
+\indexentry{homeomorphic|hyperpage}{208}
+\indexentry{Open function|hyperpage}{208}
+\indexentry{open|hyperpage}{208}
+\indexentry{Closed function|hyperpage}{208}
+\indexentry{closed|hyperpage}{208}
+\indexentry{topological subspace|hyperpage}{208}
+\indexentry{subspace topology|hyperpage}{208}
+\indexentry{Cantor set|hyperpage}{209}
+\indexentry{product topology|hyperpage}{209}
+\indexentry{box topology|hyperpage}{209}
+\indexentry{infinite product topology|hyperpage}{209}
+\indexentry{$n-1$-th sphere|hyperpage}{210}
+\indexentry{$n$-th ball|hyperpage}{210}
+\indexentry{Torus|hyperpage}{210}
+\indexentry{torus|hyperpage}{210}
+\indexentry{quotient topology|hyperpage}{210}
+\indexentry{quotient map|hyperpage}{210}
+\indexentry{quotient space|hyperpage}{210}
+\indexentry{quotient space of collapsing a set to a point|hyperpage}{211}
+\indexentry{action|hyperpage}{211}
+\indexentry{$(G,\cdot )$-space|hyperpage}{211}
+\indexentry{Möbius band|hyperpage}{211}
+\indexentry{Klein bottle|hyperpage}{211}
+\indexentry{$T_0$ space|hyperpage}{212}
+\indexentry{Kolmogorov|hyperpage}{212}
+\indexentry{$T_1$ space|hyperpage}{212}
+\indexentry{Fréchet|hyperpage}{212}
+\indexentry{$T_2$ space|hyperpage}{212}
+\indexentry{Hausdorff|hyperpage}{212}
+\indexentry{$T_{2\frac {1}{2}}$ space|hyperpage}{212}
+\indexentry{regular|hyperpage}{212}
+\indexentry{$T_3$ space|hyperpage}{212}
+\indexentry{normal|hyperpage}{212}
+\indexentry{$T_4$ space|hyperpage}{212}
+\indexentry{Urysohn's lemma|hyperpage}{212}
+\indexentry{Tietze extension theorem|hyperpage}{212}
+\indexentry{metrizable|hyperpage}{212}
+\indexentry{Urysohn's metrization theorem|hyperpage}{212}
+\indexentry{topological property|hyperpage}{213}
+\indexentry{Cover|hyperpage}{213}
+\indexentry{cover|hyperpage}{213}
+\indexentry{finite|hyperpage}{213}
+\indexentry{countable|hyperpage}{213}
+\indexentry{open cover|hyperpage}{213}
+\indexentry{cover|hyperpage}{213}
+\indexentry{subcover|hyperpage}{213}
+\indexentry{Compact space|hyperpage}{213}
+\indexentry{compact|hyperpage}{213}
+\indexentry{compactness|hyperpage}{213}
+\indexentry{compact subset|hyperpage}{213}
+\indexentry{Tychonoff's theorem|hyperpage}{213}
+\indexentry{Axiom of choice|hyperpage}{213}
+\indexentry{Kelley's theorem|hyperpage}{213}
+\indexentry{topological embedding|hyperpage}{214}
+\indexentry{One-point compactification|hyperpage}{214}
+\indexentry{one-point compactification|hyperpage}{214}
+\indexentry{locally|hyperpage}{214}
+\indexentry{locally compact|hyperpage}{214}
+\indexentry{Heine-Borel theorem|hyperpage}{214}
+\indexentry{Heine-Borel theorem|hyperpage}{214}
+\indexentry{Weierstra\ss ' theorem|hyperpage}{214}
+\indexentry{Connected space|hyperpage}{214}
+\indexentry{connected|hyperpage}{214}
+\indexentry{disconnected|hyperpage}{214}
+\indexentry{connected subset|hyperpage}{214}
+\indexentry{totally disconnected|hyperpage}{215}
+\indexentry{Intermediate value theorem|hyperpage}{215}
+\indexentry{Bolzano's theorem|hyperpage}{215}
+\indexentry{Brouwer's fixed-point theorem|hyperpage}{215}
+\indexentry{Borsuk-Ulam theorem|hyperpage}{215}
+\indexentry{connected components|hyperpage}{215}
+\indexentry{locally connected|hyperpage}{215}
+\indexentry{path|hyperpage}{215}
+\indexentry{initial point|hyperpage}{215}
+\indexentry{terminal point|hyperpage}{215}
+\indexentry{path from $x$ to $y$|hyperpage}{215}
+\indexentry{loop|hyperpage}{215}
\indexentry{path-connected|hyperpage}{215}
-\indexentry{path-connected components|hyperpage}{215}
-\indexentry{locally path-connected|hyperpage}{215}
-\indexentry{simply connected|hyperpage}{215}
-\indexentry{Topological manifold|hyperpage}{215}
-\indexentry{topological manifold|hyperpage}{215}
-\indexentry{coordinate chart|hyperpage}{215}
-\indexentry{atlas|hyperpage}{215}
-\indexentry{transition functions|hyperpage}{215}
-\indexentry{piecewise linear manifold|hyperpage}{215}
-\indexentry{differentiable manifold|hyperpage}{215}
-\indexentry{holes|hyperpage}{215}
-\indexentry{Connected sum|hyperpage}{216}
-\indexentry{connected sum|hyperpage}{216}
-\indexentry{same orientation|hyperpage}{216}
-\indexentry{opposite orientations|hyperpage}{216}
-\indexentry{orientation|hyperpage}{216}
-\indexentry{oriented vector space|hyperpage}{216}
-\indexentry{unoriented vector space|hyperpage}{216}
-\indexentry{orientation-preserving|hyperpage}{216}
-\indexentry{not orientation-preserving|hyperpage}{216}
-\indexentry{orientation-preserving|hyperpage}{216}
-\indexentry{not orientation-preserving|hyperpage}{216}
-\indexentry{orientable|hyperpage}{216}
-\indexentry{Classification of connected 1-manifolds|hyperpage}{216}
-\indexentry{surface|hyperpage}{216}
-\indexentry{Connected sum of surfaces|hyperpage}{216}
-\indexentry{genus $g$ orientable surface|hyperpage}{216}
-\indexentry{genus $h$ non-orientable surface|hyperpage}{216}
-\indexentry{standard $n$-simplex|hyperpage}{217}
-\indexentry{triangularization|hyperpage}{217}
-\indexentry{simple curve|hyperpage}{217}
-\indexentry{Jordan curve theorem|hyperpage}{217}
-\indexentry{Radó theorem|hyperpage}{217}
-\indexentry{fundamental polygon of the surface|hyperpage}{217}
-\indexentry{normalized|hyperpage}{217}
-\indexentry{Euler characteristic|hyperpage}{217}
-\indexentry{Classification of compact connected surfaces|hyperpage}{218}
-\indexentry{equilibrium point|hyperpage}{220}
-\indexentry{fixed point|hyperpage}{220}
-\indexentry{periodic orbit of period $T$|hyperpage}{220}
-\indexentry{symmetric with respect to the $x$-axis|hyperpage}{220}
-\indexentry{symmetric with respect to the $y$-axis|hyperpage}{220}
-\indexentry{holomorphic differential equation|hyperpage}{220}
-\indexentry{linearization|hyperpage}{220}
-\indexentry{minimal|hyperpage}{220}
-\indexentry{Kolmogorov system|hyperpage}{220}
-\indexentry{homogeneous of degree $k$|hyperpage}{220}
-\indexentry{homogeneous of degree $k$|hyperpage}{220}
-\indexentry{discrete map of order $m$|hyperpage}{221}
-\indexentry{Characteristic equation|hyperpage}{221}
-\indexentry{linear discrete map|hyperpage}{221}
-\indexentry{Hartman-Grobman theorem|hyperpage}{221}
-\indexentry{The stable manifold theorem|hyperpage}{221}
-\indexentry{stable manifold|hyperpage}{221}
-\indexentry{unstable manifold|hyperpage}{221}
-\indexentry{global stable manifold|hyperpage}{221}
-\indexentry{global unstable manifold|hyperpage}{221}
-\indexentry{The center manifold theorem|hyperpage}{222}
-\indexentry{central manifolds|hyperpage}{222}
-\indexentry{local bifurcation|hyperpage}{222}
-\indexentry{normal form|hyperpage}{222}
-\indexentry{codimension|hyperpage}{222}
-\indexentry{Saddle-node bifurcation|hyperpage}{222}
-\indexentry{saddle-node bifurcation|hyperpage}{222}
-\indexentry{Transcritical bifurcation|hyperpage}{222}
-\indexentry{transcritical bifurcation|hyperpage}{222}
-\indexentry{Pitchfork bifurcation|hyperpage}{222}
-\indexentry{pitchfork bifurcation|hyperpage}{222}
-\indexentry{Lyapunov's theorem|hyperpage}{222}
-\indexentry{Lyapunov's theorem|hyperpage}{222}
-\indexentry{Semi-hyperbolic singular points classification theorem|hyperpage}{222}
-\indexentry{saddle-node|hyperpage}{223}
-\indexentry{nilpotent|hyperpage}{223}
-\indexentry{Nilpotent singular points classification theorem|hyperpage}{223}
-\indexentry{cusp|hyperpage}{223}
-\indexentry{Blow-up in polar coordinates|hyperpage}{224}
-\indexentry{blowing-up|hyperpage}{224}
-\indexentry{blow-down|hyperpage}{224}
-\indexentry{Blow-up in generalized polar coordinates|hyperpage}{224}
-\indexentry{Blow-up in cartesian coordinates|hyperpage}{225}
-\indexentry{Lyapunov's method|hyperpage}{225}
-\indexentry{$n$-th Lyapunov constant|hyperpage}{225}
-\indexentry{Hopf bifurcation theorem|hyperpage}{225}
-\indexentry{Hopf-bifurcation|hyperpage}{225}
-\indexentry{Poincaré's method|hyperpage}{225}
-\indexentry{Bautin's theorem|hyperpage}{225}
-\indexentry{Homoclinic bifurcation|hyperpage}{225}
-\indexentry{homoclinic bifurcation|hyperpage}{225}
-\indexentry{Bogdanov-Takens bifurcation|hyperpage}{226}
-\indexentry{Bogdanov-Takens bifurcation|hyperpage}{226}
-\indexentry{Routh-Hurwitz stability criterion|hyperpage}{226}
-\indexentry{Routh-Hurwitz stability criterion|hyperpage}{226}
-\indexentry{one-parameter family of rotated vector fields|hyperpage}{226}
-\indexentry{positively rotated|hyperpage}{226}
-\indexentry{negatively rotated|hyperpage}{226}
-\indexentry{Melnikov's method|hyperpage}{226}
-\indexentry{Melnikov's method|hyperpage}{226}
-\indexentry{graph|hyperpage}{226}
-\indexentry{non-degenerated|hyperpage}{226}
-\indexentry{linear saddles|hyperpage}{226}
-\indexentry{Liénard system|hyperpage}{227}
-\indexentry{Liénard's theorem|hyperpage}{227}
-\indexentry{Van der Pol oscillator|hyperpage}{227}
-\indexentry{Lorenz system|hyperpage}{227}
-\indexentry{periodic point|hyperpage}{227}
-\indexentry{prime period|hyperpage}{227}
-\indexentry{set of periodic points|hyperpage}{227}
-\indexentry{set of periods|hyperpage}{227}
-\indexentry{logistic map|hyperpage}{227}
-\indexentry{Period-doubling bifurcation|hyperpage}{228}
-\indexentry{period-doubling bifurcation|hyperpage}{228}
-\indexentry{period-halving bifurcation|hyperpage}{228}
-\indexentry{period-doubling cascade|hyperpage}{228}
-\indexentry{Sharkovskii's order|hyperpage}{228}
-\indexentry{Expansive fixed point theorem|hyperpage}{228}
-\indexentry{Itinerary lemma|hyperpage}{228}
-\indexentry{Sharkovskii's theorem|hyperpage}{228}
-\indexentry{Period three theorem|hyperpage}{228}
-\indexentry{Proximity theorem|hyperpage}{228}
-\indexentry{Shift map|hyperpage}{228}
-\indexentry{shift map|hyperpage}{228}
-\indexentry{itinerary|hyperpage}{229}
-\indexentry{topologically transitive|hyperpage}{229}
-\indexentry{sensitive dependence on initial conditions|hyperpage}{229}
-\indexentry{Chaos|hyperpage}{229}
-\indexentry{chaotic|hyperpage}{229}
-\indexentry{Poisson kernel|hyperpage}{230}
-\indexentry{Poisson kernel|hyperpage}{230}
-\indexentry{Fourier transform|hyperpage}{230}
-\indexentry{inverse Fourier transform|hyperpage}{230}
-\indexentry{Fourier transform operator|hyperpage}{231}
-\indexentry{Riemann-Lebesgue lemma|hyperpage}{231}
-\indexentry{Inversion theorem|hyperpage}{232}
-\indexentry{partial inverse Fourier transform|hyperpage}{232}
-\indexentry{Dirichlet kernel|hyperpage}{232}
-\indexentry{Dirichlet kernel|hyperpage}{232}
-\indexentry{Dini's theorem|hyperpage}{233}
-\indexentry{Fejér mean|hyperpage}{233}
-\indexentry{Fejér kernel|hyperpage}{233}
-\indexentry{Poisson kernel|hyperpage}{233}
-\indexentry{Weierstra\ss \ kernel|hyperpage}{233}
-\indexentry{approximations of the identity|hyperpage}{234}
-\indexentry{Minkowski's integral inequality|hyperpage}{234}
-\indexentry{Plancherel theorem|hyperpage}{235}
-\indexentry{Generalized Hölder's inequality|hyperpage}{235}
-\indexentry{Young's convolution inequality|hyperpage}{236}
-\indexentry{Fourier transform|hyperpage}{236}
-\indexentry{Fourier transform|hyperpage}{236}
-\indexentry{inverse Fourier transform|hyperpage}{236}
-\indexentry{Riemann-Lebesgue lemma|hyperpage}{237}
-\indexentry{Plancherel theorem|hyperpage}{237}
-\indexentry{Uncertainty principle|hyperpage}{237}
-\indexentry{Uncertainty principle in $\ensuremath {\mathbb {R}}^n$|hyperpage}{237}
-\indexentry{Poisson summation formula|hyperpage}{237}
-\indexentry{bandlimited|hyperpage}{238}
-\indexentry{Nyquist-Shannon sampling theorem|hyperpage}{238}
-\indexentry{discrete Fourier transform|hyperpage}{238}
-\indexentry{DFT|hyperpage}{238}
-\indexentry{inverse discrete Fourier transform|hyperpage}{238}
+\indexentry{path-connected|hyperpage}{216}
+\indexentry{path-connected components|hyperpage}{216}
+\indexentry{locally path-connected|hyperpage}{216}
+\indexentry{simply connected|hyperpage}{216}
+\indexentry{Topological manifold|hyperpage}{216}
+\indexentry{topological manifold|hyperpage}{216}
+\indexentry{coordinate chart|hyperpage}{216}
+\indexentry{atlas|hyperpage}{216}
+\indexentry{transition functions|hyperpage}{216}
+\indexentry{piecewise linear manifold|hyperpage}{216}
+\indexentry{differentiable manifold|hyperpage}{216}
+\indexentry{holes|hyperpage}{216}
+\indexentry{Connected sum|hyperpage}{217}
+\indexentry{connected sum|hyperpage}{217}
+\indexentry{same orientation|hyperpage}{217}
+\indexentry{opposite orientations|hyperpage}{217}
+\indexentry{orientation|hyperpage}{217}
+\indexentry{oriented vector space|hyperpage}{217}
+\indexentry{unoriented vector space|hyperpage}{217}
+\indexentry{orientation-preserving|hyperpage}{217}
+\indexentry{not orientation-preserving|hyperpage}{217}
+\indexentry{orientation-preserving|hyperpage}{217}
+\indexentry{not orientation-preserving|hyperpage}{217}
+\indexentry{orientable|hyperpage}{217}
+\indexentry{Classification of connected 1-manifolds|hyperpage}{217}
+\indexentry{surface|hyperpage}{217}
+\indexentry{Connected sum of surfaces|hyperpage}{217}
+\indexentry{genus $g$ orientable surface|hyperpage}{217}
+\indexentry{genus $h$ non-orientable surface|hyperpage}{217}
+\indexentry{standard $n$-simplex|hyperpage}{218}
+\indexentry{triangularization|hyperpage}{218}
+\indexentry{simple curve|hyperpage}{218}
+\indexentry{Jordan curve theorem|hyperpage}{218}
+\indexentry{Radó theorem|hyperpage}{218}
+\indexentry{fundamental polygon of the surface|hyperpage}{218}
+\indexentry{normalized|hyperpage}{218}
+\indexentry{Euler characteristic|hyperpage}{218}
+\indexentry{Classification of compact connected surfaces|hyperpage}{219}
+\indexentry{equilibrium point|hyperpage}{221}
+\indexentry{fixed point|hyperpage}{221}
+\indexentry{periodic orbit of period $T$|hyperpage}{221}
+\indexentry{symmetric with respect to the $x$-axis|hyperpage}{221}
+\indexentry{symmetric with respect to the $y$-axis|hyperpage}{221}
+\indexentry{holomorphic differential equation|hyperpage}{221}
+\indexentry{linearization|hyperpage}{221}
+\indexentry{minimal|hyperpage}{221}
+\indexentry{Kolmogorov system|hyperpage}{221}
+\indexentry{homogeneous of degree $k$|hyperpage}{221}
+\indexentry{homogeneous of degree $k$|hyperpage}{221}
+\indexentry{discrete map of order $m$|hyperpage}{222}
+\indexentry{Characteristic equation|hyperpage}{222}
+\indexentry{linear discrete map|hyperpage}{222}
+\indexentry{Hartman-Grobman theorem|hyperpage}{222}
+\indexentry{The stable manifold theorem|hyperpage}{222}
+\indexentry{stable manifold|hyperpage}{222}
+\indexentry{unstable manifold|hyperpage}{222}
+\indexentry{global stable manifold|hyperpage}{222}
+\indexentry{global unstable manifold|hyperpage}{222}
+\indexentry{The center manifold theorem|hyperpage}{223}
+\indexentry{central manifolds|hyperpage}{223}
+\indexentry{local bifurcation|hyperpage}{223}
+\indexentry{normal form|hyperpage}{223}
+\indexentry{codimension|hyperpage}{223}
+\indexentry{Saddle-node bifurcation|hyperpage}{223}
+\indexentry{saddle-node bifurcation|hyperpage}{223}
+\indexentry{Transcritical bifurcation|hyperpage}{223}
+\indexentry{transcritical bifurcation|hyperpage}{223}
+\indexentry{Pitchfork bifurcation|hyperpage}{223}
+\indexentry{pitchfork bifurcation|hyperpage}{223}
+\indexentry{Lyapunov's theorem|hyperpage}{223}
+\indexentry{Lyapunov's theorem|hyperpage}{223}
+\indexentry{Semi-hyperbolic singular points classification theorem|hyperpage}{223}
+\indexentry{saddle-node|hyperpage}{224}
+\indexentry{nilpotent|hyperpage}{224}
+\indexentry{Nilpotent singular points classification theorem|hyperpage}{224}
+\indexentry{cusp|hyperpage}{224}
+\indexentry{Blow-up in polar coordinates|hyperpage}{225}
+\indexentry{blowing-up|hyperpage}{225}
+\indexentry{blow-down|hyperpage}{225}
+\indexentry{Blow-up in generalized polar coordinates|hyperpage}{225}
+\indexentry{Blow-up in cartesian coordinates|hyperpage}{226}
+\indexentry{Lyapunov's method|hyperpage}{226}
+\indexentry{$n$-th Lyapunov constant|hyperpage}{226}
+\indexentry{Hopf bifurcation theorem|hyperpage}{226}
+\indexentry{Hopf-bifurcation|hyperpage}{226}
+\indexentry{Poincaré's method|hyperpage}{226}
+\indexentry{Bautin's theorem|hyperpage}{226}
+\indexentry{Homoclinic bifurcation|hyperpage}{226}
+\indexentry{homoclinic bifurcation|hyperpage}{226}
+\indexentry{Bogdanov-Takens bifurcation|hyperpage}{227}
+\indexentry{Bogdanov-Takens bifurcation|hyperpage}{227}
+\indexentry{Routh-Hurwitz stability criterion|hyperpage}{227}
+\indexentry{Routh-Hurwitz stability criterion|hyperpage}{227}
+\indexentry{one-parameter family of rotated vector fields|hyperpage}{227}
+\indexentry{positively rotated|hyperpage}{227}
+\indexentry{negatively rotated|hyperpage}{227}
+\indexentry{Melnikov's method|hyperpage}{227}
+\indexentry{Melnikov's method|hyperpage}{227}
+\indexentry{graph|hyperpage}{227}
+\indexentry{non-degenerated|hyperpage}{227}
+\indexentry{linear saddles|hyperpage}{227}
+\indexentry{Liénard system|hyperpage}{228}
+\indexentry{Liénard's theorem|hyperpage}{228}
+\indexentry{Van der Pol oscillator|hyperpage}{228}
+\indexentry{Lorenz system|hyperpage}{228}
+\indexentry{periodic point|hyperpage}{228}
+\indexentry{prime period|hyperpage}{228}
+\indexentry{set of periodic points|hyperpage}{228}
+\indexentry{set of periods|hyperpage}{228}
+\indexentry{logistic map|hyperpage}{228}
+\indexentry{Period-doubling bifurcation|hyperpage}{229}
+\indexentry{period-doubling bifurcation|hyperpage}{229}
+\indexentry{period-halving bifurcation|hyperpage}{229}
+\indexentry{period-doubling cascade|hyperpage}{229}
+\indexentry{Sharkovskii's order|hyperpage}{229}
+\indexentry{Expansive fixed point theorem|hyperpage}{229}
+\indexentry{Itinerary lemma|hyperpage}{229}
+\indexentry{Sharkovskii's theorem|hyperpage}{229}
+\indexentry{Period three theorem|hyperpage}{229}
+\indexentry{Proximity theorem|hyperpage}{229}
+\indexentry{Shift map|hyperpage}{229}
+\indexentry{shift map|hyperpage}{229}
+\indexentry{itinerary|hyperpage}{230}
+\indexentry{topologically transitive|hyperpage}{230}
+\indexentry{sensitive dependence on initial conditions|hyperpage}{230}
+\indexentry{Chaos|hyperpage}{230}
+\indexentry{chaotic|hyperpage}{230}
+\indexentry{Poisson kernel|hyperpage}{231}
+\indexentry{Poisson kernel|hyperpage}{231}
+\indexentry{Fourier transform|hyperpage}{231}
+\indexentry{inverse Fourier transform|hyperpage}{231}
+\indexentry{Fourier transform operator|hyperpage}{232}
+\indexentry{Riemann-Lebesgue lemma|hyperpage}{232}
+\indexentry{Inversion theorem|hyperpage}{233}
+\indexentry{partial inverse Fourier transform|hyperpage}{233}
+\indexentry{Dirichlet kernel|hyperpage}{233}
+\indexentry{Dirichlet kernel|hyperpage}{233}
+\indexentry{Dini's theorem|hyperpage}{234}
+\indexentry{Fejér mean|hyperpage}{234}
+\indexentry{Fejér kernel|hyperpage}{234}
+\indexentry{Poisson kernel|hyperpage}{234}
+\indexentry{Weierstra\ss \ kernel|hyperpage}{234}
+\indexentry{approximations of the identity|hyperpage}{235}
+\indexentry{Minkowski's integral inequality|hyperpage}{235}
+\indexentry{Plancherel theorem|hyperpage}{236}
+\indexentry{Jensen's inequality|hyperpage}{236}
+\indexentry{Generalized Hölder's inequality|hyperpage}{237}
+\indexentry{Young's convolution inequality|hyperpage}{237}
+\indexentry{Fourier transform|hyperpage}{237}
+\indexentry{Fourier transform|hyperpage}{237}
+\indexentry{inverse Fourier transform|hyperpage}{237}
+\indexentry{Riemann-Lebesgue lemma|hyperpage}{238}
\indexentry{Plancherel theorem|hyperpage}{238}
-\indexentry{convolution|hyperpage}{239}
-\indexentry{Poisson summation formula|hyperpage}{239}
-\indexentry{fast Fourier transform|hyperpage}{239}
-\indexentry{FFT|hyperpage}{239}
-\indexentry{Radix-2 DIT Cooley-Tukey FFT algorithm|hyperpage}{239}
-\indexentry{radix-2 decimation-in-time (DIT) FFT|hyperpage}{239}
-\indexentry{bump functions|hyperpage}{239}
-\indexentry{test functions|hyperpage}{239}
-\indexentry{Distribution|hyperpage}{239}
-\indexentry{distribution|hyperpage}{239}
-\indexentry{Fundamental lemma of calculus of variations|hyperpage}{239}
-\indexentry{regular distributions|hyperpage}{240}
-\indexentry{Dirac's $\delta $ distribution|hyperpage}{240}
-\indexentry{Dirac's $\delta $ distribution|hyperpage}{240}
-\indexentry{Cauchy principal value|hyperpage}{240}
-\indexentry{Cauchy principal value|hyperpage}{240}
-\indexentry{distribution of order $N\in \ensuremath {\mathbb {N}}\cup \{0\}$|hyperpage}{240}
-\indexentry{infinite order|hyperpage}{240}
-\indexentry{approximation of identity|hyperpage}{240}
-\indexentry{support|hyperpage}{241}
-\indexentry{distributional derivative|hyperpage}{241}
-\indexentry{Heaviside step function|hyperpage}{241}
-\indexentry{Schwarz theorem|hyperpage}{241}
-\indexentry{Leibnitz rule|hyperpage}{241}
-\indexentry{Schwartz space|hyperpage}{242}
-\indexentry{space of rapidly decreasing functions|hyperpage}{242}
-\indexentry{tempered distribution|hyperpage}{242}
-\indexentry{convolution|hyperpage}{243}
-\indexentry{Fourier transform|hyperpage}{243}
-\indexentry{inverse Fourier transform|hyperpage}{243}
-\indexentry{direct product|hyperpage}{243}
-\indexentry{Homogeneous distribution|hyperpage}{244}
-\indexentry{homogeneous of degree $r\in \ensuremath {\mathbb {R}}$|hyperpage}{244}
-\indexentry{differential operator over distributions|hyperpage}{244}
-\indexentry{generalized solution|hyperpage}{244}
-\indexentry{fundamental solution|hyperpage}{244}
-\indexentry{fundamental solution|hyperpage}{244}
-\indexentry{Malgrange-Ehrenpreis theorem|hyperpage}{246}
-\indexentry{truncated Hilbert transform|hyperpage}{246}
-\indexentry{Hilbert transform|hyperpage}{246}
-\indexentry{Hölder condition|hyperpage}{246}
-\indexentry{Riesz theorem|hyperpage}{246}
-\indexentry{conjugate Poisson kernel|hyperpage}{247}
-\indexentry{Riesz transform|hyperpage}{247}
-\indexentry{Sample variance and covariance|hyperpage}{248}
-\indexentry{sample covariance|hyperpage}{248}
-\indexentry{sample variance|hyperpage}{248}
-\indexentry{sample correlation coefficient|hyperpage}{248}
-\indexentry{expectation|hyperpage}{248}
-\indexentry{covariance matrix|hyperpage}{248}
-\indexentry{covariance|hyperpage}{248}
-\indexentry{Simple model|hyperpage}{249}
-\indexentry{preditions|hyperpage}{249}
-\indexentry{Least-squares method|hyperpage}{249}
-\indexentry{least-squares method|hyperpage}{249}
-\indexentry{residuals|hyperpage}{249}
-\indexentry{General linear model|hyperpage}{249}
-\indexentry{design matrix|hyperpage}{249}
-\indexentry{regressor coefficients|hyperpage}{249}
-\indexentry{regression coefficients|hyperpage}{249}
-\indexentry{preditions|hyperpage}{249}
-\indexentry{Least-squares method|hyperpage}{249}
-\indexentry{MLE method|hyperpage}{250}
-\indexentry{mean square error|hyperpage}{250}
-\indexentry{Gau\ss -Markov|hyperpage}{250}
-\indexentry{BLUE|hyperpage}{250}
-\indexentry{the Best Linear Unbiased Estimator|hyperpage}{250}
-\indexentry{no-intercept|hyperpage}{251}
-\indexentry{coefficient of determination|hyperpage}{251}
-\indexentry{regression sum of squares|hyperpage}{251}
-\indexentry{total sum of squares|hyperpage}{251}
-\indexentry{error sum of squares|hyperpage}{251}
-\indexentry{adjusted coefficient of determination|hyperpage}{251}
-\indexentry{total mean of squares|hyperpage}{251}
-\indexentry{$F$-distribution with degrees of freedom $d_1$ and $d_2$|hyperpage}{251}
-\indexentry{Cochran's theorem|hyperpage}{251}
-\indexentry{Bonferroni's method|hyperpage}{251}
-\indexentry{Model without interaction|hyperpage}{252}
-\indexentry{dummy variable|hyperpage}{252}
-\indexentry{Model with interaction|hyperpage}{252}
-\indexentry{model with interaction|hyperpage}{252}
-\indexentry{Segmented regression|hyperpage}{252}
-\indexentry{response|hyperpage}{252}
-\indexentry{prediction|hyperpage}{252}
-\indexentry{average response|hyperpage}{252}
-\indexentry{estimated average response|hyperpage}{252}
-\indexentry{estimation of the prediction|hyperpage}{252}
-\indexentry{Confidence interval for the average response|hyperpage}{252}
-\indexentry{leverage|hyperpage}{252}
-\indexentry{confidence band|hyperpage}{253}
-\indexentry{Confidence interval for the predicted value|hyperpage}{253}
-\indexentry{prediction band|hyperpage}{253}
-\indexentry{LOF test|hyperpage}{253}
-\indexentry{lack of fit test|hyperpage}{253}
-\indexentry{LOF test|hyperpage}{253}
-\indexentry{internally studentized residuals|hyperpage}{253}
-\indexentry{externally studentized residuals|hyperpage}{253}
-\indexentry{high-leverage points|hyperpage}{254}
-\indexentry{outliars|hyperpage}{254}
-\indexentry{high-leverage point|hyperpage}{254}
-\indexentry{Cook's distance|hyperpage}{254}
-\indexentry{multicollinearity|hyperpage}{254}
-\indexentry{variance inflation factor|hyperpage}{254}
-\indexentry{VIF|hyperpage}{254}
-\indexentry{tolerance|hyperpage}{254}
-\indexentry{Bias on the estimations|hyperpage}{254}
-\indexentry{Bias on the predictions|hyperpage}{254}
-\indexentry{Mallow's $C_p$ statistic|hyperpage}{255}
-\indexentry{Mallow's $C_p$ statistic|hyperpage}{255}
-\indexentry{Information|hyperpage}{255}
-\indexentry{information of an event|hyperpage}{255}
-\indexentry{Cauchy's functional equation|hyperpage}{255}
-\indexentry{Entropy|hyperpage}{255}
-\indexentry{entropy|hyperpage}{255}
-\indexentry{Kullback-Leibler divergence|hyperpage}{255}
-\indexentry{Akaike information criterion|hyperpage}{256}
-\indexentry{Akaike information criterion|hyperpage}{256}
-\indexentry{AIC|hyperpage}{256}
-\indexentry{Box-Cox transformation|hyperpage}{256}
-\indexentry{exponential|hyperpage}{256}
-\indexentry{odds|hyperpage}{256}
-\indexentry{log-odds|hyperpage}{256}
-\indexentry{logit|hyperpage}{256}
-\indexentry{well-posed in the Hadamard sense|hyperpage}{257}
-\indexentry{well-posed|hyperpage}{257}
-\indexentry{step size|hyperpage}{257}
-\indexentry{mesh-points|hyperpage}{257}
-\indexentry{explicit|hyperpage}{257}
-\indexentry{implicit|hyperpage}{257}
-\indexentry{one-step method|hyperpage}{257}
-\indexentry{incremental function|hyperpage}{257}
-\indexentry{local truncation errors|hyperpage}{257}
-\indexentry{global truncation error|hyperpage}{257}
-\indexentry{Euler method|hyperpage}{257}
-\indexentry{forward Euler method|hyperpage}{257}
-\indexentry{explicit Euler method|hyperpage}{257}
-\indexentry{backward Euler method|hyperpage}{257}
-\indexentry{implicit Euler method|hyperpage}{257}
-\indexentry{implicit|hyperpage}{257}
-\indexentry{Trapezoidal method|hyperpage}{258}
-\indexentry{Trapezoidal method|hyperpage}{258}
-\indexentry{Heun method|hyperpage}{258}
-\indexentry{Heun method|hyperpage}{258}
-\indexentry{Taylor method|hyperpage}{258}
-\indexentry{Taylor method of order $r$|hyperpage}{258}
-\indexentry{consistent|hyperpage}{258}
-\indexentry{order of consistency|hyperpage}{258}
-\indexentry{order of accuracy|hyperpage}{258}
-\indexentry{order|hyperpage}{258}
-\indexentry{convergent|hyperpage}{258}
-\indexentry{order of convergence|hyperpage}{258}
-\indexentry{$s$-stage Runge-Kutta methods|hyperpage}{259}
-\indexentry{RK methods|hyperpage}{259}
-\indexentry{Butcher tableau|hyperpage}{259}
-\indexentry{Richardson extrapolation|hyperpage}{259}
-\indexentry{Runge-Kutta-Fehlberg method|hyperpage}{259}
-\indexentry{embedded methods|hyperpage}{259}
-\indexentry{stability function|hyperpage}{260}
-\indexentry{stable|hyperpage}{260}
-\indexentry{absolutely stable|hyperpage}{260}
-\indexentry{stability region|hyperpage}{260}
-\indexentry{A-stable|hyperpage}{260}
-\indexentry{unconditionally absolutely stable|hyperpage}{260}
-\indexentry{conditionally absolutely stable|hyperpage}{260}
-\indexentry{stiff equations|hyperpage}{260}
-\indexentry{Lax theorem|hyperpage}{260}
-\indexentry{test problem|hyperpage}{260}
-\indexentry{Linear multistep method|hyperpage}{260}
-\indexentry{linear $k$-step method|hyperpage}{260}
-\indexentry{first and second characteristic polynomials|hyperpage}{260}
-\indexentry{zero-stable|hyperpage}{261}
-\indexentry{root condition|hyperpage}{261}
-\indexentry{Adams method|hyperpage}{261}
-\indexentry{Adams method|hyperpage}{261}
-\indexentry{Adams-Bashforth method|hyperpage}{261}
-\indexentry{Adams-Moulton method|hyperpage}{261}
-\indexentry{local truncation error|hyperpage}{261}
-\indexentry{consistent|hyperpage}{261}
-\indexentry{order of consistency|hyperpage}{261}
-\indexentry{order of accuracy|hyperpage}{261}
-\indexentry{Dahlquist's theorem|hyperpage}{261}
-\indexentry{Newton method|hyperpage}{261}
-\indexentry{Newton method|hyperpage}{261}
-\indexentry{quasi-Newton method|hyperpage}{262}
-\indexentry{damping parameter|hyperpage}{262}
-\indexentry{Broyden's method|hyperpage}{262}
-\indexentry{Broyden's method|hyperpage}{262}
-\indexentry{secant-like method|hyperpage}{262}
-\indexentry{Descent method|hyperpage}{263}
-\indexentry{descent method|hyperpage}{263}
-\indexentry{step size|hyperpage}{263}
-\indexentry{descent direction|hyperpage}{263}
-\indexentry{Newton method|hyperpage}{263}
-\indexentry{Inexact Newton method|hyperpage}{263}
-\indexentry{Steepest descent|hyperpage}{263}
-\indexentry{Gradient descent|hyperpage}{263}
-\indexentry{Conjugate gradient method|hyperpage}{263}
-\indexentry{line search method|hyperpage}{263}
-\indexentry{Broyden-Fletcher-Goldfarb-Shanno method|hyperpage}{263}
-\indexentry{Broyden-Fletcher-Goldfarb-Shanno method|hyperpage}{263}
-\indexentry{BFGS method|hyperpage}{263}
-\indexentry{Shooting method|hyperpage}{263}
-\indexentry{shooting method|hyperpage}{263}
-\indexentry{Multiple shooting method|hyperpage}{263}
-\indexentry{multiple shooting method|hyperpage}{263}
-\indexentry{finite difference method|hyperpage}{264}
-\indexentry{Singular value|hyperpage}{264}
-\indexentry{singular values|hyperpage}{264}
-\indexentry{Singular value decomposition|hyperpage}{264}
-\indexentry{singular value decomposition|hyperpage}{264}
-\indexentry{SVD|hyperpage}{264}
-\indexentry{left singular vectors|hyperpage}{264}
-\indexentry{right singular vectors|hyperpage}{264}
-\indexentry{truncated|hyperpage}{265}
-\indexentry{truncated singular value decomposition|hyperpage}{265}
-\indexentry{TSVD|hyperpage}{265}
-\indexentry{QR descompostion|hyperpage}{266}
-\indexentry{QR decomposition|hyperpage}{266}
-\indexentry{thin QR decomposition|hyperpage}{266}
-\indexentry{full QR decomposition|hyperpage}{266}
-\indexentry{hyperbolic|hyperpage}{267}
-\indexentry{grid|hyperpage}{267}
-\indexentry{finite difference scheme|hyperpage}{267}
-\indexentry{number of steps|hyperpage}{267}
-\indexentry{one-step|hyperpage}{267}
-\indexentry{multistep|hyperpage}{267}
-\indexentry{Forward-time forward-space|hyperpage}{267}
-\indexentry{FTFS|hyperpage}{267}
-\indexentry{Forward-time backward-space|hyperpage}{267}
-\indexentry{FTBS|hyperpage}{267}
-\indexentry{Forward-time central-space|hyperpage}{267}
-\indexentry{FTCS|hyperpage}{267}
-\indexentry{Backward-time central-space|hyperpage}{267}
-\indexentry{BTCS|hyperpage}{267}
-\indexentry{Leapfrog scheme|hyperpage}{267}
-\indexentry{Lax-Friedrichs scheme|hyperpage}{267}
-\indexentry{stability region|hyperpage}{267}
-\indexentry{unconditionally convergent|hyperpage}{267}
-\indexentry{conditionally convergent|hyperpage}{268}
-\indexentry{consistent|hyperpage}{268}
-\indexentry{conditional consistency|hyperpage}{268}
-\indexentry{upwind condition|hyperpage}{268}
-\indexentry{stable|hyperpage}{268}
-\indexentry{Courant-Friedrichs-Lewy condition|hyperpage}{269}
-\indexentry{Semidiscrete Fourier transform|hyperpage}{269}
-\indexentry{semidiscrete Fourier transform|hyperpage}{269}
-\indexentry{inverse semidiscrete Fourier transform|hyperpage}{269}
-\indexentry{Semidiscrete Parseval identity|hyperpage}{269}
-\indexentry{amplification factor|hyperpage}{269}
-\indexentry{Lax-Wendroff|hyperpage}{270}
-\indexentry{Lax-Wendroff scheme|hyperpage}{270}
-\indexentry{Crank-Nicolson|hyperpage}{271}
-\indexentry{Crank-Nicolson scheme|hyperpage}{271}
-\indexentry{numerical boundary condition|hyperpage}{271}
-\indexentry{Lax-Richtmyer equivalence theorem|hyperpage}{272}
-\indexentry{amplification polynomial|hyperpage}{272}
-\indexentry{compatibility condition|hyperpage}{272}
-\indexentry{elliptic|hyperpage}{272}
-\indexentry{hyperbolic|hyperpage}{272}
-\indexentry{parabolic|hyperpage}{272}
-\indexentry{stable|hyperpage}{273}
-\indexentry{Forward-time central-space|hyperpage}{273}
-\indexentry{Backward-time central-space|hyperpage}{273}
-\indexentry{Crank-Nicolson scheme|hyperpage}{273}
-\indexentry{Leapfrog scheme|hyperpage}{273}
-\indexentry{Du-Fort-Frankel scheme|hyperpage}{273}
-\indexentry{Dirichlet|hyperpage}{273}
-\indexentry{Neumann|hyperpage}{273}
-\indexentry{Robin|hyperpage}{273}
-\indexentry{discrete laplacian|hyperpage}{273}
-\indexentry{Discrete maximum principle|hyperpage}{273}
-\indexentry{Discrete minimum principle|hyperpage}{273}
-\indexentry{finite element method|hyperpage}{274}
-\indexentry{variational formulation|hyperpage}{274}
-\indexentry{weak formulation|hyperpage}{274}
-\indexentry{Galerkin approximation|hyperpage}{274}
-\indexentry{Galerkin approximation|hyperpage}{274}
-\indexentry{Mesh|hyperpage}{274}
-\indexentry{mesh|hyperpage}{274}
-\indexentry{cells|hyperpage}{274}
-\indexentry{finite element method|hyperpage}{274}
-\indexentry{FEM|hyperpage}{274}
-\indexentry{nodes|hyperpage}{274}
-\indexentry{nodes|hyperpage}{274}
-\indexentry{nodal basis|hyperpage}{274}
-\indexentry{stiffness matrix|hyperpage}{275}
-\indexentry{load vector|hyperpage}{275}
-\indexentry{Wave equation|hyperpage}{276}
-\indexentry{hyperbolic equations|hyperpage}{276}
-\indexentry{Navier-Cauchy equation|hyperpage}{276}
-\indexentry{Lamé coefficients|hyperpage}{276}
-\indexentry{elastodynamics|hyperpage}{276}
-\indexentry{material derivative operator|hyperpage}{276}
-\indexentry{incompressible flow|hyperpage}{276}
-\indexentry{Continuous equation|hyperpage}{276}
-\indexentry{continuous equation|hyperpage}{276}
-\indexentry{Cauchy momentum equation|hyperpage}{276}
-\indexentry{Cauchy momentum equation|hyperpage}{276}
-\indexentry{Inviscid flow|hyperpage}{276}
-\indexentry{Viscid flow|hyperpage}{276}
-\indexentry{potential|hyperpage}{276}
-\indexentry{Poisson equation|hyperpage}{276}
-\indexentry{elliptic equation|hyperpage}{276}
-\indexentry{Fick's law of diffusion|hyperpage}{277}
-\indexentry{diffusivity|hyperpage}{277}
-\indexentry{diffusion coefficient|hyperpage}{277}
-\indexentry{diffusion flux|hyperpage}{277}
-\indexentry{Fick's law|hyperpage}{277}
-\indexentry{Diffusion equation|hyperpage}{277}
-\indexentry{Fourier's law|hyperpage}{277}
-\indexentry{thermal conductivity|hyperpage}{277}
-\indexentry{heat flux|hyperpage}{277}
-\indexentry{Fourier's law|hyperpage}{277}
-\indexentry{Heat equation|hyperpage}{277}
-\indexentry{specific heat capacity|hyperpage}{277}
-\indexentry{density|hyperpage}{277}
-\indexentry{thermal diffusivity|hyperpage}{277}
-\indexentry{Gau\ss ' law|hyperpage}{277}
-\indexentry{Gau\ss ' law|hyperpage}{277}
-\indexentry{Gau\ss ' law for magnetism|hyperpage}{277}
-\indexentry{Gau\ss ' law for magnetism|hyperpage}{277}
-\indexentry{Maxwell-Faraday equation|hyperpage}{277}
-\indexentry{Maxwell-Faraday equation|hyperpage}{277}
-\indexentry{Ampère-Maxwell circuital law|hyperpage}{277}
-\indexentry{Ampère's law|hyperpage}{277}
-\indexentry{displacement current|hyperpage}{277}
-\indexentry{refractive index|hyperpage}{277}
-\indexentry{Fermat's principle|hyperpage}{277}
-\indexentry{Fermat's principle|hyperpage}{277}
-\indexentry{Eikonal equation|hyperpage}{277}
-\indexentry{action|hyperpage}{277}
-\indexentry{Principle of least action|hyperpage}{278}
-\indexentry{small change|hyperpage}{278}
-\indexentry{Hamilton-Jacobi equation|hyperpage}{278}
-\indexentry{Schrödinger equation|hyperpage}{278}
-\indexentry{Schrödinger equation|hyperpage}{278}
-\indexentry{wave function|hyperpage}{278}
-\indexentry{Fundamental lemma of calculus of variations|hyperpage}{278}
-\indexentry{Green identities|hyperpage}{278}
-\indexentry{Method of characteristics|hyperpage}{278}
-\indexentry{characteristic curves|hyperpage}{278}
-\indexentry{Traffic flow equation|hyperpage}{279}
-\indexentry{Rankine-Hugoniot equation|hyperpage}{279}
-\indexentry{Entropy condition|hyperpage}{279}
-\indexentry{D'Alembert formula|hyperpage}{280}
-\indexentry{Conservation of energy|hyperpage}{281}
-\indexentry{even periodic extension|hyperpage}{282}
-\indexentry{odd periodic extension|hyperpage}{282}
-\indexentry{Separation of variables|hyperpage}{282}
-\indexentry{separation of variables|hyperpage}{282}
-\indexentry{Sturm-Picone comparison theorem|hyperpage}{282}
-\indexentry{self-similar|hyperpage}{283}
-\indexentry{Distribution|hyperpage}{284}
-\indexentry{distribution|hyperpage}{284}
-\indexentry{Dirac's $\delta $ distribution|hyperpage}{284}
-\indexentry{differentiation operator|hyperpage}{284}
-\indexentry{distributional derivative|hyperpage}{284}
-\indexentry{Heaviside step function|hyperpage}{284}
-\indexentry{fundamental solution|hyperpage}{284}
-\indexentry{heat kernel|hyperpage}{284}
-\indexentry{generalized heat kernel|hyperpage}{285}
-\indexentry{Explicit scheme in finite differences|hyperpage}{285}
-\indexentry{Implicit scheme in finite differences|hyperpage}{285}
-\indexentry{Duhamel principle|hyperpage}{286}
-\indexentry{parabolic cylinder|hyperpage}{286}
-\indexentry{parabolic boundary|hyperpage}{286}
-\indexentry{Maximum principle|hyperpage}{286}
-\indexentry{Minimum principle|hyperpage}{286}
-\indexentry{Uniqueness of the heat equation|hyperpage}{286}
-\indexentry{Maximum principle on unbounded domains|hyperpage}{286}
-\indexentry{Minimum principle on unbounded domains|hyperpage}{287}
-\indexentry{Uniqueness of the heat equation on the unbounded domains|hyperpage}{287}
-\indexentry{Laplace equation|hyperpage}{287}
-\indexentry{Laplace equation|hyperpage}{287}
-\indexentry{Dirichlet problem in the disc|hyperpage}{287}
-\indexentry{Dirichlet problem|hyperpage}{287}
-\indexentry{Dirichlet problem|hyperpage}{287}
-\indexentry{Uniqueness of Dirichlet problem|hyperpage}{287}
-\indexentry{energy functional|hyperpage}{287}
-\indexentry{Dirichlet's principle|hyperpage}{287}
-\indexentry{Sobolev space|hyperpage}{288}
-\indexentry{average|hyperpage}{288}
-\indexentry{Trace theorem|hyperpage}{288}
-\indexentry{trace|hyperpage}{288}
-\indexentry{Poincaré inequality|hyperpage}{288}
-\indexentry{$\sigma $-algebra|hyperpage}{290}
-\indexentry{$\sigma $-algebra|hyperpage}{290}
-\indexentry{Measure|hyperpage}{290}
-\indexentry{measure|hyperpage}{290}
-\indexentry{$\sigma $-additivity|hyperpage}{290}
-\indexentry{interval|hyperpage}{290}
-\indexentry{volume|hyperpage}{290}
-\indexentry{$m$-th dyadic cube|hyperpage}{290}
-\indexentry{Outer measure|hyperpage}{291}
-\indexentry{outer measure|hyperpage}{291}
-\indexentry{null set|hyperpage}{292}
-\indexentry{almost everywhere|hyperpage}{292}
-\indexentry{a.e.|hyperpage}{292}
-\indexentry{Lebesgue measure|hyperpage}{292}
-\indexentry{Lebesgue measurable|hyperpage}{292}
-\indexentry{measurable|hyperpage}{292}
-\indexentry{Lebesgue measure|hyperpage}{292}
-\indexentry{real function|hyperpage}{293}
-\indexentry{finite|hyperpage}{293}
+\indexentry{Uncertainty principle|hyperpage}{238}
+\indexentry{Uncertainty principle in $\ensuremath {\mathbb {R}}^n$|hyperpage}{238}
+\indexentry{Poisson summation formula|hyperpage}{238}
+\indexentry{bandlimited|hyperpage}{239}
+\indexentry{Nyquist-Shannon sampling theorem|hyperpage}{239}
+\indexentry{discrete Fourier transform|hyperpage}{239}
+\indexentry{DFT|hyperpage}{239}
+\indexentry{inverse discrete Fourier transform|hyperpage}{239}
+\indexentry{Plancherel theorem|hyperpage}{240}
+\indexentry{convolution|hyperpage}{240}
+\indexentry{Poisson summation formula|hyperpage}{240}
+\indexentry{fast Fourier transform|hyperpage}{240}
+\indexentry{FFT|hyperpage}{240}
+\indexentry{Radix-2 DIT Cooley-Tukey FFT algorithm|hyperpage}{240}
+\indexentry{radix-2 decimation-in-time (DIT) FFT|hyperpage}{240}
+\indexentry{bump functions|hyperpage}{240}
+\indexentry{test functions|hyperpage}{240}
+\indexentry{Distribution|hyperpage}{240}
+\indexentry{distribution|hyperpage}{240}
+\indexentry{Fundamental lemma of calculus of variations|hyperpage}{240}
+\indexentry{regular distributions|hyperpage}{241}
+\indexentry{Dirac's $\delta $ distribution|hyperpage}{241}
+\indexentry{Dirac's $\delta $ distribution|hyperpage}{241}
+\indexentry{Cauchy principal value|hyperpage}{241}
+\indexentry{Cauchy principal value|hyperpage}{241}
+\indexentry{distribution of order $N\in \ensuremath {\mathbb {N}}\cup \{0\}$|hyperpage}{241}
+\indexentry{infinite order|hyperpage}{241}
+\indexentry{approximation of identity|hyperpage}{241}
+\indexentry{support|hyperpage}{242}
+\indexentry{distributional derivative|hyperpage}{242}
+\indexentry{Heaviside step function|hyperpage}{242}
+\indexentry{Schwarz theorem|hyperpage}{243}
+\indexentry{Leibnitz rule|hyperpage}{243}
+\indexentry{Schwartz space|hyperpage}{243}
+\indexentry{space of rapidly decreasing functions|hyperpage}{243}
+\indexentry{tempered distribution|hyperpage}{244}
+\indexentry{convolution|hyperpage}{244}
+\indexentry{Fourier transform|hyperpage}{244}
+\indexentry{inverse Fourier transform|hyperpage}{244}
+\indexentry{direct product|hyperpage}{245}
+\indexentry{Homogeneous distribution|hyperpage}{245}
+\indexentry{homogeneous of degree $r\in \ensuremath {\mathbb {R}}$|hyperpage}{245}
+\indexentry{differential operator over distributions|hyperpage}{245}
+\indexentry{generalized solution|hyperpage}{245}
+\indexentry{fundamental solution|hyperpage}{245}
+\indexentry{fundamental solution|hyperpage}{246}
+\indexentry{Malgrange-Ehrenpreis theorem|hyperpage}{247}
+\indexentry{truncated Hilbert transform|hyperpage}{247}
+\indexentry{Hilbert transform|hyperpage}{247}
+\indexentry{Hölder condition|hyperpage}{247}
+\indexentry{Riesz theorem|hyperpage}{248}
+\indexentry{conjugate Poisson kernel|hyperpage}{248}
+\indexentry{Riesz transform|hyperpage}{248}
+\indexentry{Sample variance and covariance|hyperpage}{249}
+\indexentry{sample covariance|hyperpage}{249}
+\indexentry{sample variance|hyperpage}{249}
+\indexentry{sample correlation coefficient|hyperpage}{249}
+\indexentry{expectation|hyperpage}{249}
+\indexentry{covariance matrix|hyperpage}{249}
+\indexentry{covariance|hyperpage}{249}
+\indexentry{Simple model|hyperpage}{250}
+\indexentry{preditions|hyperpage}{250}
+\indexentry{Least-squares method|hyperpage}{250}
+\indexentry{least-squares method|hyperpage}{250}
+\indexentry{residuals|hyperpage}{250}
+\indexentry{General linear model|hyperpage}{250}
+\indexentry{design matrix|hyperpage}{250}
+\indexentry{regressor coefficients|hyperpage}{250}
+\indexentry{regression coefficients|hyperpage}{250}
+\indexentry{preditions|hyperpage}{250}
+\indexentry{Least-squares method|hyperpage}{250}
+\indexentry{MLE method|hyperpage}{251}
+\indexentry{mean square error|hyperpage}{251}
+\indexentry{Gau\ss -Markov|hyperpage}{251}
+\indexentry{BLUE|hyperpage}{251}
+\indexentry{the Best Linear Unbiased Estimator|hyperpage}{251}
+\indexentry{no-intercept|hyperpage}{252}
+\indexentry{coefficient of determination|hyperpage}{252}
+\indexentry{regression sum of squares|hyperpage}{252}
+\indexentry{total sum of squares|hyperpage}{252}
+\indexentry{error sum of squares|hyperpage}{252}
+\indexentry{adjusted coefficient of determination|hyperpage}{252}
+\indexentry{total mean of squares|hyperpage}{252}
+\indexentry{$F$-distribution with degrees of freedom $d_1$ and $d_2$|hyperpage}{252}
+\indexentry{Cochran's theorem|hyperpage}{252}
+\indexentry{Bonferroni's method|hyperpage}{252}
+\indexentry{Model without interaction|hyperpage}{253}
+\indexentry{dummy variable|hyperpage}{253}
+\indexentry{Model with interaction|hyperpage}{253}
+\indexentry{model with interaction|hyperpage}{253}
+\indexentry{Segmented regression|hyperpage}{253}
+\indexentry{response|hyperpage}{253}
+\indexentry{prediction|hyperpage}{253}
+\indexentry{average response|hyperpage}{253}
+\indexentry{estimated average response|hyperpage}{253}
+\indexentry{estimation of the prediction|hyperpage}{253}
+\indexentry{Confidence interval for the average response|hyperpage}{253}
+\indexentry{leverage|hyperpage}{253}
+\indexentry{confidence band|hyperpage}{254}
+\indexentry{Confidence interval for the predicted value|hyperpage}{254}
+\indexentry{prediction band|hyperpage}{254}
+\indexentry{LOF test|hyperpage}{254}
+\indexentry{lack of fit test|hyperpage}{254}
+\indexentry{LOF test|hyperpage}{254}
+\indexentry{internally studentized residuals|hyperpage}{254}
+\indexentry{externally studentized residuals|hyperpage}{254}
+\indexentry{high-leverage points|hyperpage}{255}
+\indexentry{outliars|hyperpage}{255}
+\indexentry{high-leverage point|hyperpage}{255}
+\indexentry{Cook's distance|hyperpage}{255}
+\indexentry{multicollinearity|hyperpage}{255}
+\indexentry{variance inflation factor|hyperpage}{255}
+\indexentry{VIF|hyperpage}{255}
+\indexentry{tolerance|hyperpage}{255}
+\indexentry{Bias on the estimations|hyperpage}{255}
+\indexentry{Bias on the predictions|hyperpage}{255}
+\indexentry{Mallow's $C_p$ statistic|hyperpage}{256}
+\indexentry{Mallow's $C_p$ statistic|hyperpage}{256}
+\indexentry{Information|hyperpage}{256}
+\indexentry{information of an event|hyperpage}{256}
+\indexentry{Cauchy's functional equation|hyperpage}{256}
+\indexentry{Entropy|hyperpage}{256}
+\indexentry{entropy|hyperpage}{256}
+\indexentry{Kullback-Leibler divergence|hyperpage}{256}
+\indexentry{Akaike information criterion|hyperpage}{257}
+\indexentry{Akaike information criterion|hyperpage}{257}
+\indexentry{AIC|hyperpage}{257}
+\indexentry{Box-Cox transformation|hyperpage}{257}
+\indexentry{exponential|hyperpage}{257}
+\indexentry{odds|hyperpage}{257}
+\indexentry{log-odds|hyperpage}{257}
+\indexentry{logit|hyperpage}{257}
+\indexentry{well-posed in the Hadamard sense|hyperpage}{258}
+\indexentry{well-posed|hyperpage}{258}
+\indexentry{step size|hyperpage}{258}
+\indexentry{mesh-points|hyperpage}{258}
+\indexentry{explicit|hyperpage}{258}
+\indexentry{implicit|hyperpage}{258}
+\indexentry{one-step method|hyperpage}{258}
+\indexentry{incremental function|hyperpage}{258}
+\indexentry{local truncation errors|hyperpage}{258}
+\indexentry{global truncation error|hyperpage}{258}
+\indexentry{Euler method|hyperpage}{258}
+\indexentry{forward Euler method|hyperpage}{258}
+\indexentry{explicit Euler method|hyperpage}{258}
+\indexentry{backward Euler method|hyperpage}{258}
+\indexentry{implicit Euler method|hyperpage}{258}
+\indexentry{implicit|hyperpage}{258}
+\indexentry{Trapezoidal method|hyperpage}{259}
+\indexentry{Trapezoidal method|hyperpage}{259}
+\indexentry{Heun method|hyperpage}{259}
+\indexentry{Heun method|hyperpage}{259}
+\indexentry{Taylor method|hyperpage}{259}
+\indexentry{Taylor method of order $r$|hyperpage}{259}
+\indexentry{consistent|hyperpage}{259}
+\indexentry{order of consistency|hyperpage}{259}
+\indexentry{order of accuracy|hyperpage}{259}
+\indexentry{order|hyperpage}{259}
+\indexentry{convergent|hyperpage}{259}
+\indexentry{order of convergence|hyperpage}{259}
+\indexentry{$s$-stage Runge-Kutta methods|hyperpage}{260}
+\indexentry{RK methods|hyperpage}{260}
+\indexentry{Butcher tableau|hyperpage}{260}
+\indexentry{Richardson extrapolation|hyperpage}{260}
+\indexentry{Runge-Kutta-Fehlberg method|hyperpage}{260}
+\indexentry{embedded methods|hyperpage}{260}
+\indexentry{stability function|hyperpage}{261}
+\indexentry{stable|hyperpage}{261}
+\indexentry{absolutely stable|hyperpage}{261}
+\indexentry{stability region|hyperpage}{261}
+\indexentry{A-stable|hyperpage}{261}
+\indexentry{unconditionally absolutely stable|hyperpage}{261}
+\indexentry{conditionally absolutely stable|hyperpage}{261}
+\indexentry{stiff equations|hyperpage}{261}
+\indexentry{Lax theorem|hyperpage}{261}
+\indexentry{test problem|hyperpage}{261}
+\indexentry{Linear multistep method|hyperpage}{261}
+\indexentry{linear $k$-step method|hyperpage}{261}
+\indexentry{first and second characteristic polynomials|hyperpage}{261}
+\indexentry{zero-stable|hyperpage}{262}
+\indexentry{root condition|hyperpage}{262}
+\indexentry{Adams method|hyperpage}{262}
+\indexentry{Adams method|hyperpage}{262}
+\indexentry{Adams-Bashforth method|hyperpage}{262}
+\indexentry{Adams-Moulton method|hyperpage}{262}
+\indexentry{local truncation error|hyperpage}{262}
+\indexentry{consistent|hyperpage}{262}
+\indexentry{order of consistency|hyperpage}{262}
+\indexentry{order of accuracy|hyperpage}{262}
+\indexentry{Dahlquist's theorem|hyperpage}{262}
+\indexentry{Newton method|hyperpage}{262}
+\indexentry{Newton method|hyperpage}{262}
+\indexentry{quasi-Newton method|hyperpage}{263}
+\indexentry{damping parameter|hyperpage}{263}
+\indexentry{Broyden's method|hyperpage}{263}
+\indexentry{Broyden's method|hyperpage}{263}
+\indexentry{secant-like method|hyperpage}{263}
+\indexentry{Descent method|hyperpage}{264}
+\indexentry{descent method|hyperpage}{264}
+\indexentry{step size|hyperpage}{264}
+\indexentry{descent direction|hyperpage}{264}
+\indexentry{Newton method|hyperpage}{264}
+\indexentry{Inexact Newton method|hyperpage}{264}
+\indexentry{Steepest descent|hyperpage}{264}
+\indexentry{Gradient descent|hyperpage}{264}
+\indexentry{Conjugate gradient method|hyperpage}{264}
+\indexentry{line search method|hyperpage}{264}
+\indexentry{Broyden-Fletcher-Goldfarb-Shanno method|hyperpage}{264}
+\indexentry{Broyden-Fletcher-Goldfarb-Shanno method|hyperpage}{264}
+\indexentry{BFGS method|hyperpage}{264}
+\indexentry{Shooting method|hyperpage}{264}
+\indexentry{shooting method|hyperpage}{264}
+\indexentry{Multiple shooting method|hyperpage}{264}
+\indexentry{multiple shooting method|hyperpage}{264}
+\indexentry{finite difference method|hyperpage}{265}
+\indexentry{Singular value|hyperpage}{265}
+\indexentry{singular values|hyperpage}{265}
+\indexentry{Singular value decomposition|hyperpage}{265}
+\indexentry{singular value decomposition|hyperpage}{265}
+\indexentry{SVD|hyperpage}{265}
+\indexentry{left singular vectors|hyperpage}{265}
+\indexentry{right singular vectors|hyperpage}{265}
+\indexentry{truncated|hyperpage}{266}
+\indexentry{truncated singular value decomposition|hyperpage}{266}
+\indexentry{TSVD|hyperpage}{266}
+\indexentry{QR descompostion|hyperpage}{267}
+\indexentry{QR decomposition|hyperpage}{267}
+\indexentry{thin QR decomposition|hyperpage}{267}
+\indexentry{full QR decomposition|hyperpage}{267}
+\indexentry{hyperbolic|hyperpage}{268}
+\indexentry{grid|hyperpage}{268}
+\indexentry{finite difference scheme|hyperpage}{268}
+\indexentry{number of steps|hyperpage}{268}
+\indexentry{one-step|hyperpage}{268}
+\indexentry{multistep|hyperpage}{268}
+\indexentry{Forward-time forward-space|hyperpage}{268}
+\indexentry{FTFS|hyperpage}{268}
+\indexentry{Forward-time backward-space|hyperpage}{268}
+\indexentry{FTBS|hyperpage}{268}
+\indexentry{Forward-time central-space|hyperpage}{268}
+\indexentry{FTCS|hyperpage}{268}
+\indexentry{Backward-time central-space|hyperpage}{268}
+\indexentry{BTCS|hyperpage}{268}
+\indexentry{Leapfrog scheme|hyperpage}{268}
+\indexentry{Lax-Friedrichs scheme|hyperpage}{268}
+\indexentry{stability region|hyperpage}{268}
+\indexentry{unconditionally convergent|hyperpage}{268}
+\indexentry{conditionally convergent|hyperpage}{269}
+\indexentry{consistent|hyperpage}{269}
+\indexentry{conditional consistency|hyperpage}{269}
+\indexentry{upwind condition|hyperpage}{269}
+\indexentry{stable|hyperpage}{269}
+\indexentry{Courant-Friedrichs-Lewy condition|hyperpage}{270}
+\indexentry{Semidiscrete Fourier transform|hyperpage}{270}
+\indexentry{semidiscrete Fourier transform|hyperpage}{270}
+\indexentry{inverse semidiscrete Fourier transform|hyperpage}{270}
+\indexentry{Semidiscrete Parseval identity|hyperpage}{270}
+\indexentry{amplification factor|hyperpage}{270}
+\indexentry{Lax-Wendroff|hyperpage}{271}
+\indexentry{Lax-Wendroff scheme|hyperpage}{271}
+\indexentry{Crank-Nicolson|hyperpage}{272}
+\indexentry{Crank-Nicolson scheme|hyperpage}{272}
+\indexentry{numerical boundary condition|hyperpage}{272}
+\indexentry{Lax-Richtmyer equivalence theorem|hyperpage}{273}
+\indexentry{amplification polynomial|hyperpage}{273}
+\indexentry{compatibility condition|hyperpage}{273}
+\indexentry{elliptic|hyperpage}{273}
+\indexentry{hyperbolic|hyperpage}{273}
+\indexentry{parabolic|hyperpage}{273}
+\indexentry{stable|hyperpage}{274}
+\indexentry{Forward-time central-space|hyperpage}{274}
+\indexentry{Backward-time central-space|hyperpage}{274}
+\indexentry{Crank-Nicolson scheme|hyperpage}{274}
+\indexentry{Leapfrog scheme|hyperpage}{274}
+\indexentry{Du-Fort-Frankel scheme|hyperpage}{274}
+\indexentry{Dirichlet|hyperpage}{274}
+\indexentry{Neumann|hyperpage}{274}
+\indexentry{Robin|hyperpage}{274}
+\indexentry{discrete laplacian|hyperpage}{274}
+\indexentry{Discrete maximum principle|hyperpage}{274}
+\indexentry{Discrete minimum principle|hyperpage}{274}
+\indexentry{finite element method|hyperpage}{275}
+\indexentry{variational formulation|hyperpage}{275}
+\indexentry{weak formulation|hyperpage}{275}
+\indexentry{Galerkin approximation|hyperpage}{275}
+\indexentry{Galerkin approximation|hyperpage}{275}
+\indexentry{Mesh|hyperpage}{275}
+\indexentry{mesh|hyperpage}{275}
+\indexentry{cells|hyperpage}{275}
+\indexentry{finite element method|hyperpage}{275}
+\indexentry{FEM|hyperpage}{275}
+\indexentry{nodes|hyperpage}{275}
+\indexentry{nodes|hyperpage}{275}
+\indexentry{nodal basis|hyperpage}{275}
+\indexentry{stiffness matrix|hyperpage}{276}
+\indexentry{load vector|hyperpage}{276}
+\indexentry{Wave equation|hyperpage}{277}
+\indexentry{hyperbolic equations|hyperpage}{277}
+\indexentry{Navier-Cauchy equation|hyperpage}{277}
+\indexentry{Lamé coefficients|hyperpage}{277}
+\indexentry{elastodynamics|hyperpage}{277}
+\indexentry{material derivative operator|hyperpage}{277}
+\indexentry{incompressible flow|hyperpage}{277}
+\indexentry{Continuous equation|hyperpage}{277}
+\indexentry{continuous equation|hyperpage}{277}
+\indexentry{Cauchy momentum equation|hyperpage}{277}
+\indexentry{Cauchy momentum equation|hyperpage}{277}
+\indexentry{Inviscid flow|hyperpage}{277}
+\indexentry{Viscid flow|hyperpage}{277}
+\indexentry{potential|hyperpage}{277}
+\indexentry{Poisson equation|hyperpage}{277}
+\indexentry{elliptic equation|hyperpage}{277}
+\indexentry{Fick's law of diffusion|hyperpage}{278}
+\indexentry{diffusivity|hyperpage}{278}
+\indexentry{diffusion coefficient|hyperpage}{278}
+\indexentry{diffusion flux|hyperpage}{278}
+\indexentry{Fick's law|hyperpage}{278}
+\indexentry{Diffusion equation|hyperpage}{278}
+\indexentry{Fourier's law|hyperpage}{278}
+\indexentry{thermal conductivity|hyperpage}{278}
+\indexentry{heat flux|hyperpage}{278}
+\indexentry{Fourier's law|hyperpage}{278}
+\indexentry{Heat equation|hyperpage}{278}
+\indexentry{specific heat capacity|hyperpage}{278}
+\indexentry{density|hyperpage}{278}
+\indexentry{thermal diffusivity|hyperpage}{278}
+\indexentry{Gau\ss ' law|hyperpage}{278}
+\indexentry{Gau\ss ' law|hyperpage}{278}
+\indexentry{Gau\ss ' law for magnetism|hyperpage}{278}
+\indexentry{Gau\ss ' law for magnetism|hyperpage}{278}
+\indexentry{Maxwell-Faraday equation|hyperpage}{278}
+\indexentry{Maxwell-Faraday equation|hyperpage}{278}
+\indexentry{Ampère-Maxwell circuital law|hyperpage}{278}
+\indexentry{Ampère's law|hyperpage}{278}
+\indexentry{displacement current|hyperpage}{278}
+\indexentry{refractive index|hyperpage}{278}
+\indexentry{Fermat's principle|hyperpage}{278}
+\indexentry{Fermat's principle|hyperpage}{278}
+\indexentry{Eikonal equation|hyperpage}{278}
+\indexentry{action|hyperpage}{278}
+\indexentry{Principle of least action|hyperpage}{279}
+\indexentry{small change|hyperpage}{279}
+\indexentry{Hamilton-Jacobi equation|hyperpage}{279}
+\indexentry{Schrödinger equation|hyperpage}{279}
+\indexentry{Schrödinger equation|hyperpage}{279}
+\indexentry{wave function|hyperpage}{279}
+\indexentry{Fundamental lemma of calculus of variations|hyperpage}{279}
+\indexentry{Green identities|hyperpage}{279}
+\indexentry{Method of characteristics|hyperpage}{279}
+\indexentry{characteristic curves|hyperpage}{279}
+\indexentry{Traffic flow equation|hyperpage}{280}
+\indexentry{Rankine-Hugoniot equation|hyperpage}{280}
+\indexentry{Entropy condition|hyperpage}{280}
+\indexentry{D'Alembert formula|hyperpage}{281}
+\indexentry{Conservation of energy|hyperpage}{282}
+\indexentry{even periodic extension|hyperpage}{283}
+\indexentry{odd periodic extension|hyperpage}{283}
+\indexentry{Separation of variables|hyperpage}{283}
+\indexentry{separation of variables|hyperpage}{283}
+\indexentry{Sturm-Picone comparison theorem|hyperpage}{283}
+\indexentry{self-similar|hyperpage}{284}
+\indexentry{Distribution|hyperpage}{285}
+\indexentry{distribution|hyperpage}{285}
+\indexentry{Dirac's $\delta $ distribution|hyperpage}{285}
+\indexentry{differentiation operator|hyperpage}{285}
+\indexentry{distributional derivative|hyperpage}{285}
+\indexentry{Heaviside step function|hyperpage}{285}
+\indexentry{fundamental solution|hyperpage}{285}
+\indexentry{heat kernel|hyperpage}{285}
+\indexentry{generalized heat kernel|hyperpage}{286}
+\indexentry{Explicit scheme in finite differences|hyperpage}{286}
+\indexentry{Implicit scheme in finite differences|hyperpage}{286}
+\indexentry{Duhamel principle|hyperpage}{287}
+\indexentry{parabolic cylinder|hyperpage}{287}
+\indexentry{parabolic boundary|hyperpage}{287}
+\indexentry{Maximum principle|hyperpage}{287}
+\indexentry{Minimum principle|hyperpage}{287}
+\indexentry{Uniqueness of the heat equation|hyperpage}{287}
+\indexentry{Maximum principle on unbounded domains|hyperpage}{287}
+\indexentry{Minimum principle on unbounded domains|hyperpage}{288}
+\indexentry{Uniqueness of the heat equation on the unbounded domains|hyperpage}{288}
+\indexentry{Laplace equation|hyperpage}{288}
+\indexentry{Laplace equation|hyperpage}{288}
+\indexentry{Dirichlet problem in the disc|hyperpage}{288}
+\indexentry{Dirichlet problem|hyperpage}{288}
+\indexentry{Dirichlet problem|hyperpage}{288}
+\indexentry{Uniqueness of Dirichlet problem|hyperpage}{288}
+\indexentry{energy functional|hyperpage}{288}
+\indexentry{Dirichlet's principle|hyperpage}{288}
+\indexentry{Sobolev space|hyperpage}{289}
+\indexentry{average|hyperpage}{289}
+\indexentry{Trace theorem|hyperpage}{289}
+\indexentry{trace|hyperpage}{289}
+\indexentry{Poincaré inequality|hyperpage}{289}
+\indexentry{$\sigma $-algebra|hyperpage}{291}
+\indexentry{$\sigma $-algebra|hyperpage}{291}
+\indexentry{Measure|hyperpage}{291}
+\indexentry{measure|hyperpage}{291}
+\indexentry{$\sigma $-additivity|hyperpage}{291}
+\indexentry{interval|hyperpage}{291}
+\indexentry{volume|hyperpage}{291}
+\indexentry{$m$-th dyadic cube|hyperpage}{291}
+\indexentry{Outer measure|hyperpage}{292}
+\indexentry{outer measure|hyperpage}{292}
+\indexentry{null set|hyperpage}{293}
+\indexentry{almost everywhere|hyperpage}{293}
+\indexentry{a.e.|hyperpage}{293}
+\indexentry{Lebesgue measure|hyperpage}{293}
\indexentry{Lebesgue measurable|hyperpage}{293}
\indexentry{measurable|hyperpage}{293}
-\indexentry{Borel $\sigma $-algebra|hyperpage}{294}
-\indexentry{Borel measurable|hyperpage}{294}
-\indexentry{simple function|hyperpage}{294}
-\indexentry{integral of $s$ over $\ensuremath {\mathbb {R}}^n$|hyperpage}{294}
-\indexentry{integral of $s$ over a measurable set $E$|hyperpage}{294}
-\indexentry{integral of $f$ over $\ensuremath {\mathbb {R}}^n$|hyperpage}{295}
-\indexentry{integral of $f$ over a measurable set $E\subseteq \ensuremath {\mathbb {R}}^n$|hyperpage}{295}
-\indexentry{Monotone convergence theorem|hyperpage}{295}
-\indexentry{Chebyshev's inequality|hyperpage}{296}
-\indexentry{Fatou's lemma|hyperpage}{296}
-\indexentry{integral of $f$ over $E$|hyperpage}{296}
-\indexentry{integrable function over $E$|hyperpage}{296}
-\indexentry{Dominated convergence theorem|hyperpage}{296}
-\indexentry{converge in mean|hyperpage}{297}
-\indexentry{exists and it is finite|hyperpage}{297}
-\indexentry{Mean value theorem for integrals|hyperpage}{297}
-\indexentry{Barrow's law|hyperpage}{297}
-\indexentry{Fundamental theorem of calculus|hyperpage}{297}
-\indexentry{Integration by parts|hyperpage}{297}
-\indexentry{Hardy-Littlewood maximal function|hyperpage}{297}
-\indexentry{Hardy-Littlewood maximal function|hyperpage}{297}
-\indexentry{Lebesgue differentiation theorem|hyperpage}{298}
-\indexentry{section|hyperpage}{298}
-\indexentry{Tonelli's theorem|hyperpage}{298}
-\indexentry{Fubini's theorem|hyperpage}{299}
-\indexentry{change of variables|hyperpage}{299}
-\indexentry{Change of variables|hyperpage}{299}
-\indexentry{distance|hyperpage}{299}
-\indexentry{triangular inequality|hyperpage}{299}
-\indexentry{metric space|hyperpage}{299}
-\indexentry{complete|hyperpage}{299}
-\indexentry{norm|hyperpage}{299}
-\indexentry{triangular inequality|hyperpage}{299}
-\indexentry{normed vector space|hyperpage}{299}
-\indexentry{convergent series|hyperpage}{299}
-\indexentry{absolutely convergent|hyperpage}{299}
-\indexentry{Banach space|hyperpage}{300}
-\indexentry{Banach space|hyperpage}{300}
-\indexentry{uniform norm|hyperpage}{300}
-\indexentry{total subset|hyperpage}{300}
-\indexentry{separable|hyperpage}{300}
-\indexentry{quotient space|hyperpage}{301}
-\indexentry{Young's inequality for products|hyperpage}{301}
-\indexentry{Hölder conjugates|hyperpage}{301}
-\indexentry{Hölder's inequality|hyperpage}{301}
-\indexentry{Minkowski inequality|hyperpage}{302}
-\indexentry{uniform norm|hyperpage}{302}
-\indexentry{uniform norm|hyperpage}{302}
-\indexentry{supremum norm|hyperpage}{302}
-\indexentry{subalgebra|hyperpage}{302}
-\indexentry{separating set|hyperpage}{302}
-\indexentry{separate the points|hyperpage}{302}
-\indexentry{vanishes nowhere|hyperpage}{302}
-\indexentry{self-conjugate|hyperpage}{303}
-\indexentry{Stone-Weierstra\ss \ theorem|hyperpage}{303}
-\indexentry{pointwise bounded|hyperpage}{303}
-\indexentry{locally bounded|hyperpage}{303}
-\indexentry{uniformly bounded|hyperpage}{303}
-\indexentry{equicontinuous at a point|hyperpage}{303}
-\indexentry{pointwise equicontinuous|hyperpage}{303}
-\indexentry{uniformly equicontinuous|hyperpage}{303}
-\indexentry{Arzelà-Ascoli theorem|hyperpage}{303}
-\indexentry{operator|hyperpage}{304}
-\indexentry{norm|hyperpage}{304}
-\indexentry{sublinear|hyperpage}{305}
-\indexentry{Marcinkiewicz interpolation theorem|hyperpage}{305}
-\indexentry{topological homeomorphism|hyperpage}{305}
-\indexentry{isomorphic|hyperpage}{305}
-\indexentry{is finer than|hyperpage}{305}
-\indexentry{equivalent|hyperpage}{305}
-\indexentry{Almost orthogonality lemma|hyperpage}{305}
-\indexentry{Riesz's theorem|hyperpage}{305}
-\indexentry{normed algebra|hyperpage}{306}
-\indexentry{dual space|hyperpage}{306}
-\indexentry{compact operator|hyperpage}{306}
-\indexentry{Fredholm operator with kernel $K$|hyperpage}{306}
-\indexentry{Volterra operator with kernel $K$|hyperpage}{306}
-\indexentry{Hilbert-Schmidt operator with kernel $K$|hyperpage}{306}
-\indexentry{finite-rank operator|hyperpage}{306}
-\indexentry{Neumann series|hyperpage}{307}
-\indexentry{convex functional|hyperpage}{307}
-\indexentry{Hahn-Banach theorem|hyperpage}{307}
-\indexentry{prolongation|hyperpage}{307}
-\indexentry{Seminorm|hyperpage}{307}
-\indexentry{seminorm|hyperpage}{307}
-\indexentry{Hahn-Banach theorem|hyperpage}{307}
-\indexentry{Hahn-Banach theorem|hyperpage}{307}
-\indexentry{reflexive|hyperpage}{307}
-\indexentry{dual map|hyperpage}{307}
-\indexentry{proper subspace of $T$|hyperpage}{308}
-\indexentry{eigenvectors|hyperpage}{308}
-\indexentry{eigenvalue|hyperpage}{308}
-\indexentry{spectrum|hyperpage}{308}
-\indexentry{spectral values|hyperpage}{308}
-\indexentry{Baire's theorem|hyperpage}{308}
-\indexentry{Open mapping theorem|hyperpage}{308}
-\indexentry{Closed graph theorem|hyperpage}{308}
-\indexentry{Banach-Steinhaus theorem|hyperpage}{308}
-\indexentry{semilinear|hyperpage}{309}
-\indexentry{inner product|hyperpage}{309}
-\indexentry{pre-Hilbert space|hyperpage}{309}
-\indexentry{Cauchy-Schwarz inequality|hyperpage}{309}
-\indexentry{Minkowski inequality|hyperpage}{309}
-\indexentry{Polarization identity|hyperpage}{309}
-\indexentry{orthogonal|hyperpage}{309}
-\indexentry{orthogonal complement|hyperpage}{309}
-\indexentry{Pythagorean theorem|hyperpage}{309}
-\indexentry{Parallelogram law|hyperpage}{309}
-\indexentry{Hilbert space|hyperpage}{309}
-\indexentry{Hilbert space|hyperpage}{309}
-\indexentry{minimizer|hyperpage}{310}
-\indexentry{Projection theorem|hyperpage}{310}
-\indexentry{orthogonal projection on $F$|hyperpage}{310}
-\indexentry{Riesz representation theorem|hyperpage}{311}
-\indexentry{adjoint operator|hyperpage}{311}
-\indexentry{self-adjoint|hyperpage}{311}
-\indexentry{orthogonal system|hyperpage}{311}
-\indexentry{orthonormal system|hyperpage}{311}
-\indexentry{complete|hyperpage}{311}
-\indexentry{Hilbert basis|hyperpage}{311}
-\indexentry{Fourier coefficients|hyperpage}{312}
-\indexentry{Fourier series|hyperpage}{312}
-\indexentry{Gram-Schmidt process|hyperpage}{312}
-\indexentry{orthonormalization|hyperpage}{312}
-\indexentry{Bessel's inequality|hyperpage}{312}
-\indexentry{Fourier transform|hyperpage}{312}
-\indexentry{Riesz-Fischer theorem|hyperpage}{312}
-\indexentry{Parseval identity|hyperpage}{312}
-\indexentry{Spectral theorem|hyperpage}{312}
-\indexentry{Hilbert-Schmidt spectral representation theorem|hyperpage}{312}
-\indexentry{Fredholm alternative|hyperpage}{313}
-\indexentry{Law of total probability|hyperpage}{314}
-\indexentry{Substitution principle|hyperpage}{314}
-\indexentry{Law of total expectation|hyperpage}{314}
-\indexentry{Wald theorem|hyperpage}{314}
-\indexentry{probability-generating function|hyperpage}{315}
-\indexentry{pgf|hyperpage}{315}
-\indexentry{Stochastic process|hyperpage}{315}
-\indexentry{stochastic process|hyperpage}{315}
-\indexentry{parameter set|hyperpage}{315}
-\indexentry{state space|hyperpage}{315}
-\indexentry{independent|hyperpage}{315}
-\indexentry{Gambler's ruin problem|hyperpage}{317}
-\indexentry{Markov chain|hyperpage}{317}
-\indexentry{Markov property|hyperpage}{317}
-\indexentry{time-homogeneous Markov chain|hyperpage}{317}
-\indexentry{state space|hyperpage}{317}
-\indexentry{states|hyperpage}{317}
-\indexentry{Stochastic matrix|hyperpage}{317}
-\indexentry{stochastic matrix|hyperpage}{317}
-\indexentry{transition probabilities|hyperpage}{317}
-\indexentry{transition matrix|hyperpage}{317}
-\indexentry{initial distribution|hyperpage}{317}
-\indexentry{Random walk|hyperpage}{318}
-\indexentry{random walk|hyperpage}{318}
-\indexentry{simple random walk|hyperpage}{318}
-\indexentry{$n$-step transition probabilities|hyperpage}{318}
-\indexentry{$n$-step transition matrix|hyperpage}{318}
-\indexentry{$n$-step distribution|hyperpage}{318}
-\indexentry{Chapman-Kolmogorov equation|hyperpage}{319}
-\indexentry{reachable|hyperpage}{319}
-\indexentry{communicate|hyperpage}{319}
-\indexentry{irreducible class|hyperpage}{319}
-\indexentry{irreducible chain|hyperpage}{319}
-\indexentry{period|hyperpage}{319}
-\indexentry{aperiodic|hyperpage}{319}
-\indexentry{aperiodic|hyperpage}{319}
-\indexentry{filtration|hyperpage}{320}
-\indexentry{filtration space|hyperpage}{320}
-\indexentry{$\sigma $-algebra generated by $\boldsymbol {\mathrm {X}}$|hyperpage}{320}
-\indexentry{stopping time|hyperpage}{320}
-\indexentry{Strong Markov property|hyperpage}{320}
+\indexentry{Lebesgue measure|hyperpage}{293}
+\indexentry{real function|hyperpage}{294}
+\indexentry{finite|hyperpage}{294}
+\indexentry{Lebesgue measurable|hyperpage}{294}
+\indexentry{measurable|hyperpage}{294}
+\indexentry{Borel $\sigma $-algebra|hyperpage}{295}
+\indexentry{Borel measurable|hyperpage}{295}
+\indexentry{simple function|hyperpage}{295}
+\indexentry{integral of $s$ over $\ensuremath {\mathbb {R}}^n$|hyperpage}{295}
+\indexentry{integral of $s$ over a measurable set $E$|hyperpage}{295}
+\indexentry{integral of $f$ over $\ensuremath {\mathbb {R}}^n$|hyperpage}{296}
+\indexentry{integral of $f$ over a measurable set $E\subseteq \ensuremath {\mathbb {R}}^n$|hyperpage}{296}
+\indexentry{Monotone convergence theorem|hyperpage}{296}
+\indexentry{Chebyshev's inequality|hyperpage}{297}
+\indexentry{Fatou's lemma|hyperpage}{297}
+\indexentry{integral of $f$ over $E$|hyperpage}{297}
+\indexentry{integrable function over $E$|hyperpage}{297}
+\indexentry{Dominated convergence theorem|hyperpage}{297}
+\indexentry{converge in mean|hyperpage}{298}
+\indexentry{exists and it is finite|hyperpage}{298}
+\indexentry{Mean value theorem for integrals|hyperpage}{298}
+\indexentry{Barrow's law|hyperpage}{298}
+\indexentry{Fundamental theorem of calculus|hyperpage}{298}
+\indexentry{Integration by parts|hyperpage}{298}
+\indexentry{Hardy-Littlewood maximal function|hyperpage}{298}
+\indexentry{Hardy-Littlewood maximal function|hyperpage}{298}
+\indexentry{Lebesgue differentiation theorem|hyperpage}{299}
+\indexentry{section|hyperpage}{299}
+\indexentry{Tonelli's theorem|hyperpage}{299}
+\indexentry{Fubini's theorem|hyperpage}{300}
+\indexentry{change of variables|hyperpage}{300}
+\indexentry{Change of variables|hyperpage}{300}
+\indexentry{distance|hyperpage}{300}
+\indexentry{triangular inequality|hyperpage}{300}
+\indexentry{metric space|hyperpage}{300}
+\indexentry{complete|hyperpage}{300}
+\indexentry{norm|hyperpage}{300}
+\indexentry{triangular inequality|hyperpage}{300}
+\indexentry{normed vector space|hyperpage}{300}
+\indexentry{convergent series|hyperpage}{300}
+\indexentry{absolutely convergent|hyperpage}{300}
+\indexentry{Banach space|hyperpage}{301}
+\indexentry{Banach space|hyperpage}{301}
+\indexentry{uniform norm|hyperpage}{301}
+\indexentry{total subset|hyperpage}{301}
+\indexentry{separable|hyperpage}{301}
+\indexentry{quotient space|hyperpage}{302}
+\indexentry{Young's inequality for products|hyperpage}{302}
+\indexentry{Hölder conjugates|hyperpage}{302}
+\indexentry{Hölder's inequality|hyperpage}{302}
+\indexentry{Hölder's inequality|hyperpage}{303}
+\indexentry{Interpolation inequality|hyperpage}{303}
+\indexentry{Minkowski inequality|hyperpage}{303}
+\indexentry{uniform norm|hyperpage}{303}
+\indexentry{uniform norm|hyperpage}{303}
+\indexentry{supremum norm|hyperpage}{303}
+\indexentry{subalgebra|hyperpage}{303}
+\indexentry{separating set|hyperpage}{303}
+\indexentry{separate the points|hyperpage}{303}
+\indexentry{vanishes nowhere|hyperpage}{304}
+\indexentry{self-conjugate|hyperpage}{304}
+\indexentry{Stone-Weierstra\ss \ theorem|hyperpage}{304}
+\indexentry{pointwise bounded|hyperpage}{304}
+\indexentry{locally bounded|hyperpage}{304}
+\indexentry{uniformly bounded|hyperpage}{304}
+\indexentry{equicontinuous at a point|hyperpage}{304}
+\indexentry{pointwise equicontinuous|hyperpage}{304}
+\indexentry{uniformly equicontinuous|hyperpage}{304}
+\indexentry{Arzelà-Ascoli theorem|hyperpage}{304}
+\indexentry{operator|hyperpage}{305}
+\indexentry{norm|hyperpage}{305}
+\indexentry{sublinear|hyperpage}{306}
+\indexentry{Marcinkiewicz interpolation theorem|hyperpage}{306}
+\indexentry{topological homeomorphism|hyperpage}{306}
+\indexentry{isomorphic|hyperpage}{306}
+\indexentry{is finer than|hyperpage}{306}
+\indexentry{equivalent|hyperpage}{306}
+\indexentry{Almost orthogonality lemma|hyperpage}{306}
+\indexentry{Riesz's theorem|hyperpage}{306}
+\indexentry{normed algebra|hyperpage}{307}
+\indexentry{dual space|hyperpage}{307}
+\indexentry{compact operator|hyperpage}{307}
+\indexentry{Fredholm operator with kernel $K$|hyperpage}{307}
+\indexentry{Volterra operator with kernel $K$|hyperpage}{307}
+\indexentry{Hilbert-Schmidt operator with kernel $K$|hyperpage}{307}
+\indexentry{finite-rank operator|hyperpage}{307}
+\indexentry{Neumann series|hyperpage}{308}
+\indexentry{convex functional|hyperpage}{308}
+\indexentry{Hahn-Banach theorem|hyperpage}{308}
+\indexentry{prolongation|hyperpage}{308}
+\indexentry{Seminorm|hyperpage}{308}
+\indexentry{seminorm|hyperpage}{308}
+\indexentry{Hahn-Banach theorem|hyperpage}{308}
+\indexentry{Hahn-Banach theorem|hyperpage}{308}
+\indexentry{reflexive|hyperpage}{308}
+\indexentry{dual map|hyperpage}{308}
+\indexentry{proper subspace of $T$|hyperpage}{309}
+\indexentry{eigenvectors|hyperpage}{309}
+\indexentry{eigenvalue|hyperpage}{309}
+\indexentry{spectrum|hyperpage}{309}
+\indexentry{spectral values|hyperpage}{309}
+\indexentry{Baire's theorem|hyperpage}{309}
+\indexentry{Open mapping theorem|hyperpage}{309}
+\indexentry{Closed graph theorem|hyperpage}{309}
+\indexentry{Banach-Steinhaus theorem|hyperpage}{309}
+\indexentry{semilinear|hyperpage}{310}
+\indexentry{inner product|hyperpage}{310}
+\indexentry{pre-Hilbert space|hyperpage}{310}
+\indexentry{Cauchy-Schwarz inequality|hyperpage}{310}
+\indexentry{Minkowski inequality|hyperpage}{310}
+\indexentry{Polarization identity|hyperpage}{310}
+\indexentry{orthogonal|hyperpage}{310}
+\indexentry{orthogonal complement|hyperpage}{310}
+\indexentry{Pythagorean theorem|hyperpage}{310}
+\indexentry{Parallelogram law|hyperpage}{311}
+\indexentry{Hilbert space|hyperpage}{311}
+\indexentry{Hilbert space|hyperpage}{311}
+\indexentry{minimizer|hyperpage}{311}
+\indexentry{Projection theorem|hyperpage}{311}
+\indexentry{orthogonal projection on $F$|hyperpage}{311}
+\indexentry{Riesz representation theorem|hyperpage}{312}
+\indexentry{adjoint operator|hyperpage}{312}
+\indexentry{self-adjoint|hyperpage}{312}
+\indexentry{orthogonal system|hyperpage}{313}
+\indexentry{orthonormal system|hyperpage}{313}
+\indexentry{complete|hyperpage}{313}
+\indexentry{Hilbert basis|hyperpage}{313}
+\indexentry{Fourier coefficients|hyperpage}{313}
+\indexentry{Fourier series|hyperpage}{313}
+\indexentry{Gram-Schmidt process|hyperpage}{313}
+\indexentry{orthonormalization|hyperpage}{313}
+\indexentry{Bessel's inequality|hyperpage}{313}
+\indexentry{Fourier transform|hyperpage}{313}
+\indexentry{Riesz-Fischer theorem|hyperpage}{313}
+\indexentry{Parseval identity|hyperpage}{313}
+\indexentry{Spectral theorem|hyperpage}{313}
+\indexentry{Hilbert-Schmidt spectral representation theorem|hyperpage}{314}
+\indexentry{Fredholm alternative|hyperpage}{314}
+\indexentry{Law of total probability|hyperpage}{315}
+\indexentry{Substitution principle|hyperpage}{315}
+\indexentry{Law of total expectation|hyperpage}{315}
+\indexentry{Wald theorem|hyperpage}{315}
+\indexentry{probability-generating function|hyperpage}{316}
+\indexentry{pgf|hyperpage}{316}
+\indexentry{Stochastic process|hyperpage}{316}
+\indexentry{stochastic process|hyperpage}{316}
+\indexentry{parameter set|hyperpage}{316}
+\indexentry{state space|hyperpage}{316}
+\indexentry{independent|hyperpage}{316}
+\indexentry{Gambler's ruin problem|hyperpage}{318}
+\indexentry{Markov chain|hyperpage}{318}
+\indexentry{Markov property|hyperpage}{318}
+\indexentry{time-homogeneous Markov chain|hyperpage}{318}
+\indexentry{state space|hyperpage}{318}
+\indexentry{states|hyperpage}{318}
+\indexentry{Stochastic matrix|hyperpage}{318}
+\indexentry{stochastic matrix|hyperpage}{318}
+\indexentry{transition probabilities|hyperpage}{318}
+\indexentry{transition matrix|hyperpage}{318}
+\indexentry{initial distribution|hyperpage}{318}
+\indexentry{Random walk|hyperpage}{319}
+\indexentry{random walk|hyperpage}{319}
+\indexentry{simple random walk|hyperpage}{319}
+\indexentry{$n$-step transition probabilities|hyperpage}{319}
+\indexentry{$n$-step transition matrix|hyperpage}{319}
+\indexentry{$n$-step distribution|hyperpage}{319}
+\indexentry{Chapman-Kolmogorov equation|hyperpage}{320}
+\indexentry{reachable|hyperpage}{320}
+\indexentry{communicate|hyperpage}{320}
+\indexentry{irreducible class|hyperpage}{320}
+\indexentry{irreducible chain|hyperpage}{320}
+\indexentry{period|hyperpage}{320}
+\indexentry{aperiodic|hyperpage}{320}
+\indexentry{aperiodic|hyperpage}{320}
+\indexentry{filtration|hyperpage}{321}
+\indexentry{filtration space|hyperpage}{321}
+\indexentry{$\sigma $-algebra generated by $\boldsymbol {\mathrm {X}}$|hyperpage}{321}
+\indexentry{stopping time|hyperpage}{321}
\indexentry{Strong Markov property|hyperpage}{321}
-\indexentry{transient|hyperpage}{321}
-\indexentry{recurrent|hyperpage}{321}
-\indexentry{$k$-th hitting time|hyperpage}{321}
-\indexentry{recurrent|hyperpage}{323}
-\indexentry{transient|hyperpage}{323}
-\indexentry{Polya's theorem on $\ensuremath {\mathbb {Z}}$|hyperpage}{323}
-\indexentry{Polya's theorem on $\ensuremath {\mathbb {Z}}^2$|hyperpage}{323}
-\indexentry{Polya's theorem on $\ensuremath {\mathbb {Z}}^3$|hyperpage}{323}
-\indexentry{positive recurrent|hyperpage}{323}
-\indexentry{null recurrent|hyperpage}{323}
-\indexentry{Ergotic theorem|hyperpage}{323}
+\indexentry{Strong Markov property|hyperpage}{322}
+\indexentry{transient|hyperpage}{322}
+\indexentry{recurrent|hyperpage}{322}
+\indexentry{$k$-th hitting time|hyperpage}{322}
+\indexentry{recurrent|hyperpage}{324}
+\indexentry{transient|hyperpage}{324}
+\indexentry{Polya's theorem on $\ensuremath {\mathbb {Z}}$|hyperpage}{324}
+\indexentry{Polya's theorem on $\ensuremath {\mathbb {Z}}^2$|hyperpage}{324}
+\indexentry{Polya's theorem on $\ensuremath {\mathbb {Z}}^3$|hyperpage}{324}
+\indexentry{positive recurrent|hyperpage}{324}
+\indexentry{null recurrent|hyperpage}{324}
\indexentry{Ergotic theorem|hyperpage}{324}
-\indexentry{stationary distribution|hyperpage}{324}
-\indexentry{continuous-time Markov chain|hyperpage}{325}
-\indexentry{transition probabilities|hyperpage}{325}
-\indexentry{Chapman-Kolmogorov equation|hyperpage}{325}
-\indexentry{Poisson process|hyperpage}{325}
-\indexentry{independent increments|hyperpage}{325}
-\indexentry{stationary increments|hyperpage}{325}
-\indexentry{trajectories|hyperpage}{325}
-\indexentry{càd|hyperpage}{325}
-\indexentry{holding times|hyperpage}{326}
-\indexentry{inter-arrival times|hyperpage}{326}
-\indexentry{infinitesimal generator|hyperpage}{327}
-\indexentry{infinitesimal transition scheme|hyperpage}{327}
-\indexentry{Kolmogorov's backward equation|hyperpage}{327}
-\indexentry{Kolmogorov's forward equation|hyperpage}{327}
-\indexentry{jump process|hyperpage}{327}
-\indexentry{regular|hyperpage}{327}
-\indexentry{stable|hyperpage}{327}
-\indexentry{conservative|hyperpage}{327}
-\indexentry{stationary distribution|hyperpage}{328}
-\indexentry{balance equation|hyperpage}{328}
-\indexentry{irreducible|hyperpage}{328}
-\indexentry{limit distribution|hyperpage}{328}
-\indexentry{birth and death process|hyperpage}{328}
-\indexentry{pure death process|hyperpage}{328}
-\indexentry{pure birth process|hyperpage}{328}
-\indexentry{Reuter criterion|hyperpage}{329}
-\indexentry{gaussian vector|hyperpage}{329}
-\indexentry{gaussian process|hyperpage}{329}
-\indexentry{mean function|hyperpage}{329}
-\indexentry{covariance function|hyperpage}{329}
-\indexentry{Brownian motion|hyperpage}{329}
-\indexentry{Wiener process|hyperpage}{329}
-\indexentry{standard|hyperpage}{329}
-\indexentry{stochastically equivalent|hyperpage}{330}
-\indexentry{version|hyperpage}{330}
-\indexentry{indistinguishable|hyperpage}{330}
-\indexentry{Kolmogorov's continuity theorem|hyperpage}{330}
-\indexentry{Paley-Wiener-Zygmund theorem|hyperpage}{330}
-\indexentry{$d$-dimensional standard Brownian motion|hyperpage}{331}
-\indexentry{Law of the iterated logarithm|hyperpage}{332}
-\indexentry{Finite-dimensional distributions|hyperpage}{332}
-\indexentry{finite-dimensional distributions|hyperpage}{332}
-\indexentry{consistency condition|hyperpage}{332}
-\indexentry{Kolmogorov extension theorem|hyperpage}{332}
+\indexentry{Ergotic theorem|hyperpage}{325}
+\indexentry{stationary distribution|hyperpage}{325}
+\indexentry{continuous-time Markov chain|hyperpage}{326}
+\indexentry{transition probabilities|hyperpage}{326}
+\indexentry{Chapman-Kolmogorov equation|hyperpage}{326}
+\indexentry{Poisson process|hyperpage}{326}
+\indexentry{independent increments|hyperpage}{326}
+\indexentry{stationary increments|hyperpage}{326}
+\indexentry{trajectories|hyperpage}{326}
+\indexentry{càd|hyperpage}{326}
+\indexentry{holding times|hyperpage}{327}
+\indexentry{inter-arrival times|hyperpage}{327}
+\indexentry{infinitesimal generator|hyperpage}{328}
+\indexentry{infinitesimal transition scheme|hyperpage}{328}
+\indexentry{Kolmogorov's backward equation|hyperpage}{328}
+\indexentry{Kolmogorov's forward equation|hyperpage}{328}
+\indexentry{jump process|hyperpage}{328}
+\indexentry{regular|hyperpage}{328}
+\indexentry{stable|hyperpage}{328}
+\indexentry{conservative|hyperpage}{328}
+\indexentry{stationary distribution|hyperpage}{329}
+\indexentry{balance equation|hyperpage}{329}
+\indexentry{irreducible|hyperpage}{329}
+\indexentry{limit distribution|hyperpage}{329}
+\indexentry{birth and death process|hyperpage}{329}
+\indexentry{pure death process|hyperpage}{329}
+\indexentry{pure birth process|hyperpage}{329}
+\indexentry{Reuter criterion|hyperpage}{330}
+\indexentry{gaussian vector|hyperpage}{330}
+\indexentry{gaussian process|hyperpage}{330}
+\indexentry{mean function|hyperpage}{330}
+\indexentry{covariance function|hyperpage}{330}
+\indexentry{Brownian motion|hyperpage}{330}
+\indexentry{Wiener process|hyperpage}{330}
+\indexentry{standard|hyperpage}{330}
+\indexentry{stochastically equivalent|hyperpage}{331}
+\indexentry{version|hyperpage}{331}
+\indexentry{indistinguishable|hyperpage}{331}
+\indexentry{Kolmogorov's continuity theorem|hyperpage}{331}
+\indexentry{Paley-Wiener-Zygmund theorem|hyperpage}{331}
+\indexentry{$d$-dimensional standard Brownian motion|hyperpage}{332}
+\indexentry{Law of the iterated logarithm|hyperpage}{333}
+\indexentry{Finite-dimensional distributions|hyperpage}{333}
+\indexentry{finite-dimensional distributions|hyperpage}{333}
+\indexentry{consistency condition|hyperpage}{333}
+\indexentry{Kolmogorov extension theorem|hyperpage}{333}
+\indexentry{$\sigma $-algebra|hyperpage}{335}
+\indexentry{$\sigma $-algebra|hyperpage}{335}
+\indexentry{measurable space|hyperpage}{335}
+\indexentry{$\sigma $-algebra generated by $\mathcal {F}$|hyperpage}{335}
+\indexentry{measurable|hyperpage}{335}
+\indexentry{Measure|hyperpage}{335}
+\indexentry{measure|hyperpage}{335}
+\indexentry{measurable space|hyperpage}{335}
+\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{335}
+\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{335}
+\indexentry{Monotone convergence theorem|hyperpage}{335}
+\indexentry{Fatou's lemma|hyperpage}{335}
+\indexentry{Dominated convergence theorem|hyperpage}{335}
+\indexentry{Product measure|hyperpage}{335}
+\indexentry{product measure|hyperpage}{335}
+\indexentry{$\sigma $-finite|hyperpage}{335}
+\indexentry{Fubini|hyperpage}{335}
+\indexentry{density|hyperpage}{336}
+\indexentry{absolutely continuous|hyperpage}{336}
+\indexentry{Radon-Nikodym|hyperpage}{336}
+\indexentry{probability space|hyperpage}{336}
+\indexentry{events|hyperpage}{336}
+\indexentry{Random variable|hyperpage}{336}
+\indexentry{$E$-valued random variable|hyperpage}{336}
+\indexentry{Expectation|hyperpage}{336}
+\indexentry{expectation of $X$|hyperpage}{336}
+\indexentry{law of $X$|hyperpage}{336}
+\indexentry{$\sigma $-algebra generated by $X$|hyperpage}{336}
+\indexentry{Jensen's inequality|hyperpage}{336}
+\indexentry{conditional expectation of $X$ given $\mathcal {G}$|hyperpage}{336}
+\indexentry{Tower property|hyperpage}{337}
+\indexentry{conditional expectation of $X$ given $Y$|hyperpage}{337}
+\indexentry{probability kernel|hyperpage}{337}
+\indexentry{conditional law of $X$ given $Y$|hyperpage}{337}
+\indexentry{Sobolev spaces|hyperpage}{338}
+\indexentry{Sobolev spaces|hyperpage}{338}
+\indexentry{Poincaré's inequality|hyperpage}{338}
+\indexentry{Poincaré-Wirtinger's inequality|hyperpage}{338}
diff --git a/main_math.ilg b/main_math.ilg
index 1e7cd1c..ce7d395 100644
--- a/main_math.ilg
+++ b/main_math.ilg
@@ -1,6 +1,6 @@
This is makeindex, version 2.17 [TeX Live 2023] (kpathsea + Thai support).
-Scanning input file main_math.idx.......done (3055 entries accepted, 0 rejected).
-Sorting entries..............................done (39602 comparisons).
-Generating output file main_math.ind......done (2608 lines written, 0 warnings).
+Scanning input file main_math.idx.......done (3096 entries accepted, 0 rejected).
+Sorting entries..............................done (40266 comparisons).
+Generating output file main_math.ind......done (2638 lines written, 0 warnings).
Output written in main_math.ind.
Transcript written in main_math.ilg.
diff --git a/main_math.ind b/main_math.ind
index e5869d4..a53789b 100644
--- a/main_math.ind
+++ b/main_math.ind
@@ -1,2608 +1,2638 @@
\begin{theindex}
- \item $(G,\cdot )$-space, \hyperpage{210}
+ \item $(G,\cdot )$-space, \hyperpage{211}
+ \item $E$-valued random variable, \hyperpage{336}
\item $F$-distribution with degrees of freedom $d_1$ and $d_2$,
- \hyperpage{251}
- \item $F$-linearly independent, \hyperpage{169}
- \item $K$-field morphism, \hyperpage{164}
- \item $N$-th partial sum of $Sf$, \hyperpage{82}
- \item $N$-th partial sum of the series, \hyperpage{75},
- \hyperpage{104}
- \item $P$ and $Q$ are both true, \hyperpage{7}
- \item $P$ and $Q$ have the same truth-value, \hyperpage{7}
- \item $Q$ is true whenever $P$ is true, \hyperpage{7}
- \item $T$-periodic, \hyperpage{80}
- \item $T_0$ space, \hyperpage{211}
- \item $T_1$ space, \hyperpage{211}
- \item $T_2$ space, \hyperpage{211}
- \item $T_3$ space, \hyperpage{211}
- \item $T_4$ space, \hyperpage{211}
- \item $T_{2\frac {1}{2}}$ space, \hyperpage{211}
- \item $\alpha $-limit point, \hyperpage{130}
- \item $\alpha $-limit set, \hyperpage{130}
- \item $\ensuremath {\mathbb {C}}$-differentiable, \hyperpage{108}
- \item $\ensuremath {\mathbb {R}}$-differentiable, \hyperpage{109}
- \item $\omega $-limit point, \hyperpage{130}
- \item $\omega $-limit set, \hyperpage{130}
- \item $\sigma $-additivity, \hyperpage{172}, \hyperpage{290}
- \item $\sigma $-algebra, \hyperpage{171}, \hyperpage{290}
- \item $\sigma $-algebra generated, \hyperpage{171}
+ \hyperpage{252}
+ \item $F$-linearly independent, \hyperpage{170}
+ \item $K$-field morphism, \hyperpage{165}
+ \item $N$-th partial sum of $Sf$, \hyperpage{83}
+ \item $N$-th partial sum of the series, \hyperpage{76},
+ \hyperpage{105}
+ \item $P$ and $Q$ are both true, \hyperpage{8}
+ \item $P$ and $Q$ have the same truth-value, \hyperpage{8}
+ \item $Q$ is true whenever $P$ is true, \hyperpage{8}
+ \item $T$-periodic, \hyperpage{81}
+ \item $T_0$ space, \hyperpage{212}
+ \item $T_1$ space, \hyperpage{212}
+ \item $T_2$ space, \hyperpage{212}
+ \item $T_3$ space, \hyperpage{212}
+ \item $T_4$ space, \hyperpage{212}
+ \item $T_{2\frac {1}{2}}$ space, \hyperpage{212}
+ \item $\alpha $-limit point, \hyperpage{131}
+ \item $\alpha $-limit set, \hyperpage{131}
+ \item $\ensuremath {\mathbb {C}}$-differentiable, \hyperpage{109}
+ \item $\ensuremath {\mathbb {R}}$-differentiable, \hyperpage{110}
+ \item $\omega $-limit point, \hyperpage{131}
+ \item $\omega $-limit set, \hyperpage{131}
+ \item $\sigma $-additivity, \hyperpage{173}, \hyperpage{291}
+ \item $\sigma $-algebra, \hyperpage{172}, \hyperpage{291},
+ \hyperpage{335}
+ \item $\sigma $-algebra generated, \hyperpage{172}
+ \item $\sigma $-algebra generated by $X$, \hyperpage{336}
\item $\sigma $-algebra generated by $\boldsymbol {\mathrm {X}}$,
- \hyperpage{320}
+ \hyperpage{321}
+ \item $\sigma $-algebra generated by $\mathcal {F}$, \hyperpage{335}
\item $\sigma $-algebra of all Lebesgue measurable sets in $\ensuremath {\mathbb {R}}^n$,
- \hyperpage{174}
- \item $d$-dimensional standard Brownian motion, \hyperpage{331}
- \item $i$-th pivot, \hyperpage{13}
- \item $k$-linear map, \hyperpage{154}
- \item $k$-th hitting time, \hyperpage{321}
- \item $m$-dimensional projective subvariety, \hyperpage{66}
- \item $m$-th dyadic cube, \hyperpage{290}
- \item $n$-dimensional projective space, \hyperpage{66}
- \item $n$-dimensional volume, \hyperpage{57, 58}
- \item $n$-periodic, \hyperpage{89}
- \item $n$-step distribution, \hyperpage{318}
- \item $n$-step transition matrix, \hyperpage{318}
- \item $n$-step transition probabilities, \hyperpage{318}
- \item $n$-th Fourier coefficient, \hyperpage{82}
- \item $n$-th Lyapunov constant, \hyperpage{225}
- \item $n$-th ball, \hyperpage{209}
- \item $n$-th cyclotomic polynomial, \hyperpage{163}
+ \hyperpage{175}
+ \item $\sigma $-finite, \hyperpage{335}
+ \item $d$-dimensional standard Brownian motion, \hyperpage{332}
+ \item $i$-th pivot, \hyperpage{14}
+ \item $k$-linear map, \hyperpage{155}
+ \item $k$-th hitting time, \hyperpage{322}
+ \item $m$-dimensional projective subvariety, \hyperpage{67}
+ \item $m$-th dyadic cube, \hyperpage{291}
+ \item $n$-dimensional projective space, \hyperpage{67}
+ \item $n$-dimensional volume, \hyperpage{58, 59}
+ \item $n$-periodic, \hyperpage{90}
+ \item $n$-step distribution, \hyperpage{319}
+ \item $n$-step transition matrix, \hyperpage{319}
+ \item $n$-step transition probabilities, \hyperpage{319}
+ \item $n$-th Fourier coefficient, \hyperpage{83}
+ \item $n$-th Lyapunov constant, \hyperpage{226}
+ \item $n$-th ball, \hyperpage{210}
+ \item $n$-th cyclotomic polynomial, \hyperpage{164}
\item $n$-th derivative of $f$ at the point $a\in \ensuremath {\mathbb {R}}$,
- \hyperpage{30}
- \item $n$-th primitive root of unity, \hyperpage{169}
- \item $n$-th root of unity, \hyperpage{169}
- \item $n-1$-th sphere, \hyperpage{209}
- \item $p$-group, \hyperpage{40}
- \item $p$-value, \hyperpage{198}
- \item $s$-stage Runge-Kutta methods, \hyperpage{259}
- \item $t$-test, \hyperpage{200}
- \item $x$-simple, \hyperpage{58}
- \item $xy$-simple, \hyperpage{58}
- \item $xz$-simple, \hyperpage{58}
- \item $y$-simple, \hyperpage{58}
- \item $yz$-simple, \hyperpage{58}
- \item (left) $G$-set, \hyperpage{39}
- \item (left) group action, \hyperpage{39}
- \item 2-forms, \hyperpage{61}
- \item 3-forms, \hyperpage{61}
+ \hyperpage{31}
+ \item $n$-th primitive root of unity, \hyperpage{170}
+ \item $n$-th root of unity, \hyperpage{170}
+ \item $n-1$-th sphere, \hyperpage{210}
+ \item $p$-group, \hyperpage{41}
+ \item $p$-value, \hyperpage{199}
+ \item $s$-stage Runge-Kutta methods, \hyperpage{260}
+ \item $t$-test, \hyperpage{201}
+ \item $x$-simple, \hyperpage{59}
+ \item $xy$-simple, \hyperpage{59}
+ \item $xz$-simple, \hyperpage{59}
+ \item $y$-simple, \hyperpage{59}
+ \item $yz$-simple, \hyperpage{59}
+ \item (left) $G$-set, \hyperpage{40}
+ \item (left) group action, \hyperpage{40}
+ \item 2-forms, \hyperpage{62}
+ \item 3-forms, \hyperpage{62}
\indexspace
- \item A-stable, \hyperpage{260}
- \item a.e., \hyperpage{292}
- \item Abel's summation formula, \hyperpage{76}, \hyperpage{105}
- \item Abel's test, \hyperpage{76, 77}, \hyperpage{79},
- \hyperpage{106}
- \item Abel's theorem, \hyperpage{78}, \hyperpage{107}
- \item Abel-Ruffini theorem, \hyperpage{170}
- \item abelian, \hyperpage{36}, \hyperpage{169}
- \item absolute condition numbers, \hyperpage{88}
- \item absolute error, \hyperpage{88}
- \item Absolute geometry, \hyperpage{63}
- \item absolute value, \hyperpage{24}
- \item absolutely continuous, \hyperpage{177}, \hyperpage{179}
- \item absolutely convergent, \hyperpage{76}, \hyperpage{105},
- \hyperpage{116}, \hyperpage{299}
- \item absolutely stable, \hyperpage{260}
- \item acceptation region, \hyperpage{198}
- \item ACCP, \hyperpage{45}
- \item accumulation point, \hyperpage{25}, \hyperpage{53}
- \item action, \hyperpage{210}, \hyperpage{277}
- \item Adams method, \hyperpage{261}
- \item Adams-Bashforth method, \hyperpage{261}
- \item Adams-Moulton method, \hyperpage{261}
- \item adherence, \hyperpage{53}
- \item adherent point, \hyperpage{53}, \hyperpage{206}
- \item adjacency matrix, \hyperpage{49}
- \item adjacent, \hyperpage{48}
- \item adjoint, \hyperpage{23}
- \item adjoint operator, \hyperpage{311}
- \item adjugate matrix, \hyperpage{14}
- \item adjusted coefficient of determination, \hyperpage{251}
- \item affine combination, \hyperpage{68}
- \item affine coordinates, \hyperpage{69}
- \item Affine Gra\ss mann formulas, \hyperpage{69}
- \item affine plane, \hyperpage{65}
- \item affine space, \hyperpage{68}
- \item affine subvariety, \hyperpage{69}
- \item affinely independents, \hyperpage{68}
- \item affinity, \hyperpage{69}
- \item AIC, \hyperpage{256}
- \item Aitken's $\Delta ^2$ method, \hyperpage{90}
- \item Akaike information criterion, \hyperpage{256}
- \item Algebra, \hyperpage{171}
- \item algebra, \hyperpage{171}
- \item algebraic, \hyperpage{163, 164}
- \item algebraic closure, \hyperpage{169}
- \item algebraic curve, \hyperpage{134}
- \item algebraic multiplicity, \hyperpage{19}
- \item algebraic value, \hyperpage{152}
- \item algebraically closed, \hyperpage{169}
- \item algebraically closed field, \hyperpage{20}
- \item almost everywhere, \hyperpage{292}
- \item Almost orthogonality lemma, \hyperpage{305}
- \item alternating, \hyperpage{154}
- \item alternating group, \hyperpage{41}
- \item alternating series, \hyperpage{76}
- \item alternative hypothesis, \hyperpage{198}
- \item amplification factor, \hyperpage{269}
- \item amplification polynomial, \hyperpage{272}
- \item Ampère's law, \hyperpage{277}
- \item Ampère-Maxwell circuital law, \hyperpage{277}
- \item an asymptotically normal estimator, \hyperpage{193}
- \item analytic, \hyperpage{78}, \hyperpage{112}
- \item analytic at $a$, \hyperpage{31}
- \item Analytic continuation theorem, \hyperpage{113}
- \item angle, \hyperpage{23}, \hyperpage{62}
- \item angle-preserving, \hyperpage{148}
- \item anisotropic, \hyperpage{73}
- \item annihilator, \hyperpage{18}
- \item aperiodic, \hyperpage{319}
- \item approximation of identity, \hyperpage{78}, \hyperpage{240}
- \item approximations of the identity, \hyperpage{234}
- \item arc length, \hyperpage{59}
- \item arc length parameter, \hyperpage{59}
- \item arc-length function, \hyperpage{141}
- \item arc-length parameter, \hyperpage{140}
- \item Archimedean, \hyperpage{63}
- \item Archimedean property, \hyperpage{24}
- \item argument, \hyperpage{103}
- \item Argument principle, \hyperpage{117}
- \item Artin's lemma, \hyperpage{168}
- \item Arzelà-Ascoli theorem, \hyperpage{120}, \hyperpage{124},
- \hyperpage{303}
- \item ASA criterion, \hyperpage{63}
- \item ascending chain condition on principal ideals, \hyperpage{45}
- \item associated, \hyperpage{44}
- \item associated multivalued function, \hyperpage{109}
- \item Associative property, \hyperpage{75}
- \item Asymptotic behaviour of the LRT, \hyperpage{199}
- \item asymptotic direction, \hyperpage{149}
- \item asymptotic efficient estimator, \hyperpage{195}
- \item asymptotic error constant, \hyperpage{90}
- \item asymptotic line, \hyperpage{149}
- \item asymptotically stable, \hyperpage{130}
- \item asymptotically unbiased estimator, \hyperpage{193}
- \item atlas, \hyperpage{215}
- \item attracting, \hyperpage{130}
- \item attracting parabolic sector, \hyperpage{132}
- \item attractor fixed point, \hyperpage{90}
- \item auto-adjoint, \hyperpage{23}
- \item autonomous, \hyperpage{121}
- \item average, \hyperpage{288}
- \item average response, \hyperpage{252}
- \item Axiom of Archimedes, \hyperpage{62}
- \item Axiom of choice, \hyperpage{212}
- \item Axiom of completeness, \hyperpage{62}
- \item Axiom of extensionality, \hyperpage{5}
- \item Axiom of Parallels, \hyperpage{63}
- \item axiomatic projective space, \hyperpage{65}
- \item axis of perspectivity, \hyperpage{67}
+ \item A-stable, \hyperpage{261}
+ \item a.e., \hyperpage{293}
+ \item Abel's summation formula, \hyperpage{77}, \hyperpage{106}
+ \item Abel's test, \hyperpage{77, 78}, \hyperpage{80},
+ \hyperpage{107}
+ \item Abel's theorem, \hyperpage{79}, \hyperpage{108}
+ \item Abel-Ruffini theorem, \hyperpage{171}
+ \item abelian, \hyperpage{37}, \hyperpage{170}
+ \item absolute condition numbers, \hyperpage{89}
+ \item absolute error, \hyperpage{89}
+ \item Absolute geometry, \hyperpage{64}
+ \item absolute value, \hyperpage{25}
+ \item absolutely continuous, \hyperpage{178}, \hyperpage{180},
+ \hyperpage{336}
+ \item absolutely convergent, \hyperpage{77}, \hyperpage{106},
+ \hyperpage{117}, \hyperpage{300}
+ \item absolutely stable, \hyperpage{261}
+ \item acceptation region, \hyperpage{199}
+ \item ACCP, \hyperpage{46}
+ \item accumulation point, \hyperpage{26}, \hyperpage{54}
+ \item action, \hyperpage{211}, \hyperpage{278}
+ \item Adams method, \hyperpage{262}
+ \item Adams-Bashforth method, \hyperpage{262}
+ \item Adams-Moulton method, \hyperpage{262}
+ \item adherence, \hyperpage{54}
+ \item adherent point, \hyperpage{54}, \hyperpage{207}
+ \item adjacency matrix, \hyperpage{50}
+ \item adjacent, \hyperpage{49}
+ \item adjoint, \hyperpage{24}
+ \item adjoint operator, \hyperpage{312}
+ \item adjugate matrix, \hyperpage{15}
+ \item adjusted coefficient of determination, \hyperpage{252}
+ \item affine combination, \hyperpage{69}
+ \item affine coordinates, \hyperpage{70}
+ \item Affine Gra\ss mann formulas, \hyperpage{70}
+ \item affine plane, \hyperpage{66}
+ \item affine space, \hyperpage{69}
+ \item affine subvariety, \hyperpage{70}
+ \item affinely independents, \hyperpage{69}
+ \item affinity, \hyperpage{70}
+ \item AIC, \hyperpage{257}
+ \item Aitken's $\Delta ^2$ method, \hyperpage{91}
+ \item Akaike information criterion, \hyperpage{257}
+ \item Algebra, \hyperpage{172}
+ \item algebra, \hyperpage{172}
+ \item algebraic, \hyperpage{164, 165}
+ \item algebraic closure, \hyperpage{170}
+ \item algebraic curve, \hyperpage{135}
+ \item algebraic multiplicity, \hyperpage{20}
+ \item algebraic value, \hyperpage{153}
+ \item algebraically closed, \hyperpage{170}
+ \item algebraically closed field, \hyperpage{21}
+ \item almost everywhere, \hyperpage{293}
+ \item Almost orthogonality lemma, \hyperpage{306}
+ \item alternating, \hyperpage{155}
+ \item alternating group, \hyperpage{42}
+ \item alternating series, \hyperpage{77}
+ \item alternative hypothesis, \hyperpage{199}
+ \item amplification factor, \hyperpage{270}
+ \item amplification polynomial, \hyperpage{273}
+ \item Ampère's law, \hyperpage{278}
+ \item Ampère-Maxwell circuital law, \hyperpage{278}
+ \item an asymptotically normal estimator, \hyperpage{194}
+ \item analytic, \hyperpage{79}, \hyperpage{113}
+ \item analytic at $a$, \hyperpage{32}
+ \item Analytic continuation theorem, \hyperpage{114}
+ \item angle, \hyperpage{24}, \hyperpage{63}
+ \item angle-preserving, \hyperpage{149}
+ \item anisotropic, \hyperpage{74}
+ \item annihilator, \hyperpage{19}
+ \item aperiodic, \hyperpage{320}
+ \item approximation of identity, \hyperpage{79}, \hyperpage{241}
+ \item approximations of the identity, \hyperpage{235}
+ \item arc length, \hyperpage{60}
+ \item arc length parameter, \hyperpage{60}
+ \item arc-length function, \hyperpage{142}
+ \item arc-length parameter, \hyperpage{141}
+ \item Archimedean, \hyperpage{64}
+ \item Archimedean property, \hyperpage{25}
+ \item argument, \hyperpage{104}
+ \item Argument principle, \hyperpage{118}
+ \item Artin's lemma, \hyperpage{169}
+ \item Arzelà-Ascoli theorem, \hyperpage{121}, \hyperpage{125},
+ \hyperpage{304}
+ \item ASA criterion, \hyperpage{64}
+ \item ascending chain condition on principal ideals, \hyperpage{46}
+ \item associated, \hyperpage{45}
+ \item associated multivalued function, \hyperpage{110}
+ \item Associative property, \hyperpage{76}
+ \item Asymptotic behaviour of the LRT, \hyperpage{200}
+ \item asymptotic direction, \hyperpage{150}
+ \item asymptotic efficient estimator, \hyperpage{196}
+ \item asymptotic error constant, \hyperpage{91}
+ \item asymptotic line, \hyperpage{150}
+ \item asymptotically stable, \hyperpage{131}
+ \item asymptotically unbiased estimator, \hyperpage{194}
+ \item atlas, \hyperpage{216}
+ \item attracting, \hyperpage{131}
+ \item attracting parabolic sector, \hyperpage{133}
+ \item attractor fixed point, \hyperpage{91}
+ \item auto-adjoint, \hyperpage{24}
+ \item autonomous, \hyperpage{122}
+ \item average, \hyperpage{289}
+ \item average response, \hyperpage{253}
+ \item Axiom of Archimedes, \hyperpage{63}
+ \item Axiom of choice, \hyperpage{213}
+ \item Axiom of completeness, \hyperpage{63}
+ \item Axiom of extensionality, \hyperpage{6}
+ \item Axiom of Parallels, \hyperpage{64}
+ \item axiomatic projective space, \hyperpage{66}
+ \item axis of perspectivity, \hyperpage{68}
\indexspace
- \item backward Euler method, \hyperpage{257}
- \item Backward-time central-space, \hyperpage{267}, \hyperpage{273}
- \item Baire's theorem, \hyperpage{308}
- \item balance equation, \hyperpage{328}
- \item ball, \hyperpage{204}
- \item Banach fixed-point theorem, \hyperpage{124}
- \item Banach space, \hyperpage{300}
- \item Banach-Steinhaus theorem, \hyperpage{308}
- \item bandlimited, \hyperpage{238}
- \item Barrow's law, \hyperpage{297}
- \item barycenter, \hyperpage{68}
- \item Basic bootstrap confidence interval, \hyperpage{201}
- \item basic bootstrap confidence interval, \hyperpage{201}
- \item basic feasible solutions, \hyperpage{50}
- \item basin, \hyperpage{130}
- \item basis, \hyperpage{15}, \hyperpage{205}
- \item Bautin's theorem, \hyperpage{225}
- \item Bayes estimate, \hyperpage{202}
- \item Bayes' formula, \hyperpage{173}
- \item Bayesian point estimates, \hyperpage{202}
- \item Bendixson's theorem, \hyperpage{136}
- \item Bendixson-Dulac theorem, \hyperpage{136}
- \item Bernoulli differential equation, \hyperpage{122}
- \item Bernoulli distribution, \hyperpage{176}
- \item Bernoulli numbers, \hyperpage{95}
- \item Bernoulli polynomials, \hyperpage{95}
- \item Bessel's inequality, \hyperpage{86}, \hyperpage{312}
- \item Beta distribution, \hyperpage{178}
- \item beta distribution, \hyperpage{178}
- \item beta function, \hyperpage{178}
- \item BFGS method, \hyperpage{263}
- \item Bias, \hyperpage{192}
- \item bias, \hyperpage{192}
- \item Bias on the estimations, \hyperpage{254}
- \item Bias on the predictions, \hyperpage{254}
- \item biased estimator, \hyperpage{192}
- \item bijective, \hyperpage{6}
- \item bilinear, \hyperpage{21}
- \item bilinear form, \hyperpage{21}
- \item Binomial coefficient formulas, \hyperpage{8}
- \item Binomial distribution, \hyperpage{176}
- \item binomial distribution, \hyperpage{176}
- \item Binomial theorem, \hyperpage{118}
- \item binormal vector, \hyperpage{142}
- \item bipartite, \hyperpage{49}
- \item birth and death process, \hyperpage{328}
- \item Bisection method, \hyperpage{89}
- \item block matrix, \hyperpage{14}
- \item blow-down, \hyperpage{224}
- \item Blow-up in cartesian coordinates, \hyperpage{225}
- \item Blow-up in generalized polar coordinates, \hyperpage{224}
- \item Blow-up in polar coordinates, \hyperpage{224}
- \item blowing-up, \hyperpage{224}
- \item BLUE, \hyperpage{250}
- \item Bogdanov-Takens bifurcation, \hyperpage{226}
- \item Bolzano's theorem, \hyperpage{27}, \hyperpage{214}
- \item Bolzano-Weierstra\ss \ theorem, \hyperpage{26}, \hyperpage{53}
- \item Bonferroni's method, \hyperpage{251}
- \item Bonnet's theorem, \hyperpage{151}
- \item Boolean ring, \hyperpage{41}
- \item bootstrap distribution, \hyperpage{201}
- \item Bootstrap-t confidence interval, \hyperpage{201}
- \item bootstrap-t confidence interval, \hyperpage{201}
- \item Borel $\sigma $-algebra, \hyperpage{171}, \hyperpage{294}
- \item Borel measurable, \hyperpage{180}, \hyperpage{294}
- \item Borel's theorem, \hyperpage{189}
- \item Borsuk-Ulam theorem, \hyperpage{214}
- \item Boundary, \hyperpage{206}
- \item boundary, \hyperpage{53}, \hyperpage{156}, \hyperpage{206}
- \item boundary point, \hyperpage{53}
- \item bounded, \hyperpage{25, 26}, \hyperpage{104}
- \item bounded by compact sets, \hyperpage{120}
- \item bounded from above, \hyperpage{24, 25}
- \item bounded from below, \hyperpage{24, 25}
- \item bounded set, \hyperpage{53}
- \item box topology, \hyperpage{208}
- \item Box-Cox transformation, \hyperpage{256}
- \item bridge, \hyperpage{49}
- \item Brouwer's fixed-point theorem, \hyperpage{214}
- \item Brownian motion, \hyperpage{329}
- \item Broyden's method, \hyperpage{262}
- \item Broyden-Fletcher-Goldfarb-Shanno method, \hyperpage{263}
- \item BTCS, \hyperpage{267}
- \item Budan-Fourier theorem, \hyperpage{91}
- \item bump functions, \hyperpage{239}
- \item Butcher tableau, \hyperpage{259}
- \item Bézout's theorem, \hyperpage{9, 10}
+ \item backward Euler method, \hyperpage{258}
+ \item Backward-time central-space, \hyperpage{268}, \hyperpage{274}
+ \item Baire's theorem, \hyperpage{309}
+ \item balance equation, \hyperpage{329}
+ \item ball, \hyperpage{205}
+ \item Banach fixed-point theorem, \hyperpage{125}
+ \item Banach space, \hyperpage{301}
+ \item Banach-Steinhaus theorem, \hyperpage{309}
+ \item bandlimited, \hyperpage{239}
+ \item Barrow's law, \hyperpage{298}
+ \item barycenter, \hyperpage{69}
+ \item Basic bootstrap confidence interval, \hyperpage{202}
+ \item basic bootstrap confidence interval, \hyperpage{202}
+ \item basic feasible solutions, \hyperpage{51}
+ \item basin, \hyperpage{131}
+ \item basis, \hyperpage{16}, \hyperpage{206}
+ \item Bautin's theorem, \hyperpage{226}
+ \item Bayes estimate, \hyperpage{203}
+ \item Bayes' formula, \hyperpage{174}
+ \item Bayesian point estimates, \hyperpage{203}
+ \item Bendixson's theorem, \hyperpage{137}
+ \item Bendixson-Dulac theorem, \hyperpage{137}
+ \item Bernoulli differential equation, \hyperpage{123}
+ \item Bernoulli distribution, \hyperpage{177}
+ \item Bernoulli numbers, \hyperpage{96}
+ \item Bernoulli polynomials, \hyperpage{96}
+ \item Bessel's inequality, \hyperpage{87}, \hyperpage{313}
+ \item Beta distribution, \hyperpage{179}
+ \item beta distribution, \hyperpage{179}
+ \item beta function, \hyperpage{179}
+ \item BFGS method, \hyperpage{264}
+ \item Bias, \hyperpage{193}
+ \item bias, \hyperpage{193}
+ \item Bias on the estimations, \hyperpage{255}
+ \item Bias on the predictions, \hyperpage{255}
+ \item biased estimator, \hyperpage{193}
+ \item bijective, \hyperpage{7}
+ \item bilinear, \hyperpage{22}
+ \item bilinear form, \hyperpage{22}
+ \item Binomial coefficient formulas, \hyperpage{9}
+ \item Binomial distribution, \hyperpage{177}
+ \item binomial distribution, \hyperpage{177}
+ \item Binomial theorem, \hyperpage{119}
+ \item binormal vector, \hyperpage{143}
+ \item bipartite, \hyperpage{50}
+ \item birth and death process, \hyperpage{329}
+ \item Bisection method, \hyperpage{90}
+ \item block matrix, \hyperpage{15}
+ \item blow-down, \hyperpage{225}
+ \item Blow-up in cartesian coordinates, \hyperpage{226}
+ \item Blow-up in generalized polar coordinates, \hyperpage{225}
+ \item Blow-up in polar coordinates, \hyperpage{225}
+ \item blowing-up, \hyperpage{225}
+ \item BLUE, \hyperpage{251}
+ \item Bogdanov-Takens bifurcation, \hyperpage{227}
+ \item Bolzano's theorem, \hyperpage{28}, \hyperpage{215}
+ \item Bolzano-Weierstra\ss \ theorem, \hyperpage{27}, \hyperpage{54}
+ \item Bonferroni's method, \hyperpage{252}
+ \item Bonnet's theorem, \hyperpage{152}
+ \item Boolean ring, \hyperpage{42}
+ \item bootstrap distribution, \hyperpage{202}
+ \item Bootstrap-t confidence interval, \hyperpage{202}
+ \item bootstrap-t confidence interval, \hyperpage{202}
+ \item Borel $\sigma $-algebra, \hyperpage{172}, \hyperpage{295}
+ \item Borel measurable, \hyperpage{181}, \hyperpage{295}
+ \item Borel's theorem, \hyperpage{191}
+ \item Borsuk-Ulam theorem, \hyperpage{215}
+ \item Boundary, \hyperpage{207}
+ \item boundary, \hyperpage{54}, \hyperpage{157}, \hyperpage{207}
+ \item boundary point, \hyperpage{54}
+ \item bounded, \hyperpage{26, 27}, \hyperpage{105}
+ \item bounded by compact sets, \hyperpage{121}
+ \item bounded from above, \hyperpage{25, 26}
+ \item bounded from below, \hyperpage{25, 26}
+ \item bounded set, \hyperpage{54}
+ \item box topology, \hyperpage{209}
+ \item Box-Cox transformation, \hyperpage{257}
+ \item bridge, \hyperpage{50}
+ \item Brouwer's fixed-point theorem, \hyperpage{215}
+ \item Brownian motion, \hyperpage{330}
+ \item Broyden's method, \hyperpage{263}
+ \item Broyden-Fletcher-Goldfarb-Shanno method, \hyperpage{264}
+ \item BTCS, \hyperpage{268}
+ \item Budan-Fourier theorem, \hyperpage{92}
+ \item bump functions, \hyperpage{240}
+ \item Butcher tableau, \hyperpage{260}
+ \item Bézout's theorem, \hyperpage{10, 11}
\indexspace
- \item Calculation of integrals, \hyperpage{116}
+ \item Calculation of integrals, \hyperpage{117}
\item canonical form of a linear programming to maximize,
- \hyperpage{50}
+ \hyperpage{51}
\item canonical form of a linear programming to minimize,
- \hyperpage{50}
- \item Cantor set, \hyperpage{208}
- \item Cantor's theorem, \hyperpage{8}
- \item Cantor-Bernstein theorem, \hyperpage{8}
- \item Cardano-Vieta's formulas, \hyperpage{113}
- \item cardinal, \hyperpage{5}
- \item Cartesian equations, \hyperpage{69}
- \item Cartesian form, \hyperpage{103}
- \item Cartesian geometry, \hyperpage{63}
- \item Cartesian product, \hyperpage{6}
- \item Casorati-Weierstra\ss \ theorem, \hyperpage{117}
- \item Cauchy, \hyperpage{104}
- \item Cauchy condition in $p$-th mean, \hyperpage{188}
- \item Cauchy condition in probability, \hyperpage{186}
- \item Cauchy distribution, \hyperpage{178}
- \item Cauchy in $p$-th mean, \hyperpage{188}
- \item Cauchy in probability, \hyperpage{186}
- \item Cauchy momentum equation, \hyperpage{276}
- \item Cauchy principal value, \hyperpage{240}
- \item Cauchy problem, \hyperpage{121}
- \item Cauchy product, \hyperpage{105}
- \item Cauchy sequence, \hyperpage{26}, \hyperpage{53}
- \item Cauchy's functional equation, \hyperpage{255}
- \item Cauchy's inequality, \hyperpage{113}
- \item Cauchy's integral theorem, \hyperpage{115}
- \item Cauchy's mean value theorem, \hyperpage{29}
- \item Cauchy's test, \hyperpage{75}, \hyperpage{77}, \hyperpage{79},
- \hyperpage{106}
- \item Cauchy's theorem, \hyperpage{40}
- \item Cauchy-Hadamard theorem, \hyperpage{106}
- \item Cauchy-Riemann equations, \hyperpage{110}
- \item Cauchy-Riemann theorem, \hyperpage{110}
- \item Cauchy-Schwarz inequality, \hyperpage{23}, \hyperpage{52},
- \hyperpage{81}, \hyperpage{184}, \hyperpage{309}
- \item Cavalieri's principle, \hyperpage{58}
- \item Cayley's theorem, \hyperpage{38}
- \item Cayley-Hamilton theorem, \hyperpage{20}
- \item CC, \hyperpage{63}
- \item cdf, \hyperpage{175}
- \item cells, \hyperpage{274}
- \item Center, \hyperpage{119}
- \item center, \hyperpage{40}, \hyperpage{130}, \hyperpage{132}
- \item Center of a group, \hyperpage{40}
- \item Center of mass, \hyperpage{58}
- \item center of mass, \hyperpage{58}
- \item Center of masses, \hyperpage{34}
- \item center of masses, \hyperpage{34}
- \item central manifolds, \hyperpage{222}
- \item centre of perspectivity, \hyperpage{67}
- \item Cesàro summable, \hyperpage{84}
- \item chain, \hyperpage{125}
- \item chain of paths, \hyperpage{114}
- \item Chain rule, \hyperpage{28}, \hyperpage{55}, \hyperpage{108}
- \item Change of basis formula, \hyperpage{17}
- \item change of parameter, \hyperpage{140}
- \item Change of variable theorem, \hyperpage{59}
- \item Change of variables, \hyperpage{158}, \hyperpage{299}
- \item change of variables, \hyperpage{299}
- \item change-of-basis matrix, \hyperpage{17}
- \item Chaos, \hyperpage{229}
- \item chaotic, \hyperpage{229}
- \item chaotic behavior, \hyperpage{90}
- \item Chapman-Kolmogorov equation, \hyperpage{319}, \hyperpage{325}
- \item characteristic, \hyperpage{161}
- \item characteristic curves, \hyperpage{278}
- \item Characteristic equation, \hyperpage{122}, \hyperpage{221}
- \item characteristic equation, \hyperpage{122}
- \item Characteristic function, \hyperpage{190}
- \item characteristic function, \hyperpage{8}, \hyperpage{190}
- \item characteristic polynomial, \hyperpage{19}, \hyperpage{48}
- \item Chebyshev method, \hyperpage{89}
- \item Chebyshev polynomials, \hyperpage{95}
- \item Chebyshev's inequality, \hyperpage{185}, \hyperpage{296}
+ \hyperpage{51}
+ \item Cantor set, \hyperpage{209}
+ \item Cantor's theorem, \hyperpage{9}
+ \item Cantor-Bernstein theorem, \hyperpage{9}
+ \item Cardano-Vieta's formulas, \hyperpage{114}
+ \item cardinal, \hyperpage{6}
+ \item Cartesian equations, \hyperpage{70}
+ \item Cartesian form, \hyperpage{104}
+ \item Cartesian geometry, \hyperpage{64}
+ \item Cartesian product, \hyperpage{7}
+ \item Casorati-Weierstra\ss \ theorem, \hyperpage{118}
+ \item Cauchy, \hyperpage{105}
+ \item Cauchy condition in $p$-th mean, \hyperpage{189}
+ \item Cauchy condition in probability, \hyperpage{187}
+ \item Cauchy distribution, \hyperpage{179}
+ \item Cauchy in $p$-th mean, \hyperpage{189}
+ \item Cauchy in probability, \hyperpage{187}
+ \item Cauchy momentum equation, \hyperpage{277}
+ \item Cauchy principal value, \hyperpage{241}
+ \item Cauchy problem, \hyperpage{122}
+ \item Cauchy product, \hyperpage{106}
+ \item Cauchy sequence, \hyperpage{27}, \hyperpage{54}
+ \item Cauchy's functional equation, \hyperpage{256}
+ \item Cauchy's inequality, \hyperpage{114}
+ \item Cauchy's integral theorem, \hyperpage{116}
+ \item Cauchy's mean value theorem, \hyperpage{30}
+ \item Cauchy's test, \hyperpage{76}, \hyperpage{78}, \hyperpage{80},
+ \hyperpage{107}
+ \item Cauchy's theorem, \hyperpage{41}
+ \item Cauchy-Hadamard theorem, \hyperpage{107}
+ \item Cauchy-Riemann equations, \hyperpage{111}
+ \item Cauchy-Riemann theorem, \hyperpage{111}
+ \item Cauchy-Schwarz inequality, \hyperpage{24}, \hyperpage{53},
+ \hyperpage{82}, \hyperpage{185}, \hyperpage{310}
+ \item Cavalieri's principle, \hyperpage{59}
+ \item Cayley's theorem, \hyperpage{39}
+ \item Cayley-Hamilton theorem, \hyperpage{21}
+ \item CC, \hyperpage{64}
+ \item cdf, \hyperpage{176}
+ \item cells, \hyperpage{275}
+ \item Center, \hyperpage{120}
+ \item center, \hyperpage{41}, \hyperpage{131}, \hyperpage{133}
+ \item Center of a group, \hyperpage{41}
+ \item Center of mass, \hyperpage{59}
+ \item center of mass, \hyperpage{59}
+ \item Center of masses, \hyperpage{35}
+ \item center of masses, \hyperpage{35}
+ \item central manifolds, \hyperpage{223}
+ \item centre of perspectivity, \hyperpage{68}
+ \item Cesàro summable, \hyperpage{85}
+ \item chain, \hyperpage{126}
+ \item chain of paths, \hyperpage{115}
+ \item Chain rule, \hyperpage{29}, \hyperpage{56}, \hyperpage{109}
+ \item Change of basis formula, \hyperpage{18}
+ \item change of parameter, \hyperpage{141}
+ \item Change of variable theorem, \hyperpage{60}
+ \item Change of variables, \hyperpage{159}, \hyperpage{300}
+ \item change of variables, \hyperpage{300}
+ \item change-of-basis matrix, \hyperpage{18}
+ \item Chaos, \hyperpage{230}
+ \item chaotic, \hyperpage{230}
+ \item chaotic behavior, \hyperpage{91}
+ \item Chapman-Kolmogorov equation, \hyperpage{320}, \hyperpage{326}
+ \item characteristic, \hyperpage{162}
+ \item characteristic curves, \hyperpage{279}
+ \item Characteristic equation, \hyperpage{123}, \hyperpage{222}
+ \item characteristic equation, \hyperpage{123}
+ \item Characteristic function, \hyperpage{191}
+ \item characteristic function, \hyperpage{9}, \hyperpage{191}
+ \item characteristic polynomial, \hyperpage{20}, \hyperpage{49}
+ \item Chebyshev method, \hyperpage{90}
+ \item Chebyshev polynomials, \hyperpage{96}
+ \item Chebyshev's inequality, \hyperpage{186}, \hyperpage{297}
\item chi-squared distribution with $n$ degrees of freedom,
- \hyperpage{196}
- \item Chinese remainder theorem, \hyperpage{10}
- \item Christoffel symbols, \hyperpage{150}
- \item circle, \hyperpage{119}
- \item circulation, \hyperpage{60}, \hyperpage{158}
- \item class, \hyperpage{55}
- \item class $\mathcal {C}^\infty $ at $a$, \hyperpage{30}
+ \hyperpage{197}
+ \item Chinese remainder theorem, \hyperpage{11}
+ \item Christoffel symbols, \hyperpage{151}
+ \item circle, \hyperpage{120}
+ \item circulation, \hyperpage{61}, \hyperpage{159}
+ \item class, \hyperpage{56}
+ \item class $\mathcal {C}^\infty $ at $a$, \hyperpage{31}
\item class $\mathcal {C}^n$ at a point $a\in \ensuremath {\mathbb {R}}$,
- \hyperpage{30}
- \item class $\mathcal {C}^p$, \hyperpage{30}
- \item Classification of affine quadrics, \hyperpage{74}
- \item Classification of compact connected surfaces, \hyperpage{218}
- \item Classification of connected 1-manifolds, \hyperpage{216}
- \item Classification of cyclic groups, \hyperpage{37}
- \item Classification of Euclidean motions, \hyperpage{72}
- \item Classification of isometries, \hyperpage{72}
+ \hyperpage{31}
+ \item class $\mathcal {C}^p$, \hyperpage{31}
+ \item Classification of affine quadrics, \hyperpage{75}
+ \item Classification of compact connected surfaces, \hyperpage{219}
+ \item Classification of connected 1-manifolds, \hyperpage{217}
+ \item Classification of cyclic groups, \hyperpage{38}
+ \item Classification of Euclidean motions, \hyperpage{73}
+ \item Classification of isometries, \hyperpage{73}
\item Classification of projective qua\-drics in $\ensuremath {\mathbb {C}}$,
- \hyperpage{73}
- \item Classification of projective qua\-drics in $\ensuremath {\mathbb {F}}_q$,
\hyperpage{74}
+ \item Classification of projective qua\-drics in $\ensuremath {\mathbb {F}}_q$,
+ \hyperpage{75}
\item Classification of projective qua\-drics in $\ensuremath {\mathbb {R}}$,
- \hyperpage{74}
+ \hyperpage{75}
\item Classification of quadratic forms in $\ensuremath {\mathbb {C}}$,
- \hyperpage{73}
+ \hyperpage{74}
\item Classification of quadratic forms in $\ensuremath {\mathbb {F}}_q$,
- \hyperpage{73}
+ \hyperpage{74}
\item Classification of quadratic forms in $\ensuremath {\mathbb {R}}$,
- \hyperpage{73}
- \item clopen, \hyperpage{205}
- \item closed, \hyperpage{48}, \hyperpage{53}, \hyperpage{155},
- \hyperpage{205}, \hyperpage{207}
- \item closed ball, \hyperpage{53}
- \item Closed forms, \hyperpage{47}
- \item Closed function, \hyperpage{207}
- \item Closed graph theorem, \hyperpage{308}
- \item Closed interval, \hyperpage{24}
- \item Closed Newton-Cotes Formulas, \hyperpage{94}
- \item closed trail, \hyperpage{48}
- \item Closure, \hyperpage{205}
- \item closure, \hyperpage{205}
- \item Cochran's theorem, \hyperpage{251}
- \item Cocountable topology, \hyperpage{205}
- \item Codazzi-Mainardi equations, \hyperpage{151}
- \item codimension, \hyperpage{222}
- \item coefficient of determination, \hyperpage{251}
- \item coefficients, \hyperpage{10}
- \item cofactor, \hyperpage{135}
- \item cofactor matrix, \hyperpage{14}
- \item Cofinite topology, \hyperpage{205}
- \item collineation, \hyperpage{65}
- \item column rank, \hyperpage{15}
- \item Combinations with repetition, \hyperpage{9}
- \item Combinations without repetition, \hyperpage{9}
- \item communicate, \hyperpage{319}
- \item commutative, \hyperpage{36}
- \item compact, \hyperpage{53}, \hyperpage{212}
- \item compact operator, \hyperpage{306}
- \item Compact space, \hyperpage{212}
- \item compact subset, \hyperpage{212}
- \item compact support, \hyperpage{78}
- \item compactness, \hyperpage{212}
- \item Comparison test, \hyperpage{75}, \hyperpage{79},
- \hyperpage{182}
- \item compatibility condition, \hyperpage{272}
- \item compatible, \hyperpage{148}, \hyperpage{157}
- \item compatible with, \hyperpage{96}
- \item complement, \hyperpage{5}
- \item Complementary property, \hyperpage{51}
- \item complementary subspace, \hyperpage{16}
- \item complete, \hyperpage{53}, \hyperpage{299}, \hyperpage{311}
- \item complete graph, \hyperpage{48}
- \item Complete pivoting, \hyperpage{101}
- \item complex conjugate, \hyperpage{23}, \hyperpage{103}
- \item complex cosecant, \hyperpage{108}
- \item complex cosine, \hyperpage{107}
- \item complex cotangent, \hyperpage{108}
- \item complex exponential function, \hyperpage{107}
- \item complex function, \hyperpage{105}
- \item complex hyperbolic cosecant, \hyperpage{108}
- \item complex hyperbolic cosine, \hyperpage{108}
- \item complex hyperbolic cotangent, \hyperpage{108}
- \item complex hyperbolic secant, \hyperpage{108}
- \item complex hyperbolic sine, \hyperpage{108}
- \item complex hyperbolic tangent, \hyperpage{108}
- \item complex natural logarithm, \hyperpage{107}
- \item complex power series, \hyperpage{106}
- \item complex random variable, \hyperpage{190}
- \item complex secant, \hyperpage{108}
- \item complex sine, \hyperpage{107}
- \item complex tangent, \hyperpage{108}
- \item Composite Simpson's rule, \hyperpage{95}
- \item Composite Trapezoidal rule, \hyperpage{94}
- \item composition, \hyperpage{6}
- \item compositum, \hyperpage{164}
- \item Compound probability formula, \hyperpage{173}
- \item computational efficiency, \hyperpage{90}
- \item concave, \hyperpage{29}
- \item Condensation test, \hyperpage{75}
- \item condition number, \hyperpage{98}
- \item conditional consistency, \hyperpage{268}
- \item conditional expectation, \hyperpage{185}
- \item conditional probability, \hyperpage{173}
- \item conditional probability density function, \hyperpage{181}
- \item conditional probability mass function, \hyperpage{181}
- \item conditionally absolutely stable, \hyperpage{260}
- \item conditionally convergent, \hyperpage{268}
- \item cone, \hyperpage{107}
- \item confidence band, \hyperpage{253}
- \item Confidence interval for the average response, \hyperpage{252}
- \item Confidence interval for the predicted value, \hyperpage{253}
- \item confidence intervals, \hyperpage{197}
- \item confidence level, \hyperpage{197}
- \item confidence region, \hyperpage{197}
- \item configuration, \hyperpage{66}
- \item conformal, \hyperpage{118}, \hyperpage{148}
- \item conformal representation, \hyperpage{118}
- \item Congruence axioms, \hyperpage{62}
- \item congruence relation, \hyperpage{62}
- \item conic, \hyperpage{72}
- \item conjugacy, \hyperpage{131}
- \item conjugate, \hyperpage{103}, \hyperpage{131}, \hyperpage{201}
- \item conjugate dynamical systems, \hyperpage{130}
- \item Conjugate gradient method, \hyperpage{263}
- \item conjugate Poisson kernel, \hyperpage{247}
- \item conjugation action, \hyperpage{40}
- \item connected, \hyperpage{49}, \hyperpage{53}, \hyperpage{213}
- \item connected components, \hyperpage{49}, \hyperpage{214}
- \item Connected space, \hyperpage{213}
- \item connected subset, \hyperpage{213}
- \item Connected sum, \hyperpage{216}
- \item connected sum, \hyperpage{216}
- \item Connected sum of surfaces, \hyperpage{216}
- \item Conservation of energy, \hyperpage{281}
- \item conservative, \hyperpage{60}, \hyperpage{327}
- \item consistency condition, \hyperpage{332}
- \item consistent, \hyperpage{258}, \hyperpage{261}, \hyperpage{268}
- \item consistent estimator in $L^2$, \hyperpage{193}
- \item constant coefficients, \hyperpage{121}, \hyperpage{125}
- \item constant term, \hyperpage{10}, \hyperpage{12}
- \item constructible field, \hyperpage{63}
- \item Construction of a non-Paschian geometry, \hyperpage{64}
- \item Construction of a non-SAS geometry, \hyperpage{65}
- \item contact, \hyperpage{143}
- \item contact of order $\geq n$ at $a$, \hyperpage{30}
- \item Continuity axioms, \hyperpage{62}
- \item Continuity correction, \hyperpage{191}
- \item continuity correction, \hyperpage{191}
- \item Continuity from above, \hyperpage{172}
- \item Continuity from below, \hyperpage{172}
- \item continuous, \hyperpage{27}, \hyperpage{54}, \hyperpage{105},
- \hyperpage{129}
- \item continuous at $x_0$, \hyperpage{27}
- \item Continuous equation, \hyperpage{276}
- \item continuous equation, \hyperpage{276}
- \item Continuous function, \hyperpage{207}
- \item Continuous memorylessness property, \hyperpage{177}
- \item Continuous uniform distribution, \hyperpage{177}
- \item continuous uniform distribution, \hyperpage{177}
- \item continuous-time Markov chain, \hyperpage{325}
- \item contractible, \hyperpage{138}
- \item contraction, \hyperpage{54}, \hyperpage{89}
- \item contrast matrix, \hyperpage{200}
- \item converge in mean, \hyperpage{297}
- \item converge in norm $L^p$, \hyperpage{86}
- \item convergent, \hyperpage{25}, \hyperpage{53}, \hyperpage{75},
- \hyperpage{78}, \hyperpage{97}, \hyperpage{104, 105},
- \hyperpage{116}, \hyperpage{258}
- \item convergent series, \hyperpage{299}
- \item converges, \hyperpage{104}
- \item converges absolutely, \hyperpage{79}
- \item converges almost surely, \hyperpage{187}
- \item converges in distribution, \hyperpage{188}
- \item converges in probability, \hyperpage{186}
- \item converges in the $p$-th mean, \hyperpage{188}
- \item converges pointwise, \hyperpage{76, 77}, \hyperpage{105, 106}
- \item converges uniformly, \hyperpage{76, 77}, \hyperpage{105, 106}
- \item convex, \hyperpage{29}, \hyperpage{114}
- \item convex functional, \hyperpage{307}
- \item convolution, \hyperpage{78}, \hyperpage{239}, \hyperpage{243}
- \item Cook's distance, \hyperpage{254}
- \item coordinate chart, \hyperpage{146}, \hyperpage{215}
- \item coordinates, \hyperpage{15}
- \item Coordination theorem, \hyperpage{16}, \hyperpage{67}
- \item coprime, \hyperpage{9, 10}
- \item corrected sample variance, \hyperpage{192}
- \item correlation coefficient, \hyperpage{184}
- \item Correspondence theorem, \hyperpage{39}, \hyperpage{43}
- \item countable, \hyperpage{24}, \hyperpage{212}
- \item Countable subadditivity, \hyperpage{172}
- \item Courant-Friedrichs-Lewy condition, \hyperpage{269}
- \item Covariance, \hyperpage{184}
- \item covariance, \hyperpage{184}, \hyperpage{248}
- \item covariance function, \hyperpage{329}
- \item covariance matrix, \hyperpage{180}, \hyperpage{195},
- \hyperpage{248}
- \item covariant derivative, \hyperpage{151}
- \item Cover, \hyperpage{212}
- \item cover, \hyperpage{212}
- \item Cramér-Rao bound, \hyperpage{195}
- \item Crank-Nicolson, \hyperpage{271}
- \item Crank-Nicolson scheme, \hyperpage{271}, \hyperpage{273}
- \item credible interval, \hyperpage{202}
- \item credible region, \hyperpage{202}
- \item critical point, \hyperpage{56}, \hyperpage{130}
- \item critical region, \hyperpage{198}
- \item cross product, \hyperpage{141}
- \item Cross ratio, \hyperpage{68}
- \item cross ratio, \hyperpage{68}, \hyperpage{119}
- \item cubic convergence, \hyperpage{90}
- \item Cubic Hermite spline, \hyperpage{93}
- \item Cubic periodic spline, \hyperpage{93}
- \item cubic polynomial, \hyperpage{161}
- \item cubic splines, \hyperpage{93}
- \item Cumulative distribution function, \hyperpage{175}
- \item cumulative distribution function, \hyperpage{175}
- \item curl, \hyperpage{60}
- \item Curl theorem, \hyperpage{158}
- \item curvature, \hyperpage{60}, \hyperpage{142}
- \item cusp, \hyperpage{223}
- \item cycle, \hyperpage{7}, \hyperpage{48}, \hyperpage{114}
- \item cyclic, \hyperpage{169}
- \item cyclic group, \hyperpage{36}
- \item cyclotomic, \hyperpage{169}
- \item càd, \hyperpage{325}
- \item càdlàg, \hyperpage{175}
+ \hyperpage{74}
+ \item clopen, \hyperpage{206}
+ \item closed, \hyperpage{49}, \hyperpage{54}, \hyperpage{156},
+ \hyperpage{206}, \hyperpage{208}
+ \item closed ball, \hyperpage{54}
+ \item Closed forms, \hyperpage{48}
+ \item Closed function, \hyperpage{208}
+ \item Closed graph theorem, \hyperpage{309}
+ \item Closed interval, \hyperpage{25}
+ \item Closed Newton-Cotes Formulas, \hyperpage{95}
+ \item closed trail, \hyperpage{49}
+ \item Closure, \hyperpage{206}
+ \item closure, \hyperpage{206}
+ \item Cochran's theorem, \hyperpage{252}
+ \item Cocountable topology, \hyperpage{206}
+ \item Codazzi-Mainardi equations, \hyperpage{152}
+ \item codimension, \hyperpage{223}
+ \item coefficient of determination, \hyperpage{252}
+ \item coefficients, \hyperpage{11}
+ \item cofactor, \hyperpage{136}
+ \item cofactor matrix, \hyperpage{15}
+ \item Cofinite topology, \hyperpage{206}
+ \item collineation, \hyperpage{66}
+ \item column rank, \hyperpage{16}
+ \item Combinations with repetition, \hyperpage{10}
+ \item Combinations without repetition, \hyperpage{10}
+ \item communicate, \hyperpage{320}
+ \item commutative, \hyperpage{37}
+ \item compact, \hyperpage{54}, \hyperpage{213}
+ \item compact operator, \hyperpage{307}
+ \item Compact space, \hyperpage{213}
+ \item compact subset, \hyperpage{213}
+ \item compact support, \hyperpage{79}
+ \item compactness, \hyperpage{213}
+ \item Comparison test, \hyperpage{76}, \hyperpage{80},
+ \hyperpage{183}
+ \item compatibility condition, \hyperpage{273}
+ \item compatible, \hyperpage{149}, \hyperpage{158}
+ \item compatible with, \hyperpage{97}
+ \item complement, \hyperpage{6}
+ \item Complementary property, \hyperpage{52}
+ \item complementary subspace, \hyperpage{17}
+ \item complete, \hyperpage{54}, \hyperpage{300}, \hyperpage{313}
+ \item complete graph, \hyperpage{49}
+ \item Complete pivoting, \hyperpage{102}
+ \item complex conjugate, \hyperpage{24}, \hyperpage{104}
+ \item complex cosecant, \hyperpage{109}
+ \item complex cosine, \hyperpage{108}
+ \item complex cotangent, \hyperpage{109}
+ \item complex exponential function, \hyperpage{108}
+ \item complex function, \hyperpage{106}
+ \item complex hyperbolic cosecant, \hyperpage{109}
+ \item complex hyperbolic cosine, \hyperpage{109}
+ \item complex hyperbolic cotangent, \hyperpage{109}
+ \item complex hyperbolic secant, \hyperpage{109}
+ \item complex hyperbolic sine, \hyperpage{109}
+ \item complex hyperbolic tangent, \hyperpage{109}
+ \item complex natural logarithm, \hyperpage{108}
+ \item complex power series, \hyperpage{107}
+ \item complex random variable, \hyperpage{191}
+ \item complex secant, \hyperpage{109}
+ \item complex sine, \hyperpage{108}
+ \item complex tangent, \hyperpage{109}
+ \item Composite Simpson's rule, \hyperpage{96}
+ \item Composite Trapezoidal rule, \hyperpage{95}
+ \item composition, \hyperpage{7}
+ \item compositum, \hyperpage{165}
+ \item Compound probability formula, \hyperpage{174}
+ \item computational efficiency, \hyperpage{91}
+ \item concave, \hyperpage{30}
+ \item Condensation test, \hyperpage{76}
+ \item condition number, \hyperpage{99}
+ \item conditional consistency, \hyperpage{269}
+ \item conditional expectation, \hyperpage{186}
+ \item conditional expectation of $X$ given $\mathcal {G}$,
+ \hyperpage{336}
+ \item conditional expectation of $X$ given $Y$, \hyperpage{337}
+ \item conditional law of $X$ given $Y$, \hyperpage{337}
+ \item conditional probability, \hyperpage{174}
+ \item conditional probability density function, \hyperpage{182}
+ \item conditional probability mass function, \hyperpage{182}
+ \item conditionally absolutely stable, \hyperpage{261}
+ \item conditionally convergent, \hyperpage{269}
+ \item cone, \hyperpage{108}
+ \item confidence band, \hyperpage{254}
+ \item Confidence interval for the average response, \hyperpage{253}
+ \item Confidence interval for the predicted value, \hyperpage{254}
+ \item confidence intervals, \hyperpage{198}
+ \item confidence level, \hyperpage{198}
+ \item confidence region, \hyperpage{198}
+ \item configuration, \hyperpage{67}
+ \item conformal, \hyperpage{119}, \hyperpage{149}
+ \item conformal representation, \hyperpage{119}
+ \item Congruence axioms, \hyperpage{63}
+ \item congruence relation, \hyperpage{63}
+ \item conic, \hyperpage{73}
+ \item conjugacy, \hyperpage{132}
+ \item conjugate, \hyperpage{104}, \hyperpage{132}, \hyperpage{202}
+ \item conjugate dynamical systems, \hyperpage{131}
+ \item Conjugate gradient method, \hyperpage{264}
+ \item conjugate Poisson kernel, \hyperpage{248}
+ \item conjugation action, \hyperpage{41}
+ \item connected, \hyperpage{50}, \hyperpage{54}, \hyperpage{214}
+ \item connected components, \hyperpage{50}, \hyperpage{215}
+ \item Connected space, \hyperpage{214}
+ \item connected subset, \hyperpage{214}
+ \item Connected sum, \hyperpage{217}
+ \item connected sum, \hyperpage{217}
+ \item Connected sum of surfaces, \hyperpage{217}
+ \item Conservation of energy, \hyperpage{282}
+ \item conservative, \hyperpage{61}, \hyperpage{328}
+ \item consistency condition, \hyperpage{333}
+ \item consistent, \hyperpage{259}, \hyperpage{262}, \hyperpage{269}
+ \item consistent estimator in $L^2$, \hyperpage{194}
+ \item constant coefficients, \hyperpage{122}, \hyperpage{126}
+ \item constant term, \hyperpage{11}, \hyperpage{13}
+ \item constructible field, \hyperpage{64}
+ \item Construction of a non-Paschian geometry, \hyperpage{65}
+ \item Construction of a non-SAS geometry, \hyperpage{66}
+ \item contact, \hyperpage{144}
+ \item contact of order $\geq n$ at $a$, \hyperpage{31}
+ \item Continuity axioms, \hyperpage{63}
+ \item Continuity correction, \hyperpage{192}
+ \item continuity correction, \hyperpage{192}
+ \item Continuity from above, \hyperpage{173}
+ \item Continuity from below, \hyperpage{173}
+ \item continuous, \hyperpage{28}, \hyperpage{55}, \hyperpage{106},
+ \hyperpage{130}
+ \item continuous at $x_0$, \hyperpage{28}
+ \item Continuous equation, \hyperpage{277}
+ \item continuous equation, \hyperpage{277}
+ \item Continuous function, \hyperpage{208}
+ \item Continuous memorylessness property, \hyperpage{178}
+ \item Continuous uniform distribution, \hyperpage{178}
+ \item continuous uniform distribution, \hyperpage{178}
+ \item continuous-time Markov chain, \hyperpage{326}
+ \item contractible, \hyperpage{139}
+ \item contraction, \hyperpage{55}, \hyperpage{90}
+ \item contrast matrix, \hyperpage{201}
+ \item converge in mean, \hyperpage{298}
+ \item converge in norm $L^p$, \hyperpage{87}
+ \item convergent, \hyperpage{26}, \hyperpage{54}, \hyperpage{76},
+ \hyperpage{79}, \hyperpage{98}, \hyperpage{105, 106},
+ \hyperpage{117}, \hyperpage{259}
+ \item convergent series, \hyperpage{300}
+ \item converges, \hyperpage{105}
+ \item converges absolutely, \hyperpage{80}
+ \item converges almost surely, \hyperpage{188}
+ \item converges in distribution, \hyperpage{190}
+ \item converges in probability, \hyperpage{187}
+ \item converges in the $p$-th mean, \hyperpage{189}
+ \item converges pointwise, \hyperpage{77, 78}, \hyperpage{106, 107}
+ \item converges uniformly, \hyperpage{77, 78}, \hyperpage{106, 107}
+ \item convex, \hyperpage{30}, \hyperpage{115}
+ \item convex functional, \hyperpage{308}
+ \item convolution, \hyperpage{79}, \hyperpage{240}, \hyperpage{244}
+ \item Cook's distance, \hyperpage{255}
+ \item coordinate chart, \hyperpage{147}, \hyperpage{216}
+ \item coordinates, \hyperpage{16}
+ \item Coordination theorem, \hyperpage{17}, \hyperpage{68}
+ \item coprime, \hyperpage{10, 11}
+ \item corrected sample variance, \hyperpage{193}
+ \item correlation coefficient, \hyperpage{185}
+ \item Correspondence theorem, \hyperpage{40}, \hyperpage{44}
+ \item countable, \hyperpage{25}, \hyperpage{213}
+ \item Countable subadditivity, \hyperpage{173}
+ \item Courant-Friedrichs-Lewy condition, \hyperpage{270}
+ \item Covariance, \hyperpage{185}
+ \item covariance, \hyperpage{185}, \hyperpage{249}
+ \item covariance function, \hyperpage{330}
+ \item covariance matrix, \hyperpage{181}, \hyperpage{196},
+ \hyperpage{249}
+ \item covariant derivative, \hyperpage{152}
+ \item Cover, \hyperpage{213}
+ \item cover, \hyperpage{213}
+ \item Cramér-Rao bound, \hyperpage{196}
+ \item Crank-Nicolson, \hyperpage{272}
+ \item Crank-Nicolson scheme, \hyperpage{272}, \hyperpage{274}
+ \item credible interval, \hyperpage{203}
+ \item credible region, \hyperpage{203}
+ \item critical point, \hyperpage{57}, \hyperpage{131}
+ \item critical region, \hyperpage{199}
+ \item cross product, \hyperpage{142}
+ \item Cross ratio, \hyperpage{69}
+ \item cross ratio, \hyperpage{69}, \hyperpage{120}
+ \item cubic convergence, \hyperpage{91}
+ \item Cubic Hermite spline, \hyperpage{94}
+ \item Cubic periodic spline, \hyperpage{94}
+ \item cubic polynomial, \hyperpage{162}
+ \item cubic splines, \hyperpage{94}
+ \item Cumulative distribution function, \hyperpage{176}
+ \item cumulative distribution function, \hyperpage{176}
+ \item curl, \hyperpage{61}
+ \item Curl theorem, \hyperpage{159}
+ \item curvature, \hyperpage{61}, \hyperpage{143}
+ \item cusp, \hyperpage{224}
+ \item cycle, \hyperpage{8}, \hyperpage{49}, \hyperpage{115}
+ \item cyclic, \hyperpage{170}
+ \item cyclic group, \hyperpage{37}
+ \item cyclotomic, \hyperpage{170}
+ \item càd, \hyperpage{326}
+ \item càdlàg, \hyperpage{176}
\indexspace
- \item D'Alembert formula, \hyperpage{139}, \hyperpage{280}
- \item D'Alembert theorem, \hyperpage{11}
- \item Dahlquist's theorem, \hyperpage{261}
- \item damping parameter, \hyperpage{262}
- \item Darboux theorem, \hyperpage{137}
- \item Darboux's theorem, \hyperpage{29}
- \item De Moivre's formula, \hyperpage{107}
- \item De Moivre-Laplace theorem, \hyperpage{191}
- \item De Morgan's laws, \hyperpage{5}
- \item decreasing, \hyperpage{27}
- \item Dedekind's lemma, \hyperpage{169}
- \item Dedekind's test, \hyperpage{106}
- \item Degenerated distribution, \hyperpage{176}
- \item degenerated distribution, \hyperpage{176}
- \item degree, \hyperpage{10}, \hyperpage{44}, \hyperpage{134},
- \hyperpage{154}, \hyperpage{163}
- \item degree of a vertex, \hyperpage{48}
- \item degree of precision, \hyperpage{94}
- \item degree sequence, \hyperpage{48}
- \item Dehomogenization, \hyperpage{73}
- \item dehomogenization, \hyperpage{69}
- \item Delta method, \hyperpage{195}
- \item dense, \hyperpage{206}
- \item density, \hyperpage{277}
- \item density function, \hyperpage{177}
+ \item D'Alembert formula, \hyperpage{140}, \hyperpage{281}
+ \item D'Alembert theorem, \hyperpage{12}
+ \item Dahlquist's theorem, \hyperpage{262}
+ \item damping parameter, \hyperpage{263}
+ \item Darboux theorem, \hyperpage{138}
+ \item Darboux's theorem, \hyperpage{30}
+ \item De Moivre's formula, \hyperpage{108}
+ \item De Moivre-Laplace theorem, \hyperpage{192}
+ \item De Morgan's laws, \hyperpage{6}
+ \item decreasing, \hyperpage{28}
+ \item Dedekind's lemma, \hyperpage{170}
+ \item Dedekind's test, \hyperpage{107}
+ \item Degenerated distribution, \hyperpage{177}
+ \item degenerated distribution, \hyperpage{177}
+ \item degree, \hyperpage{11}, \hyperpage{45}, \hyperpage{135},
+ \hyperpage{155}, \hyperpage{164}
+ \item degree of a vertex, \hyperpage{49}
+ \item degree of precision, \hyperpage{95}
+ \item degree sequence, \hyperpage{49}
+ \item Dehomogenization, \hyperpage{74}
+ \item dehomogenization, \hyperpage{70}
+ \item Delta method, \hyperpage{196}
+ \item dense, \hyperpage{207}
+ \item density, \hyperpage{278}, \hyperpage{336}
+ \item density function, \hyperpage{178}
\item Dependence on $\boldsymbol {\mathrm {\lambda }}$,
- \hyperpage{128}
- \item Dependence on $\boldsymbol {\mathrm {x}}_0$, \hyperpage{128}
- \item Dependence on $t_0$, \hyperpage{128}
- \item depressed equation, \hyperpage{161}
- \item derivative of $f$ at $x_0$, \hyperpage{28}
- \item derivative of $f$ at $z_0$, \hyperpage{108}
- \item Desargues configuration, \hyperpage{67}
- \item Desargues' theorem, \hyperpage{67}
- \item Descartes' rule of signs, \hyperpage{23}, \hyperpage{91}
- \item descent direction, \hyperpage{263}
- \item Descent method, \hyperpage{263}
- \item descent method, \hyperpage{263}
- \item design matrix, \hyperpage{249}
- \item Determinant, \hyperpage{13}
- \item determinant, \hyperpage{141}
- \item determination, \hyperpage{109}
- \item determination of the argument of $f$, \hyperpage{103}
- \item determination of the logarithm, \hyperpage{109}
- \item determined and consistent, \hyperpage{13}
- \item developable, \hyperpage{150}
- \item dextrorotation, \hyperpage{144}
- \item DFT, \hyperpage{238}
- \item diagonal, \hyperpage{19}
- \item diagonalizable, \hyperpage{19}
- \item Diagonalization theorem, \hyperpage{19}
- \item dicyclic group, \hyperpage{41}
- \item diffeomorphism, \hyperpage{56}
- \item Differentiability criterion, \hyperpage{55}
- \item differentiable, \hyperpage{28}, \hyperpage{54}, \hyperpage{146},
- \hyperpage{151}, \hyperpage{153}, \hyperpage{155, 156}
- \item differentiable at $x_0\in (a,b)$, \hyperpage{28}
- \item differentiable manifold, \hyperpage{215}
- \item differential, \hyperpage{54}, \hyperpage{69}, \hyperpage{109},
- \hyperpage{147}, \hyperpage{154}, \hyperpage{156}
- \item differential $\ell $-form, \hyperpage{155}
- \item differential $k$-form, \hyperpage{154}
- \item differential 1-form, \hyperpage{61}
- \item differential operator over distributions, \hyperpage{244}
- \item differential system, \hyperpage{121}
- \item differentiation operator, \hyperpage{284}
- \item diffusion coefficient, \hyperpage{277}
- \item Diffusion equation, \hyperpage{277}
- \item diffusion flux, \hyperpage{277}
- \item diffusivity, \hyperpage{277}
- \item digital topology, \hyperpage{205}
- \item dihedral group, \hyperpage{41}
- \item dilatation, \hyperpage{118}
- \item dimension, \hyperpage{15}, \hyperpage{65}, \hyperpage{68},
- \hyperpage{192}
- \item Dini's theorem, \hyperpage{84}, \hyperpage{233}
- \item Dirac's $\delta $ distribution, \hyperpage{240},
- \hyperpage{284}
- \item direct, \hyperpage{15}
- \item direct product, \hyperpage{243}
- \item Direct sum, \hyperpage{15}
- \item directional derivative, \hyperpage{54}
- \item director subspace, \hyperpage{69}
- \item Dirichlet, \hyperpage{273}
- \item Dirichlet kernel, \hyperpage{83}, \hyperpage{232}
- \item Dirichlet problem, \hyperpage{139}, \hyperpage{287}
- \item Dirichlet problem in the disc, \hyperpage{287}
- \item Dirichlet's principle, \hyperpage{287}
- \item Dirichlet's test, \hyperpage{76, 77}, \hyperpage{79},
- \hyperpage{106}
- \item disconnected, \hyperpage{213}
- \item Discontinuity of the first kind, \hyperpage{27}
- \item Discontinuity of the second kind, \hyperpage{27}
- \item discrete, \hyperpage{129}, \hyperpage{175}, \hyperpage{179}
- \item discrete $\sigma $-algebra, \hyperpage{171}
- \item discrete Fourier transform, \hyperpage{238}
- \item discrete laplacian, \hyperpage{273}
- \item discrete map of order $m$, \hyperpage{221}
- \item Discrete maximum principle, \hyperpage{273}
- \item Discrete memorylessness property, \hyperpage{176}
- \item discrete metric, \hyperpage{204}
- \item Discrete minimum principle, \hyperpage{273}
- \item Discrete topology, \hyperpage{205}
- \item Discrete uniform distribution, \hyperpage{176}
- \item discrete uniform distribution, \hyperpage{176}
- \item discriminant, \hyperpage{168}
- \item displacement current, \hyperpage{277}
- \item distance, \hyperpage{52}, \hyperpage{81}, \hyperpage{204},
- \hyperpage{299}
- \item distance between two affine subvarieties, \hyperpage{71}
- \item distance between two points, \hyperpage{71}
- \item Distribution, \hyperpage{239}, \hyperpage{284}
- \item distribution, \hyperpage{175}, \hyperpage{179}, \hyperpage{239},
- \hyperpage{284}
- \item distribution functions, \hyperpage{175}
+ \hyperpage{129}
+ \item Dependence on $\boldsymbol {\mathrm {x}}_0$, \hyperpage{129}
+ \item Dependence on $t_0$, \hyperpage{129}
+ \item depressed equation, \hyperpage{162}
+ \item derivative of $f$ at $x_0$, \hyperpage{29}
+ \item derivative of $f$ at $z_0$, \hyperpage{109}
+ \item Desargues configuration, \hyperpage{68}
+ \item Desargues' theorem, \hyperpage{68}
+ \item Descartes' rule of signs, \hyperpage{24}, \hyperpage{92}
+ \item descent direction, \hyperpage{264}
+ \item Descent method, \hyperpage{264}
+ \item descent method, \hyperpage{264}
+ \item design matrix, \hyperpage{250}
+ \item Determinant, \hyperpage{14}
+ \item determinant, \hyperpage{142}
+ \item determination, \hyperpage{110}
+ \item determination of the argument of $f$, \hyperpage{104}
+ \item determination of the logarithm, \hyperpage{110}
+ \item determined and consistent, \hyperpage{14}
+ \item developable, \hyperpage{151}
+ \item dextrorotation, \hyperpage{145}
+ \item DFT, \hyperpage{239}
+ \item diagonal, \hyperpage{20}
+ \item diagonalizable, \hyperpage{20}
+ \item Diagonalization theorem, \hyperpage{20}
+ \item dicyclic group, \hyperpage{42}
+ \item diffeomorphism, \hyperpage{57}
+ \item Differentiability criterion, \hyperpage{56}
+ \item differentiable, \hyperpage{29}, \hyperpage{55}, \hyperpage{147},
+ \hyperpage{152}, \hyperpage{154}, \hyperpage{156, 157}
+ \item differentiable at $x_0\in (a,b)$, \hyperpage{29}
+ \item differentiable manifold, \hyperpage{216}
+ \item differential, \hyperpage{55}, \hyperpage{70}, \hyperpage{110},
+ \hyperpage{148}, \hyperpage{155}, \hyperpage{157}
+ \item differential $\ell $-form, \hyperpage{156}
+ \item differential $k$-form, \hyperpage{155}
+ \item differential 1-form, \hyperpage{62}
+ \item differential operator over distributions, \hyperpage{245}
+ \item differential system, \hyperpage{122}
+ \item differentiation operator, \hyperpage{285}
+ \item diffusion coefficient, \hyperpage{278}
+ \item Diffusion equation, \hyperpage{278}
+ \item diffusion flux, \hyperpage{278}
+ \item diffusivity, \hyperpage{278}
+ \item digital topology, \hyperpage{206}
+ \item dihedral group, \hyperpage{42}
+ \item dilatation, \hyperpage{119}
+ \item dimension, \hyperpage{16}, \hyperpage{66}, \hyperpage{69},
+ \hyperpage{193}
+ \item Dini's theorem, \hyperpage{85}, \hyperpage{234}
+ \item Dirac's $\delta $ distribution, \hyperpage{241},
+ \hyperpage{285}
+ \item direct, \hyperpage{16}
+ \item direct product, \hyperpage{245}
+ \item Direct sum, \hyperpage{16}
+ \item directional derivative, \hyperpage{55}
+ \item director subspace, \hyperpage{70}
+ \item Dirichlet, \hyperpage{274}
+ \item Dirichlet kernel, \hyperpage{84}, \hyperpage{233}
+ \item Dirichlet problem, \hyperpage{140}, \hyperpage{288}
+ \item Dirichlet problem in the disc, \hyperpage{288}
+ \item Dirichlet's principle, \hyperpage{288}
+ \item Dirichlet's test, \hyperpage{77, 78}, \hyperpage{80},
+ \hyperpage{107}
+ \item disconnected, \hyperpage{214}
+ \item Discontinuity of the first kind, \hyperpage{28}
+ \item Discontinuity of the second kind, \hyperpage{28}
+ \item discrete, \hyperpage{130}, \hyperpage{176}, \hyperpage{180}
+ \item discrete $\sigma $-algebra, \hyperpage{172}
+ \item discrete Fourier transform, \hyperpage{239}
+ \item discrete laplacian, \hyperpage{274}
+ \item discrete map of order $m$, \hyperpage{222}
+ \item Discrete maximum principle, \hyperpage{274}
+ \item Discrete memorylessness property, \hyperpage{177}
+ \item discrete metric, \hyperpage{205}
+ \item Discrete minimum principle, \hyperpage{274}
+ \item Discrete topology, \hyperpage{206}
+ \item Discrete uniform distribution, \hyperpage{177}
+ \item discrete uniform distribution, \hyperpage{177}
+ \item discriminant, \hyperpage{169}
+ \item displacement current, \hyperpage{278}
+ \item distance, \hyperpage{53}, \hyperpage{82}, \hyperpage{205},
+ \hyperpage{300}
+ \item distance between two affine subvarieties, \hyperpage{72}
+ \item distance between two points, \hyperpage{72}
+ \item Distribution, \hyperpage{240}, \hyperpage{285}
+ \item distribution, \hyperpage{176}, \hyperpage{180}, \hyperpage{240},
+ \hyperpage{285}
+ \item distribution functions, \hyperpage{176}
\item distribution of order $N\in \ensuremath {\mathbb {N}}\cup \{0\}$,
- \hyperpage{240}
- \item distributional derivative, \hyperpage{241}, \hyperpage{284}
- \item divergence, \hyperpage{60}
- \item Divergence theorem, \hyperpage{159}
+ \hyperpage{241}
+ \item distributional derivative, \hyperpage{242}, \hyperpage{285}
+ \item divergence, \hyperpage{61}
+ \item Divergence theorem, \hyperpage{160}
\item Divergence theorem on $\ensuremath {\mathbb {R}}^2$,
- \hyperpage{61}
+ \hyperpage{62}
\item Divergence theorem on $\ensuremath {\mathbb {R}}^3$,
- \hyperpage{61}, \hyperpage{159}
- \item divergent, \hyperpage{25}, \hyperpage{75}, \hyperpage{104, 105}
- \item divided difference, \hyperpage{92}
- \item domain, \hyperpage{114}, \hyperpage{147}
- \item dominant eigenvalue, \hyperpage{99}
- \item dominant eigenvector, \hyperpage{99}
- \item Dominated convergence theorem, \hyperpage{183}, \hyperpage{188},
- \hyperpage{296}
- \item dot product, \hyperpage{52}
- \item double, \hyperpage{89}
- \item Double dual space, \hyperpage{18}
- \item double dual space, \hyperpage{18}
- \item Du Bois-Reymond's test, \hyperpage{106}
- \item Du-Fort-Frankel scheme, \hyperpage{273}
- \item dual basis, \hyperpage{18}
- \item Dual map, \hyperpage{18}
- \item dual map, \hyperpage{18}, \hyperpage{307}
- \item dual program, \hyperpage{50}
- \item dual space, \hyperpage{18}, \hyperpage{306}
- \item Duality principle, \hyperpage{65}
- \item Duhamel principle, \hyperpage{286}
- \item dummy variable, \hyperpage{252}
- \item dyadic partition of order $n$, \hyperpage{182}
- \item dynamical system, \hyperpage{129}
+ \hyperpage{62}, \hyperpage{160}
+ \item divergent, \hyperpage{26}, \hyperpage{76}, \hyperpage{105, 106}
+ \item divided difference, \hyperpage{93}
+ \item domain, \hyperpage{115}, \hyperpage{148}
+ \item dominant eigenvalue, \hyperpage{100}
+ \item dominant eigenvector, \hyperpage{100}
+ \item Dominated convergence theorem, \hyperpage{184}, \hyperpage{189},
+ \hyperpage{297}, \hyperpage{335}
+ \item dot product, \hyperpage{53}
+ \item double, \hyperpage{90}
+ \item Double dual space, \hyperpage{19}
+ \item double dual space, \hyperpage{19}
+ \item Du Bois-Reymond's test, \hyperpage{107}
+ \item Du-Fort-Frankel scheme, \hyperpage{274}
+ \item dual basis, \hyperpage{19}
+ \item Dual map, \hyperpage{19}
+ \item dual map, \hyperpage{19}, \hyperpage{308}
+ \item dual program, \hyperpage{51}
+ \item dual space, \hyperpage{19}, \hyperpage{307}
+ \item Duality principle, \hyperpage{66}
+ \item Duhamel principle, \hyperpage{287}
+ \item dummy variable, \hyperpage{253}
+ \item dyadic partition of order $n$, \hyperpage{183}
+ \item dynamical system, \hyperpage{130}
\indexspace
- \item edges, \hyperpage{159}
- \item efficient estimator, \hyperpage{195}
- \item eigenspace, \hyperpage{19}
- \item eigenvalue, \hyperpage{308}
- \item eigenvector, \hyperpage{19}
- \item eigenvectors, \hyperpage{308}
- \item Eikonal equation, \hyperpage{277}
- \item Eisenstein's criterion, \hyperpage{44}, \hyperpage{46}
- \item either $P$ or $Q$ are true, \hyperpage{7}
- \item elastodynamics, \hyperpage{276}
- \item elementary region, \hyperpage{58}
- \item elementary symmetric polynomials, \hyperpage{162}
- \item elliptic, \hyperpage{73}, \hyperpage{272}
- \item elliptic equation, \hyperpage{276}
- \item elliptic point, \hyperpage{149}
- \item elliptic sector, \hyperpage{132}
- \item embedded methods, \hyperpage{259}
- \item empirical distribution, \hyperpage{201}
- \item empty set, \hyperpage{5}
- \item energy functional, \hyperpage{287}
- \item entire function, \hyperpage{108}
- \item Entropy, \hyperpage{255}
- \item entropy, \hyperpage{255}
- \item Entropy condition, \hyperpage{279}
- \item envelope, \hyperpage{143}
- \item equal, \hyperpage{5}
- \item equal almost surely, \hyperpage{175}
- \item equal in distribution, \hyperpage{175}
- \item equally-spaced, \hyperpage{92}
- \item equation of the hyperplane, \hyperpage{66}
- \item equicontinuous, \hyperpage{120}
- \item equicontinuous at a point, \hyperpage{124}, \hyperpage{303}
- \item equilibrium point, \hyperpage{220}
- \item equiprobable space, \hyperpage{176}
- \item equivalence, \hyperpage{130}
- \item equivalence class, \hyperpage{7}, \hyperpage{16}
- \item equivalence relation, \hyperpage{7}
- \item equivalent, \hyperpage{12}, \hyperpage{16}, \hyperpage{22},
- \hyperpage{72}, \hyperpage{129}, \hyperpage{131},
- \hyperpage{305}
- \item equivalent dynamical systems, \hyperpage{130}
- \item Ergotic theorem, \hyperpage{323, 324}
- \item error of type I, \hyperpage{198}
- \item error of type II, \hyperpage{198}
- \item error sum of squares, \hyperpage{251}
- \item Essential singularity, \hyperpage{116}
- \item essential singularity, \hyperpage{116}
- \item estimated average response, \hyperpage{252}
- \item estimation of the prediction, \hyperpage{252}
- \item estimator, \hyperpage{192}
- \item Euclid's axioms, \hyperpage{62}
- \item Euclid's theorem, \hyperpage{9}
- \item Euclidean, \hyperpage{63}
- \item Euclidean affine space, \hyperpage{71}
- \item Euclidean metric, \hyperpage{204}
- \item Euclidean motion, \hyperpage{72}
- \item Euclidean plane, \hyperpage{63}
- \item Euclidean space, \hyperpage{52}
- \item Euclidean vector space, \hyperpage{23}
- \item Euclidian division, \hyperpage{10}
- \item Euler characteristic, \hyperpage{217}
- \item Euler method, \hyperpage{257}
- \item Euler theorem, \hyperpage{49}
- \item Euler's formula, \hyperpage{107}, \hyperpage{149}
- \item Euler's theorem, \hyperpage{10}
- \item Euler's totient function, \hyperpage{10}
- \item Euler-Maclaurin formula, \hyperpage{95}
- \item Eulerian, \hyperpage{49}
- \item Eulerian circuit, \hyperpage{49}
- \item Eulerian trail, \hyperpage{49}
- \item evaluation, \hyperpage{11}, \hyperpage{161}
- \item even extension, \hyperpage{83}
- \item even periodic extension, \hyperpage{282}
- \item event, \hyperpage{172}
- \item evolute, \hyperpage{143}
- \item exact, \hyperpage{155}
- \item Examples of Euclidean motions, \hyperpage{72}
- \item Excluded point topology, \hyperpage{205}
- \item Existence of orthogonal polynomials, \hyperpage{95}
- \item Existence of the splitting field, \hyperpage{166}
- \item exists and it is finite, \hyperpage{297}
- \item Expansive fixed point theorem, \hyperpage{228}
- \item Expectation, \hyperpage{182}
- \item expectation, \hyperpage{177}, \hyperpage{181--183},
- \hyperpage{248}
- \item explicit, \hyperpage{257}
- \item explicit Euler method, \hyperpage{257}
- \item explicit form, \hyperpage{121}
- \item Explicit scheme in finite differences, \hyperpage{285}
- \item exponent, \hyperpage{88}
- \item exponential, \hyperpage{256}
- \item Exponential distribution, \hyperpage{177}
- \item exponential distribution, \hyperpage{177}
- \item exponential factor, \hyperpage{137}
- \item exponential function with base $a$, \hyperpage{28}
- \item exponential generating function, \hyperpage{47}
- \item exponential series, \hyperpage{47}
- \item extended complex plane, \hyperpage{104}
- \item extended real numbers, \hyperpage{104}
- \item extension, \hyperpage{125}
- \item exterior, \hyperpage{53}
- \item exterior angle, \hyperpage{159}
- \item Exterior angle theorem, \hyperpage{63}
- \item exterior differential, \hyperpage{155, 156}
- \item exterior point, \hyperpage{53}
- \item exterior product, \hyperpage{154}
- \item exterior vectors, \hyperpage{156}
- \item externally studentized residuals, \hyperpage{253}
+ \item edges, \hyperpage{160}
+ \item efficient estimator, \hyperpage{196}
+ \item eigenspace, \hyperpage{20}
+ \item eigenvalue, \hyperpage{309}
+ \item eigenvector, \hyperpage{20}
+ \item eigenvectors, \hyperpage{309}
+ \item Eikonal equation, \hyperpage{278}
+ \item Eisenstein's criterion, \hyperpage{45}, \hyperpage{47}
+ \item either $P$ or $Q$ are true, \hyperpage{8}
+ \item elastodynamics, \hyperpage{277}
+ \item elementary region, \hyperpage{59}
+ \item elementary symmetric polynomials, \hyperpage{163}
+ \item elliptic, \hyperpage{74}, \hyperpage{273}
+ \item elliptic equation, \hyperpage{277}
+ \item elliptic point, \hyperpage{150}
+ \item elliptic sector, \hyperpage{133}
+ \item embedded methods, \hyperpage{260}
+ \item empirical distribution, \hyperpage{202}
+ \item empty set, \hyperpage{6}
+ \item energy functional, \hyperpage{288}
+ \item entire function, \hyperpage{109}
+ \item Entropy, \hyperpage{256}
+ \item entropy, \hyperpage{256}
+ \item Entropy condition, \hyperpage{280}
+ \item envelope, \hyperpage{144}
+ \item equal, \hyperpage{6}
+ \item equal almost surely, \hyperpage{176}
+ \item equal in distribution, \hyperpage{176}
+ \item equally-spaced, \hyperpage{93}
+ \item equation of the hyperplane, \hyperpage{67}
+ \item equicontinuous, \hyperpage{121}
+ \item equicontinuous at a point, \hyperpage{125}, \hyperpage{304}
+ \item equilibrium point, \hyperpage{221}
+ \item equiprobable space, \hyperpage{177}
+ \item equivalence, \hyperpage{131}
+ \item equivalence class, \hyperpage{8}, \hyperpage{17}
+ \item equivalence relation, \hyperpage{8}
+ \item equivalent, \hyperpage{13}, \hyperpage{17}, \hyperpage{23},
+ \hyperpage{73}, \hyperpage{130}, \hyperpage{132},
+ \hyperpage{306}
+ \item equivalent dynamical systems, \hyperpage{131}
+ \item Ergotic theorem, \hyperpage{324, 325}
+ \item error of type I, \hyperpage{199}
+ \item error of type II, \hyperpage{199}
+ \item error sum of squares, \hyperpage{252}
+ \item Essential singularity, \hyperpage{117}
+ \item essential singularity, \hyperpage{117}
+ \item estimated average response, \hyperpage{253}
+ \item estimation of the prediction, \hyperpage{253}
+ \item estimator, \hyperpage{193}
+ \item Euclid's axioms, \hyperpage{63}
+ \item Euclid's theorem, \hyperpage{10}
+ \item Euclidean, \hyperpage{64}
+ \item Euclidean affine space, \hyperpage{72}
+ \item Euclidean metric, \hyperpage{205}
+ \item Euclidean motion, \hyperpage{73}
+ \item Euclidean plane, \hyperpage{64}
+ \item Euclidean space, \hyperpage{53}
+ \item Euclidean vector space, \hyperpage{24}
+ \item Euclidian division, \hyperpage{11}
+ \item Euler characteristic, \hyperpage{218}
+ \item Euler method, \hyperpage{258}
+ \item Euler theorem, \hyperpage{50}
+ \item Euler's formula, \hyperpage{108}, \hyperpage{150}
+ \item Euler's theorem, \hyperpage{11}
+ \item Euler's totient function, \hyperpage{11}
+ \item Euler-Maclaurin formula, \hyperpage{96}
+ \item Eulerian, \hyperpage{50}
+ \item Eulerian circuit, \hyperpage{50}
+ \item Eulerian trail, \hyperpage{50}
+ \item evaluation, \hyperpage{12}, \hyperpage{162}
+ \item even extension, \hyperpage{84}
+ \item even periodic extension, \hyperpage{283}
+ \item event, \hyperpage{173}
+ \item events, \hyperpage{336}
+ \item evolute, \hyperpage{144}
+ \item exact, \hyperpage{156}
+ \item Examples of Euclidean motions, \hyperpage{73}
+ \item Excluded point topology, \hyperpage{206}
+ \item Existence of orthogonal polynomials, \hyperpage{96}
+ \item Existence of the splitting field, \hyperpage{167}
+ \item exists and it is finite, \hyperpage{298}
+ \item Expansive fixed point theorem, \hyperpage{229}
+ \item Expectation, \hyperpage{183}, \hyperpage{336}
+ \item expectation, \hyperpage{178}, \hyperpage{182--184},
+ \hyperpage{249}
+ \item expectation of $X$, \hyperpage{336}
+ \item explicit, \hyperpage{258}
+ \item explicit Euler method, \hyperpage{258}
+ \item explicit form, \hyperpage{122}
+ \item Explicit scheme in finite differences, \hyperpage{286}
+ \item exponent, \hyperpage{89}
+ \item exponential, \hyperpage{257}
+ \item Exponential distribution, \hyperpage{178}
+ \item exponential distribution, \hyperpage{178}
+ \item exponential factor, \hyperpage{138}
+ \item exponential function with base $a$, \hyperpage{29}
+ \item exponential generating function, \hyperpage{48}
+ \item exponential series, \hyperpage{48}
+ \item extended complex plane, \hyperpage{105}
+ \item extended real numbers, \hyperpage{105}
+ \item extension, \hyperpage{126}
+ \item exterior, \hyperpage{54}
+ \item exterior angle, \hyperpage{160}
+ \item Exterior angle theorem, \hyperpage{64}
+ \item exterior differential, \hyperpage{156, 157}
+ \item exterior point, \hyperpage{54}
+ \item exterior product, \hyperpage{155}
+ \item exterior vectors, \hyperpage{157}
+ \item externally studentized residuals, \hyperpage{254}
\indexspace
- \item failure, \hyperpage{176}
- \item false, \hyperpage{176}
- \item Fano configuration, \hyperpage{66}
- \item fast Fourier transform, \hyperpage{239}
- \item Fatou's lemma, \hyperpage{183}, \hyperpage{296}
- \item feasible region, \hyperpage{50}
- \item feasible solution, \hyperpage{50}
- \item Fejér kernel, \hyperpage{84}, \hyperpage{233}
- \item Fejér mean, \hyperpage{233}
- \item Fejér means, \hyperpage{85}
- \item Fejér's theorem, \hyperpage{85}
- \item FEM, \hyperpage{274}
- \item Fermat's little theorem, \hyperpage{10}
- \item Fermat's principle, \hyperpage{277}
- \item FFT, \hyperpage{239}
- \item Fick's law, \hyperpage{277}
- \item Fick's law of diffusion, \hyperpage{277}
- \item Field, \hyperpage{41}
- \item field, \hyperpage{41}
- \item field extension, \hyperpage{163}
- \item field morphism, \hyperpage{161}
- \item field of complex numbers, \hyperpage{103}
- \item field of fractions, \hyperpage{45}, \hyperpage{162}
- \item field of rational functions, \hyperpage{162}
- \item filtration, \hyperpage{320}
- \item filtration space, \hyperpage{320}
- \item finer, \hyperpage{204}
- \item finer than, \hyperpage{31}, \hyperpage{57}
- \item finite, \hyperpage{24}, \hyperpage{48}, \hyperpage{163},
- \hyperpage{212}, \hyperpage{293}
- \item finite $k$-th moment, \hyperpage{184}
- \item finite difference method, \hyperpage{264}
- \item finite difference scheme, \hyperpage{267}
- \item finite element method, \hyperpage{274}
- \item finite expectation, \hyperpage{181--183}
- \item Finite field, \hyperpage{165}
- \item finite field, \hyperpage{165}
- \item finite moment of order $k$, \hyperpage{184}
- \item Finite subadditivity, \hyperpage{172}
- \item Finite-dimensional distributions, \hyperpage{332}
- \item finite-dimensional distributions, \hyperpage{332}
- \item finite-rank operator, \hyperpage{306}
- \item finitely generated, \hyperpage{164}
- \item first and second characteristic polynomials, \hyperpage{260}
- \item First Borel-Cantelli lemma, \hyperpage{187}
- \item first fundamental form, \hyperpage{147}
- \item first integral, \hyperpage{133}, \hyperpage{153}
- \item First isomorphism theorem, \hyperpage{17}, \hyperpage{38},
- \hyperpage{43}
- \item First Sylow theorem, \hyperpage{40}
- \item Fisher information, \hyperpage{194}
- \item Fisher's theorem, \hyperpage{196}
- \item Fisher-Neyman factorization theorem, \hyperpage{193}
- \item fixed field, \hyperpage{167}
- \item fixed point, \hyperpage{70}, \hyperpage{220}
- \item Fixed-point theorem, \hyperpage{89}
- \item flat, \hyperpage{202}
- \item Floating-point representation, \hyperpage{88}
- \item floating-point representation, \hyperpage{88}
- \item floating-point representation by rounding, \hyperpage{88}
- \item floating-point representation by truncation, \hyperpage{88}
- \item flow, \hyperpage{127}, \hyperpage{131}
- \item Flow box theorem, \hyperpage{131}
- \item flow of the linear ode, \hyperpage{125}
- \item flux, \hyperpage{61}, \hyperpage{158}
- \item Formal derivative, \hyperpage{166}
- \item formal derivative, \hyperpage{166}
+ \item failure, \hyperpage{177}
+ \item false, \hyperpage{177}
+ \item Fano configuration, \hyperpage{67}
+ \item fast Fourier transform, \hyperpage{240}
+ \item Fatou's lemma, \hyperpage{184}, \hyperpage{297},
+ \hyperpage{335}
+ \item feasible region, \hyperpage{51}
+ \item feasible solution, \hyperpage{51}
+ \item Fejér kernel, \hyperpage{85}, \hyperpage{234}
+ \item Fejér mean, \hyperpage{234}
+ \item Fejér means, \hyperpage{86}
+ \item Fejér's theorem, \hyperpage{86}
+ \item FEM, \hyperpage{275}
+ \item Fermat's little theorem, \hyperpage{11}
+ \item Fermat's principle, \hyperpage{278}
+ \item FFT, \hyperpage{240}
+ \item Fick's law, \hyperpage{278}
+ \item Fick's law of diffusion, \hyperpage{278}
+ \item Field, \hyperpage{42}
+ \item field, \hyperpage{42}
+ \item field extension, \hyperpage{164}
+ \item field morphism, \hyperpage{162}
+ \item field of complex numbers, \hyperpage{104}
+ \item field of fractions, \hyperpage{46}, \hyperpage{163}
+ \item field of rational functions, \hyperpage{163}
+ \item filtration, \hyperpage{321}
+ \item filtration space, \hyperpage{321}
+ \item finer, \hyperpage{205}
+ \item finer than, \hyperpage{32}, \hyperpage{58}
+ \item finite, \hyperpage{25}, \hyperpage{49}, \hyperpage{164},
+ \hyperpage{213}, \hyperpage{294}
+ \item finite $k$-th moment, \hyperpage{185}
+ \item finite difference method, \hyperpage{265}
+ \item finite difference scheme, \hyperpage{268}
+ \item finite element method, \hyperpage{275}
+ \item finite expectation, \hyperpage{182--184}
+ \item Finite field, \hyperpage{166}
+ \item finite field, \hyperpage{166}
+ \item finite moment of order $k$, \hyperpage{185}
+ \item Finite subadditivity, \hyperpage{173}
+ \item Finite-dimensional distributions, \hyperpage{333}
+ \item finite-dimensional distributions, \hyperpage{333}
+ \item finite-rank operator, \hyperpage{307}
+ \item finitely generated, \hyperpage{165}
+ \item first and second characteristic polynomials, \hyperpage{261}
+ \item First Borel-Cantelli lemma, \hyperpage{188}
+ \item first fundamental form, \hyperpage{148}
+ \item first integral, \hyperpage{134}, \hyperpage{154}
+ \item First isomorphism theorem, \hyperpage{18}, \hyperpage{39},
+ \hyperpage{44}
+ \item First Sylow theorem, \hyperpage{41}
+ \item Fisher information, \hyperpage{195}
+ \item Fisher's theorem, \hyperpage{197}
+ \item Fisher-Neyman factorization theorem, \hyperpage{194}
+ \item fixed field, \hyperpage{168}
+ \item fixed point, \hyperpage{71}, \hyperpage{221}
+ \item Fixed-point theorem, \hyperpage{90}
+ \item flat, \hyperpage{203}
+ \item Floating-point representation, \hyperpage{89}
+ \item floating-point representation, \hyperpage{89}
+ \item floating-point representation by rounding, \hyperpage{89}
+ \item floating-point representation by truncation, \hyperpage{89}
+ \item flow, \hyperpage{128}, \hyperpage{132}
+ \item Flow box theorem, \hyperpage{132}
+ \item flow of the linear ode, \hyperpage{126}
+ \item flux, \hyperpage{62}, \hyperpage{159}
+ \item Formal derivative, \hyperpage{167}
+ \item formal derivative, \hyperpage{167}
\item Forward and backward difference formula of order 1,
- \hyperpage{93}
- \item forward Euler method, \hyperpage{257}
- \item Forward-time backward-space, \hyperpage{267}
- \item Forward-time central-space, \hyperpage{267}, \hyperpage{273}
- \item Forward-time forward-space, \hyperpage{267}
- \item Fourier coefficients, \hyperpage{312}
- \item Fourier series, \hyperpage{82}, \hyperpage{312}
- \item Fourier transform, \hyperpage{230}, \hyperpage{236},
- \hyperpage{243}, \hyperpage{312}
- \item Fourier transform operator, \hyperpage{231}
- \item Fourier's law, \hyperpage{277}
- \item Fredholm alternative, \hyperpage{313}
- \item Fredholm operator with kernel $K$, \hyperpage{306}
- \item free variables, \hyperpage{13}
- \item Frenet-Serret formulas, \hyperpage{142}
- \item Frenet-Serret frame, \hyperpage{142}
- \item Fresnel integrals, \hyperpage{112}
- \item Frobenius endomorphism, \hyperpage{165}
- \item Fréchet, \hyperpage{211}
- \item FTBS, \hyperpage{267}
- \item FTCS, \hyperpage{267}
- \item FTFS, \hyperpage{267}
- \item Fubini's theorem, \hyperpage{58}, \hyperpage{174},
- \hyperpage{299}
- \item Fubini's theorem for elementary regions, \hyperpage{58}
- \item full QR decomposition, \hyperpage{266}
- \item function, \hyperpage{6}
- \item functionally independent, \hyperpage{133}
- \item Fundamental lemma of calculus of variations, \hyperpage{239},
- \hyperpage{278}
- \item fundamental matrix solution, \hyperpage{126}
- \item fundamental polygon of the surface, \hyperpage{217}
- \item fundamental solution, \hyperpage{244}, \hyperpage{284}
- \item Fundamental theorem of affine geometry, \hyperpage{71}
- \item Fundamental theorem of algebra, \hyperpage{44}, \hyperpage{113},
- \hyperpage{169}
- \item Fundamental theorem of arithmetic, \hyperpage{9}
- \item Fundamental theorem of calculus, \hyperpage{32},
- \hyperpage{297}
- \item Fundamental theorem of curves, \hyperpage{145}
- \item Fundamental theorem of Galois theory, \hyperpage{168}
- \item Fundamental theorem of projective geometry, \hyperpage{67}
- \item Fundamental theorem of symmetric polynomials, \hyperpage{163}
+ \hyperpage{94}
+ \item forward Euler method, \hyperpage{258}
+ \item Forward-time backward-space, \hyperpage{268}
+ \item Forward-time central-space, \hyperpage{268}, \hyperpage{274}
+ \item Forward-time forward-space, \hyperpage{268}
+ \item Fourier coefficients, \hyperpage{313}
+ \item Fourier series, \hyperpage{83}, \hyperpage{313}
+ \item Fourier transform, \hyperpage{231}, \hyperpage{237},
+ \hyperpage{244}, \hyperpage{313}
+ \item Fourier transform operator, \hyperpage{232}
+ \item Fourier's law, \hyperpage{278}
+ \item Fredholm alternative, \hyperpage{314}
+ \item Fredholm operator with kernel $K$, \hyperpage{307}
+ \item free variables, \hyperpage{14}
+ \item Frenet-Serret formulas, \hyperpage{143}
+ \item Frenet-Serret frame, \hyperpage{143}
+ \item Fresnel integrals, \hyperpage{113}
+ \item Frobenius endomorphism, \hyperpage{166}
+ \item Fréchet, \hyperpage{212}
+ \item FTBS, \hyperpage{268}
+ \item FTCS, \hyperpage{268}
+ \item FTFS, \hyperpage{268}
+ \item Fubini, \hyperpage{335}
+ \item Fubini's theorem, \hyperpage{59}, \hyperpage{175},
+ \hyperpage{300}
+ \item Fubini's theorem for elementary regions, \hyperpage{59}
+ \item full QR decomposition, \hyperpage{267}
+ \item function, \hyperpage{7}
+ \item functionally independent, \hyperpage{134}
+ \item Fundamental lemma of calculus of variations, \hyperpage{240},
+ \hyperpage{279}
+ \item fundamental matrix solution, \hyperpage{127}
+ \item fundamental polygon of the surface, \hyperpage{218}
+ \item fundamental solution, \hyperpage{245, 246}, \hyperpage{285}
+ \item Fundamental theorem of affine geometry, \hyperpage{72}
+ \item Fundamental theorem of algebra, \hyperpage{45}, \hyperpage{114},
+ \hyperpage{170}
+ \item Fundamental theorem of arithmetic, \hyperpage{10}
+ \item Fundamental theorem of calculus, \hyperpage{33},
+ \hyperpage{298}
+ \item Fundamental theorem of curves, \hyperpage{146}
+ \item Fundamental theorem of Galois theory, \hyperpage{169}
+ \item Fundamental theorem of projective geometry, \hyperpage{68}
+ \item Fundamental theorem of symmetric polynomials, \hyperpage{164}
\indexspace
- \item Galerkin approximation, \hyperpage{274}
- \item Galois, \hyperpage{167}
- \item Galois extension, \hyperpage{167}
- \item Galois group, \hyperpage{165}
- \item Gambler's ruin problem, \hyperpage{317}
- \item Gamma distribution, \hyperpage{178}
- \item gamma distribution, \hyperpage{178}
- \item Gamma function, \hyperpage{80}
- \item Gau\ss ' law, \hyperpage{277}
- \item Gau\ss ' law for magnetism, \hyperpage{277}
- \item Gau\ss ' lemma, \hyperpage{46}
- \item Gau\ss ' theorem, \hyperpage{9, 10}, \hyperpage{13}
- \item Gau\ss ' Theorema Egregium, \hyperpage{151}
- \item Gau\ss -Markov, \hyperpage{250}
- \item Gau\ss -Seidel method, \hyperpage{99}
- \item Gau\ss \ curvature, \hyperpage{148}
- \item Gau\ss \ equations, \hyperpage{151}
- \item Gau\ss \ map, \hyperpage{148}
- \item Gau\ss ian integers, \hyperpage{46}
- \item Gaussian elimination, \hyperpage{100}
- \item gaussian process, \hyperpage{329}
- \item gaussian vector, \hyperpage{329}
- \item General Cauchy's integral formula, \hyperpage{114}
+ \item Galerkin approximation, \hyperpage{275}
+ \item Galois, \hyperpage{168}
+ \item Galois extension, \hyperpage{168}
+ \item Galois group, \hyperpage{166}
+ \item Gambler's ruin problem, \hyperpage{318}
+ \item Gamma distribution, \hyperpage{179}
+ \item gamma distribution, \hyperpage{179}
+ \item Gamma function, \hyperpage{81}
+ \item Gau\ss ' law, \hyperpage{278}
+ \item Gau\ss ' law for magnetism, \hyperpage{278}
+ \item Gau\ss ' lemma, \hyperpage{47}
+ \item Gau\ss ' theorem, \hyperpage{10, 11}, \hyperpage{14}
+ \item Gau\ss ' Theorema Egregium, \hyperpage{152}
+ \item Gau\ss -Markov, \hyperpage{251}
+ \item Gau\ss -Seidel method, \hyperpage{100}
+ \item Gau\ss \ curvature, \hyperpage{149}
+ \item Gau\ss \ equations, \hyperpage{152}
+ \item Gau\ss \ map, \hyperpage{149}
+ \item Gau\ss ian integers, \hyperpage{47}
+ \item Gaussian elimination, \hyperpage{101}
+ \item gaussian process, \hyperpage{330}
+ \item gaussian vector, \hyperpage{330}
+ \item General Cauchy's integral formula, \hyperpage{115}
\item General Cauchy's integral formula for derivatives,
- \hyperpage{115}
- \item General Eisenstein's criterion, \hyperpage{44}
- \item General Frenet-Serret formulas, \hyperpage{142}
- \item General linear model, \hyperpage{249}
- \item general solution of the ode, \hyperpage{121}
- \item general term of the series, \hyperpage{75}, \hyperpage{104}
- \item Generalized argument principle, \hyperpage{117}
- \item Generalized Bendixson-Dulac theorem, \hyperpage{136}
- \item Generalized compound probability formula, \hyperpage{173}
- \item generalized eigenspace, \hyperpage{127}
- \item generalized eigenvector, \hyperpage{127}
- \item generalized heat kernel, \hyperpage{285}
- \item Generalized Hölder's inequality, \hyperpage{235}
- \item generalized solution, \hyperpage{244}
- \item generating set, \hyperpage{15}
- \item generator tree, \hyperpage{49}
- \item generatrix, \hyperpage{146}
- \item genus $g$ orientable surface, \hyperpage{216}
- \item genus $h$ non-orientable surface, \hyperpage{216}
- \item geodesic, \hyperpage{152}
- \item geodesic curvature, \hyperpage{152}
- \item Geometric distribution, \hyperpage{176}
- \item geometric distribution, \hyperpage{176}
- \item geometric multiplicity, \hyperpage{19}
- \item Gershgorin circle theorem, \hyperpage{91}
- \item Glide orthogonal reflections, \hyperpage{72}
- \item glide reflection, \hyperpage{71}
- \item glide vector, \hyperpage{72}
- \item Global Gau\ss -Bonnet theorem, \hyperpage{159}
- \item global maximum, \hyperpage{56}
- \item global minimum, \hyperpage{56}
- \item global stable manifold, \hyperpage{221}
- \item global truncation error, \hyperpage{257}
- \item global unstable manifold, \hyperpage{221}
- \item Goodness of fit, \hyperpage{199}
- \item Goursat's theorem, \hyperpage{111}
- \item Gra\ss mann formula, \hyperpage{15}, \hyperpage{66}
- \item gradient, \hyperpage{55}
- \item Gradient descent, \hyperpage{263}
- \item gradient vector field, \hyperpage{60}
- \item Gram-Schmidt process, \hyperpage{22}, \hyperpage{312}
- \item graph, \hyperpage{48}, \hyperpage{54}, \hyperpage{226}
- \item Graph of a function, \hyperpage{54}
- \item Great Picard's theorem, \hyperpage{117}
- \item greatest common divisor, \hyperpage{9}, \hyperpage{45}
- \item greatest element, \hyperpage{125}
- \item Green identities, \hyperpage{278}
- \item Green's formula, \hyperpage{158}
- \item Green's theorem, \hyperpage{61}
- \item grid, \hyperpage{267}
- \item Group, \hyperpage{36}
- \item group, \hyperpage{36}
- \item Group morphism, \hyperpage{37}
- \item group morphism, \hyperpage{37}
- \item Grönwall's lemma, \hyperpage{128}
+ \hyperpage{116}
+ \item General Eisenstein's criterion, \hyperpage{45}
+ \item General Frenet-Serret formulas, \hyperpage{143}
+ \item General linear model, \hyperpage{250}
+ \item general solution of the ode, \hyperpage{122}
+ \item general term of the series, \hyperpage{76}, \hyperpage{105}
+ \item Generalized argument principle, \hyperpage{118}
+ \item Generalized Bendixson-Dulac theorem, \hyperpage{137}
+ \item Generalized compound probability formula, \hyperpage{174}
+ \item generalized eigenspace, \hyperpage{128}
+ \item generalized eigenvector, \hyperpage{128}
+ \item generalized heat kernel, \hyperpage{286}
+ \item Generalized Hölder's inequality, \hyperpage{237}
+ \item generalized solution, \hyperpage{245}
+ \item generating set, \hyperpage{16}
+ \item generator tree, \hyperpage{50}
+ \item generatrix, \hyperpage{147}
+ \item genus $g$ orientable surface, \hyperpage{217}
+ \item genus $h$ non-orientable surface, \hyperpage{217}
+ \item geodesic, \hyperpage{153}
+ \item geodesic curvature, \hyperpage{153}
+ \item Geometric distribution, \hyperpage{177}
+ \item geometric distribution, \hyperpage{177}
+ \item geometric multiplicity, \hyperpage{20}
+ \item Gershgorin circle theorem, \hyperpage{92}
+ \item Glide orthogonal reflections, \hyperpage{73}
+ \item glide reflection, \hyperpage{72}
+ \item glide vector, \hyperpage{73}
+ \item Global Gau\ss -Bonnet theorem, \hyperpage{160}
+ \item global maximum, \hyperpage{57}
+ \item global minimum, \hyperpage{57}
+ \item global stable manifold, \hyperpage{222}
+ \item global truncation error, \hyperpage{258}
+ \item global unstable manifold, \hyperpage{222}
+ \item Goodness of fit, \hyperpage{200}
+ \item Goursat's theorem, \hyperpage{112}
+ \item Gra\ss mann formula, \hyperpage{16}, \hyperpage{67}
+ \item gradient, \hyperpage{56}
+ \item Gradient descent, \hyperpage{264}
+ \item gradient vector field, \hyperpage{61}
+ \item Gram-Schmidt process, \hyperpage{23}, \hyperpage{313}
+ \item graph, \hyperpage{49}, \hyperpage{55}, \hyperpage{227}
+ \item Graph of a function, \hyperpage{55}
+ \item Great Picard's theorem, \hyperpage{118}
+ \item greatest common divisor, \hyperpage{10}, \hyperpage{46}
+ \item greatest element, \hyperpage{126}
+ \item Green identities, \hyperpage{279}
+ \item Green's formula, \hyperpage{159}
+ \item Green's theorem, \hyperpage{62}
+ \item grid, \hyperpage{268}
+ \item Group, \hyperpage{37}
+ \item group, \hyperpage{37}
+ \item Group morphism, \hyperpage{38}
+ \item group morphism, \hyperpage{38}
+ \item Grönwall's lemma, \hyperpage{129}
\indexspace
- \item Hahn-Banach theorem, \hyperpage{307}
- \item half-line, \hyperpage{62}
- \item half-plane, \hyperpage{62}
- \item Hamilton-Jacobi equation, \hyperpage{278}
- \item Hamiltonian, \hyperpage{133}
- \item Hamiltonian system, \hyperpage{133}
- \item Handshaking lemma, \hyperpage{48}
- \item Hardy-Littlewood maximal function, \hyperpage{297}
- \item harmonic, \hyperpage{114}
- \item harmonic ratio, \hyperpage{68}
- \item Hartman-Grobman theorem, \hyperpage{133}, \hyperpage{221}
- \item has $t$ correct decimal digits, \hyperpage{88}
- \item has $u$ significant digits, \hyperpage{88}
- \item Hausdorff, \hyperpage{211}
- \item Heat equation, \hyperpage{139}, \hyperpage{277}
- \item heat equation, \hyperpage{139}
- \item heat flux, \hyperpage{277}
- \item heat kernel, \hyperpage{284}
- \item Heaviside step function, \hyperpage{241}, \hyperpage{284}
- \item Heine's theorem, \hyperpage{54}
- \item Heine-Borel theorem, \hyperpage{213}
- \item Hermite interpolation problem, \hyperpage{93}
- \item Hermite reduction method, \hyperpage{34}
- \item Hessian matrix, \hyperpage{55}
- \item heteroclinic orbit, \hyperpage{132}
- \item Heun method, \hyperpage{258}
- \item high-leverage point, \hyperpage{254}
- \item high-leverage points, \hyperpage{254}
- \item highest posterior density, \hyperpage{203}
- \item Hilbert basis, \hyperpage{311}
- \item Hilbert field, \hyperpage{63}
- \item Hilbert plane, \hyperpage{63}
- \item Hilbert space, \hyperpage{309}
- \item Hilbert transform, \hyperpage{246}
- \item Hilbert's basis theorem, \hyperpage{42}
- \item Hilbert's Nullstellensatz, \hyperpage{44}
- \item Hilbert-Schmidt operator with kernel $K$, \hyperpage{306}
+ \item Hahn-Banach theorem, \hyperpage{308}
+ \item half-line, \hyperpage{63}
+ \item half-plane, \hyperpage{63}
+ \item Hamilton-Jacobi equation, \hyperpage{279}
+ \item Hamiltonian, \hyperpage{134}
+ \item Hamiltonian system, \hyperpage{134}
+ \item Handshaking lemma, \hyperpage{49}
+ \item Hardy-Littlewood maximal function, \hyperpage{298}
+ \item harmonic, \hyperpage{115}
+ \item harmonic ratio, \hyperpage{69}
+ \item Hartman-Grobman theorem, \hyperpage{134}, \hyperpage{222}
+ \item has $t$ correct decimal digits, \hyperpage{89}
+ \item has $u$ significant digits, \hyperpage{89}
+ \item Hausdorff, \hyperpage{212}
+ \item Heat equation, \hyperpage{140}, \hyperpage{278}
+ \item heat equation, \hyperpage{140}
+ \item heat flux, \hyperpage{278}
+ \item heat kernel, \hyperpage{285}
+ \item Heaviside step function, \hyperpage{242}, \hyperpage{285}
+ \item Heine's theorem, \hyperpage{55}
+ \item Heine-Borel theorem, \hyperpage{214}
+ \item Hermite interpolation problem, \hyperpage{94}
+ \item Hermite reduction method, \hyperpage{35}
+ \item Hessian matrix, \hyperpage{56}
+ \item heteroclinic orbit, \hyperpage{133}
+ \item Heun method, \hyperpage{259}
+ \item high-leverage point, \hyperpage{255}
+ \item high-leverage points, \hyperpage{255}
+ \item highest posterior density, \hyperpage{204}
+ \item Hilbert basis, \hyperpage{313}
+ \item Hilbert field, \hyperpage{64}
+ \item Hilbert plane, \hyperpage{64}
+ \item Hilbert space, \hyperpage{311}
+ \item Hilbert transform, \hyperpage{247}
+ \item Hilbert's basis theorem, \hyperpage{43}
+ \item Hilbert's Nullstellensatz, \hyperpage{45}
+ \item Hilbert-Schmidt operator with kernel $K$, \hyperpage{307}
\item Hilbert-Schmidt spectral representation theorem,
- \hyperpage{312}
- \item holding times, \hyperpage{326}
- \item holes, \hyperpage{215}
- \item holomorphic, \hyperpage{108}
- \item holomorphic differential equation, \hyperpage{220}
- \item homeomorphic, \hyperpage{207}
- \item homeomorphism, \hyperpage{207}
- \item Homoclinic bifurcation, \hyperpage{225}
- \item homoclinic bifurcation, \hyperpage{225}
- \item homoclinic orbit, \hyperpage{132}
- \item homogeneous, \hyperpage{48}, \hyperpage{121}, \hyperpage{125}
- \item homogeneous coordinates, \hyperpage{66}
- \item Homogeneous distribution, \hyperpage{244}
- \item homogeneous of degree $k$, \hyperpage{220}
+ \hyperpage{314}
+ \item holding times, \hyperpage{327}
+ \item holes, \hyperpage{216}
+ \item holomorphic, \hyperpage{109}
+ \item holomorphic differential equation, \hyperpage{221}
+ \item homeomorphic, \hyperpage{208}
+ \item homeomorphism, \hyperpage{208}
+ \item Homoclinic bifurcation, \hyperpage{226}
+ \item homoclinic bifurcation, \hyperpage{226}
+ \item homoclinic orbit, \hyperpage{133}
+ \item homogeneous, \hyperpage{49}, \hyperpage{122}, \hyperpage{126}
+ \item homogeneous coordinates, \hyperpage{67}
+ \item Homogeneous distribution, \hyperpage{245}
+ \item homogeneous of degree $k$, \hyperpage{221}
\item homogeneous of degree $r\in \ensuremath {\mathbb {R}}$,
- \hyperpage{244}
- \item Homogenization, \hyperpage{73}
- \item homogenization, \hyperpage{69}
- \item homography, \hyperpage{66}
- \item homologous to zero, \hyperpage{114}
- \item Homotheties, \hyperpage{71}
- \item homothety, \hyperpage{18}, \hyperpage{71}
- \item homotopic, \hyperpage{138}
- \item homotopy, \hyperpage{138}
- \item Hopf bifurcation theorem, \hyperpage{225}
- \item Hopf-bifurcation, \hyperpage{225}
- \item Hurwitz's theorem, \hyperpage{118}
- \item hyperbolic, \hyperpage{267}, \hyperpage{272}
- \item hyperbolic critical point, \hyperpage{133}
- \item hyperbolic equations, \hyperpage{276}
- \item Hyperbolic geometry, \hyperpage{64}
- \item hyperbolic matrix, \hyperpage{133}
- \item hyperbolic periodic orbit, \hyperpage{135}
- \item hyperbolic plane, \hyperpage{73}
- \item hyperbolic point, \hyperpage{149}
- \item hyperbolic sector, \hyperpage{132}
- \item Hypergeometric distribution, \hyperpage{176}
- \item hypergeometric distribution, \hyperpage{176}
- \item hyperplane, \hyperpage{66}, \hyperpage{69}
- \item hypothesis, \hyperpage{198}
- \item Hypothesis test, \hyperpage{198}
- \item hypothesis test, \hyperpage{198}
- \item Hölder condition, \hyperpage{246}
- \item Hölder conjugates, \hyperpage{301}
- \item Hölder's inequality, \hyperpage{301}
+ \hyperpage{245}
+ \item Homogenization, \hyperpage{74}
+ \item homogenization, \hyperpage{70}
+ \item homography, \hyperpage{67}
+ \item homologous to zero, \hyperpage{115}
+ \item Homotheties, \hyperpage{72}
+ \item homothety, \hyperpage{19}, \hyperpage{72}
+ \item homotopic, \hyperpage{139}
+ \item homotopy, \hyperpage{139}
+ \item Hopf bifurcation theorem, \hyperpage{226}
+ \item Hopf-bifurcation, \hyperpage{226}
+ \item Hurwitz's theorem, \hyperpage{119}
+ \item hyperbolic, \hyperpage{268}, \hyperpage{273}
+ \item hyperbolic critical point, \hyperpage{134}
+ \item hyperbolic equations, \hyperpage{277}
+ \item Hyperbolic geometry, \hyperpage{65}
+ \item hyperbolic matrix, \hyperpage{134}
+ \item hyperbolic periodic orbit, \hyperpage{136}
+ \item hyperbolic plane, \hyperpage{74}
+ \item hyperbolic point, \hyperpage{150}
+ \item hyperbolic sector, \hyperpage{133}
+ \item Hypergeometric distribution, \hyperpage{177}
+ \item hypergeometric distribution, \hyperpage{177}
+ \item hyperplane, \hyperpage{67}, \hyperpage{70}
+ \item hypothesis, \hyperpage{199}
+ \item Hypothesis test, \hyperpage{199}
+ \item hypothesis test, \hyperpage{199}
+ \item Hölder condition, \hyperpage{247}
+ \item Hölder conjugates, \hyperpage{302}
+ \item Hölder's inequality, \hyperpage{302, 303}
\indexspace
- \item i.i.d., \hyperpage{180}
- \item Ideal, \hyperpage{42}
- \item ideal, \hyperpage{42}
- \item idempotent, \hyperpage{13}
- \item identifiable, \hyperpage{192}
- \item ill-conditioned, \hyperpage{89}
- \item image, \hyperpage{6}, \hyperpage{16}, \hyperpage{37},
- \hyperpage{114}
- \item imaginary part, \hyperpage{103}
- \item Immersion, \hyperpage{145}
- \item immersion, \hyperpage{145}
- \item implicit, \hyperpage{257}
- \item implicit Euler method, \hyperpage{257}
- \item implicit form, \hyperpage{121}
- \item Implicit function theorem, \hyperpage{56}
- \item Implicit scheme in finite differences, \hyperpage{285}
- \item improper, \hyperpage{36}, \hyperpage{202}
- \item improper integral, \hyperpage{78}
- \item in perspective with respect to a line, \hyperpage{67}
- \item in perspective with respect to a point, \hyperpage{67}
- \item Incidence axioms, \hyperpage{62}
- \item incidence relation, \hyperpage{62}
- \item incident, \hyperpage{48}
- \item incompressible flow, \hyperpage{276}
- \item inconsistent, \hyperpage{13}
- \item increasing, \hyperpage{27}, \hyperpage{180}
- \item increment, \hyperpage{180}
- \item incremental function, \hyperpage{257}
- \item independent, \hyperpage{133}, \hyperpage{180}, \hyperpage{315}
- \item independent and identically distributed, \hyperpage{180}
- \item independent events, \hyperpage{173}
- \item independent increments, \hyperpage{325}
- \item Independent samples with known variances, \hyperpage{197}
+ \item i.i.d., \hyperpage{181}
+ \item Ideal, \hyperpage{43}
+ \item ideal, \hyperpage{43}
+ \item idempotent, \hyperpage{14}
+ \item identifiable, \hyperpage{193}
+ \item ill-conditioned, \hyperpage{90}
+ \item image, \hyperpage{7}, \hyperpage{17}, \hyperpage{38},
+ \hyperpage{115}
+ \item imaginary part, \hyperpage{104}
+ \item Immersion, \hyperpage{146}
+ \item immersion, \hyperpage{146}
+ \item implicit, \hyperpage{258}
+ \item implicit Euler method, \hyperpage{258}
+ \item implicit form, \hyperpage{122}
+ \item Implicit function theorem, \hyperpage{57}
+ \item Implicit scheme in finite differences, \hyperpage{286}
+ \item improper, \hyperpage{37}, \hyperpage{203}
+ \item improper integral, \hyperpage{79}
+ \item in perspective with respect to a line, \hyperpage{68}
+ \item in perspective with respect to a point, \hyperpage{68}
+ \item Incidence axioms, \hyperpage{63}
+ \item incidence relation, \hyperpage{63}
+ \item incident, \hyperpage{49}
+ \item incompressible flow, \hyperpage{277}
+ \item inconsistent, \hyperpage{14}
+ \item increasing, \hyperpage{28}, \hyperpage{181}
+ \item increment, \hyperpage{181}
+ \item incremental function, \hyperpage{258}
+ \item independent, \hyperpage{134}, \hyperpage{181}, \hyperpage{316}
+ \item independent and identically distributed, \hyperpage{181}
+ \item independent events, \hyperpage{174}
+ \item independent increments, \hyperpage{326}
+ \item Independent samples with known variances, \hyperpage{198}
\item Independent samples with unknown equal variances,
- \hyperpage{197}
- \item Independent samples with unknown variances, \hyperpage{197}
- \item independent variable, \hyperpage{121}
- \item indeterminate, \hyperpage{10}, \hyperpage{13}
- \item index, \hyperpage{13}, \hyperpage{38}, \hyperpage{73},
- \hyperpage{112}, \hyperpage{114}, \hyperpage{137, 138},
- \hyperpage{159}
- \item indicator function, \hyperpage{8}
- \item indistinguishable, \hyperpage{330}
- \item induced subgraph, \hyperpage{48}
- \item Induction axiom, \hyperpage{5}
- \item Inexact Newton method, \hyperpage{263}
- \item infimum, \hyperpage{24}
- \item infinite, \hyperpage{24}, \hyperpage{163}
- \item infinite order, \hyperpage{240}
- \item infinite product topology, \hyperpage{208}
- \item infinitesimal generator, \hyperpage{327}
- \item infinitesimal transition scheme, \hyperpage{327}
- \item inflection point, \hyperpage{30}
- \item Information, \hyperpage{255}
- \item information of an event, \hyperpage{255}
- \item initial conditions, \hyperpage{121}
- \item initial distribution, \hyperpage{317}
- \item initial point, \hyperpage{214}
- \item Initial value problem, \hyperpage{121}
- \item initial value problem, \hyperpage{121}
- \item initial values, \hyperpage{47}
- \item injective, \hyperpage{6}
- \item inner product, \hyperpage{23}, \hyperpage{81}, \hyperpage{309}
- \item integrable, \hyperpage{31}, \hyperpage{181, 182}
- \item integrable function, \hyperpage{58}
- \item integrable function over $E$, \hyperpage{296}
- \item integral, \hyperpage{110}, \hyperpage{157, 158}
- \item integral curve, \hyperpage{153}
- \item integral domain, \hyperpage{43}
- \item Integral in cylindrical coordinates, \hyperpage{59}
- \item Integral in polar coordinates, \hyperpage{59}
- \item Integral in spherical coordinates, \hyperpage{59}
+ \hyperpage{198}
+ \item Independent samples with unknown variances, \hyperpage{198}
+ \item independent variable, \hyperpage{122}
+ \item indeterminate, \hyperpage{11}, \hyperpage{14}
+ \item index, \hyperpage{14}, \hyperpage{39}, \hyperpage{74},
+ \hyperpage{113}, \hyperpage{115}, \hyperpage{138, 139},
+ \hyperpage{160}
+ \item indicator function, \hyperpage{9}
+ \item indistinguishable, \hyperpage{331}
+ \item induced subgraph, \hyperpage{49}
+ \item Induction axiom, \hyperpage{6}
+ \item Inexact Newton method, \hyperpage{264}
+ \item infimum, \hyperpage{25}
+ \item infinite, \hyperpage{25}, \hyperpage{164}
+ \item infinite order, \hyperpage{241}
+ \item infinite product topology, \hyperpage{209}
+ \item infinitesimal generator, \hyperpage{328}
+ \item infinitesimal transition scheme, \hyperpage{328}
+ \item inflection point, \hyperpage{31}
+ \item Information, \hyperpage{256}
+ \item information of an event, \hyperpage{256}
+ \item initial conditions, \hyperpage{122}
+ \item initial distribution, \hyperpage{318}
+ \item initial point, \hyperpage{215}
+ \item Initial value problem, \hyperpage{122}
+ \item initial value problem, \hyperpage{122}
+ \item initial values, \hyperpage{48}
+ \item injective, \hyperpage{7}
+ \item inner product, \hyperpage{24}, \hyperpage{82}, \hyperpage{310}
+ \item integrable, \hyperpage{32}, \hyperpage{182, 183}
+ \item integrable function, \hyperpage{59}
+ \item integrable function over $E$, \hyperpage{297}
+ \item integral, \hyperpage{111}, \hyperpage{158, 159}
+ \item integral curve, \hyperpage{154}
+ \item integral domain, \hyperpage{44}
+ \item Integral in cylindrical coordinates, \hyperpage{60}
+ \item Integral in polar coordinates, \hyperpage{60}
+ \item Integral in spherical coordinates, \hyperpage{60}
\item integral of $f$ over $\ensuremath {\mathbb {R}}^n$,
- \hyperpage{295}
- \item integral of $f$ over $E$, \hyperpage{296}
+ \hyperpage{296}
+ \item integral of $f$ over $E$, \hyperpage{297}
\item integral of $f$ over a measurable set $E\subseteq \ensuremath {\mathbb {R}}^n$,
- \hyperpage{295}
- \item integral of $f$ over the region $R$, \hyperpage{147}
+ \hyperpage{296}
+ \item integral of $f$ over the region $R$, \hyperpage{148}
+ \item integral of $f$ with respect to $\mu $, \hyperpage{335}
\item integral of $s$ over $\ensuremath {\mathbb {R}}^n$,
- \hyperpage{294}
- \item integral of $s$ over a measurable set $E$, \hyperpage{294}
- \item Integral test, \hyperpage{76}, \hyperpage{79}
- \item Integrating factor, \hyperpage{123}
- \item integrating factor, \hyperpage{123}, \hyperpage{137}
- \item Integration by parts, \hyperpage{32}, \hyperpage{297}
- \item Integration by substitution, \hyperpage{32}
- \item inter-arrival times, \hyperpage{326}
- \item Interior, \hyperpage{205}
- \item interior, \hyperpage{53}, \hyperpage{205}
- \item interior point, \hyperpage{53}, \hyperpage{156},
- \hyperpage{206}
- \item interior product, \hyperpage{155}
- \item Intermediate value theorem, \hyperpage{27}, \hyperpage{54},
- \hyperpage{93}, \hyperpage{214}
- \item internally studentized residuals, \hyperpage{253}
- \item interpolation problem, \hyperpage{92}
- \item intersection, \hyperpage{5}
- \item interval, \hyperpage{290}
- \item Interval for $\mu $ with $\sigma $ known, \hyperpage{197}
- \item Intervals for $\mu $ and $\sigma ^2$, \hyperpage{197}
- \item invariance level, \hyperpage{70}
- \item Invariance of the MLE, \hyperpage{194}
- \item invariant, \hyperpage{130}
- \item invariant algebraic curve, \hyperpage{134}
- \item invariant subspace, \hyperpage{20}
- \item invariant under an affinity, \hyperpage{70}
- \item inverse discrete Fourier transform, \hyperpage{238}
- \item inverse Fourier transform, \hyperpage{230}, \hyperpage{236},
- \hyperpage{243}
- \item inverse function, \hyperpage{6}
- \item Inverse function rule, \hyperpage{29}
- \item Inverse function theorem, \hyperpage{56}
- \item Inverse function theorem for surfaces, \hyperpage{147}
- \item Inverse power method, \hyperpage{100}
- \item inverse power method, \hyperpage{100}
- \item inverse semidiscrete Fourier transform, \hyperpage{269}
- \item inversion, \hyperpage{118}
- \item Inversion theorem, \hyperpage{232}
- \item invertible, \hyperpage{6}, \hyperpage{13}
- \item Inviscid flow, \hyperpage{276}
- \item involute, \hyperpage{143}
- \item irreducible, \hyperpage{11}, \hyperpage{43}, \hyperpage{99},
- \hyperpage{328}
- \item irreducible chain, \hyperpage{319}
- \item irreducible class, \hyperpage{319}
- \item irreducible polynomial, \hyperpage{163}
- \item is finer than, \hyperpage{305}
- \item isolated point, \hyperpage{53}
- \item isolated singular point, \hyperpage{159}
- \item isolated singularity, \hyperpage{115}, \hyperpage{159}
- \item isometric, \hyperpage{22}
- \item isometry, \hyperpage{22}, \hyperpage{73}, \hyperpage{147}
- \item isomorphic, \hyperpage{16}, \hyperpage{37}, \hyperpage{49},
- \hyperpage{305}
- \item isomorphism, \hyperpage{37}
- \item isomorphism between projective spaces, \hyperpage{66}
- \item Isoperimetric inequality, \hyperpage{87}
- \item isotropic, \hyperpage{21}
- \item iteration matrix, \hyperpage{98}
- \item itinerary, \hyperpage{229}
- \item Itinerary lemma, \hyperpage{228}
- \item ivp, \hyperpage{121}
+ \hyperpage{295}
+ \item integral of $s$ over a measurable set $E$, \hyperpage{295}
+ \item Integral test, \hyperpage{77}, \hyperpage{80}
+ \item Integrating factor, \hyperpage{124}
+ \item integrating factor, \hyperpage{124}, \hyperpage{138}
+ \item Integration by parts, \hyperpage{33}, \hyperpage{298}
+ \item Integration by substitution, \hyperpage{33}
+ \item inter-arrival times, \hyperpage{327}
+ \item Interior, \hyperpage{206}
+ \item interior, \hyperpage{54}, \hyperpage{206}
+ \item interior point, \hyperpage{54}, \hyperpage{157},
+ \hyperpage{207}
+ \item interior product, \hyperpage{156}
+ \item Intermediate value theorem, \hyperpage{28}, \hyperpage{55},
+ \hyperpage{94}, \hyperpage{215}
+ \item internally studentized residuals, \hyperpage{254}
+ \item Interpolation inequality, \hyperpage{303}
+ \item interpolation problem, \hyperpage{93}
+ \item intersection, \hyperpage{6}
+ \item interval, \hyperpage{291}
+ \item Interval for $\mu $ with $\sigma $ known, \hyperpage{198}
+ \item Intervals for $\mu $ and $\sigma ^2$, \hyperpage{198}
+ \item invariance level, \hyperpage{71}
+ \item Invariance of the MLE, \hyperpage{195}
+ \item invariant, \hyperpage{131}
+ \item invariant algebraic curve, \hyperpage{135}
+ \item invariant subspace, \hyperpage{21}
+ \item invariant under an affinity, \hyperpage{71}
+ \item inverse discrete Fourier transform, \hyperpage{239}
+ \item inverse Fourier transform, \hyperpage{231}, \hyperpage{237},
+ \hyperpage{244}
+ \item inverse function, \hyperpage{7}
+ \item Inverse function rule, \hyperpage{30}
+ \item Inverse function theorem, \hyperpage{57}
+ \item Inverse function theorem for surfaces, \hyperpage{148}
+ \item Inverse power method, \hyperpage{101}
+ \item inverse power method, \hyperpage{101}
+ \item inverse semidiscrete Fourier transform, \hyperpage{270}
+ \item inversion, \hyperpage{119}
+ \item Inversion theorem, \hyperpage{233}
+ \item invertible, \hyperpage{7}, \hyperpage{14}
+ \item Inviscid flow, \hyperpage{277}
+ \item involute, \hyperpage{144}
+ \item irreducible, \hyperpage{12}, \hyperpage{44}, \hyperpage{100},
+ \hyperpage{329}
+ \item irreducible chain, \hyperpage{320}
+ \item irreducible class, \hyperpage{320}
+ \item irreducible polynomial, \hyperpage{164}
+ \item is finer than, \hyperpage{306}
+ \item isolated point, \hyperpage{54}
+ \item isolated singular point, \hyperpage{160}
+ \item isolated singularity, \hyperpage{116}, \hyperpage{160}
+ \item isometric, \hyperpage{23}
+ \item isometry, \hyperpage{23}, \hyperpage{74}, \hyperpage{148}
+ \item isomorphic, \hyperpage{17}, \hyperpage{38}, \hyperpage{50},
+ \hyperpage{306}
+ \item isomorphism, \hyperpage{38}
+ \item isomorphism between projective spaces, \hyperpage{67}
+ \item Isoperimetric inequality, \hyperpage{88}
+ \item isotropic, \hyperpage{22}
+ \item iteration matrix, \hyperpage{99}
+ \item itinerary, \hyperpage{230}
+ \item Itinerary lemma, \hyperpage{229}
+ \item ivp, \hyperpage{122}
\indexspace
- \item Jacobi identity, \hyperpage{141}
- \item Jacobi method, \hyperpage{99}
- \item Jacobian determinant, \hyperpage{54}
- \item Jacobian matrix, \hyperpage{54}
- \item Jeffrey's prior, \hyperpage{202}
- \item joint pdf, \hyperpage{179}
- \item joint pmf, \hyperpage{179}
- \item joint probability density function, \hyperpage{179}
- \item Joint probability mass function, \hyperpage{179}
- \item joint probability mass function, \hyperpage{179}
- \item Jordan arc, \hyperpage{60}
- \item Jordan block, \hyperpage{20}
- \item Jordan closed curve, \hyperpage{60}
- \item Jordan curve theorem, \hyperpage{217}
- \item Jordan form, \hyperpage{20}
- \item Jordan matrix, \hyperpage{20}
- \item Jump discontinuity, \hyperpage{27}
- \item jump process, \hyperpage{327}
+ \item Jacobi identity, \hyperpage{142}
+ \item Jacobi method, \hyperpage{100}
+ \item Jacobian determinant, \hyperpage{55}
+ \item Jacobian matrix, \hyperpage{55}
+ \item Jeffrey's prior, \hyperpage{203}
+ \item Jensen's inequality, \hyperpage{236}, \hyperpage{336}
+ \item joint pdf, \hyperpage{180}
+ \item joint pmf, \hyperpage{180}
+ \item joint probability density function, \hyperpage{180}
+ \item Joint probability mass function, \hyperpage{180}
+ \item joint probability mass function, \hyperpage{180}
+ \item Jordan arc, \hyperpage{61}
+ \item Jordan block, \hyperpage{21}
+ \item Jordan closed curve, \hyperpage{61}
+ \item Jordan curve theorem, \hyperpage{218}
+ \item Jordan form, \hyperpage{21}
+ \item Jordan matrix, \hyperpage{21}
+ \item Jump discontinuity, \hyperpage{28}
+ \item jump process, \hyperpage{328}
\indexspace
- \item Kelley's theorem, \hyperpage{212}
- \item kernel, \hyperpage{16}, \hyperpage{37}
- \item kernel function, \hyperpage{78}
- \item Klein bottle, \hyperpage{210}
- \item Kolmogorov, \hyperpage{211}
- \item Kolmogorov axioms, \hyperpage{172}
- \item Kolmogorov extension theorem, \hyperpage{332}
- \item Kolmogorov system, \hyperpage{220}
- \item Kolmogorov's backward equation, \hyperpage{327}
- \item Kolmogorov's continuity theorem, \hyperpage{330}
- \item Kolmogorov's forward equation, \hyperpage{327}
- \item Kolmogorov's strong law, \hyperpage{189}
- \item Kronecker delta, \hyperpage{18}
- \item Kronecker's lemma, \hyperpage{163}
- \item Kronecker's theorem, \hyperpage{166}
- \item Kullback-Leibler divergence, \hyperpage{255}
- \item Kuratowski's problem, \hyperpage{206}
+ \item Kelley's theorem, \hyperpage{213}
+ \item kernel, \hyperpage{17}, \hyperpage{38}
+ \item kernel function, \hyperpage{79}
+ \item Klein bottle, \hyperpage{211}
+ \item Kolmogorov, \hyperpage{212}
+ \item Kolmogorov axioms, \hyperpage{173}
+ \item Kolmogorov extension theorem, \hyperpage{333}
+ \item Kolmogorov system, \hyperpage{221}
+ \item Kolmogorov's backward equation, \hyperpage{328}
+ \item Kolmogorov's continuity theorem, \hyperpage{331}
+ \item Kolmogorov's forward equation, \hyperpage{328}
+ \item Kolmogorov's strong law, \hyperpage{191}
+ \item Kronecker delta, \hyperpage{19}
+ \item Kronecker's lemma, \hyperpage{164}
+ \item Kronecker's theorem, \hyperpage{167}
+ \item Kullback-Leibler divergence, \hyperpage{256}
+ \item Kuratowski's problem, \hyperpage{207}
\indexspace
- \item L'H\^opital's rule, \hyperpage{29}
- \item lack of fit test, \hyperpage{253}
- \item Lagrange basis polynomials, \hyperpage{92}
- \item Lagrange multipliers theorem, \hyperpage{57}
- \item Lagrange's interpolation problem, \hyperpage{92}
- \item Lagrange's theorem, \hyperpage{38}
- \item Laguerre polynomials, \hyperpage{95}
- \item Lamé coefficients, \hyperpage{276}
- \item Laplace equation, \hyperpage{139}, \hyperpage{287}
- \item Laplacian, \hyperpage{60}
- \item lattice of subgroups, \hyperpage{168}
- \item Laurent series, \hyperpage{116}
- \item Laurent series theorem, \hyperpage{116}
- \item Law of the iterated logarithm, \hyperpage{332}
- \item Law of total expectation, \hyperpage{185, 186}, \hyperpage{314}
- \item Law of total probability, \hyperpage{173}, \hyperpage{314}
- \item Lax theorem, \hyperpage{260}
- \item Lax-Friedrichs scheme, \hyperpage{267}
- \item Lax-Richtmyer equivalence theorem, \hyperpage{272}
- \item Lax-Wendroff, \hyperpage{270}
- \item Lax-Wendroff scheme, \hyperpage{270}
- \item leading coefficient, \hyperpage{10}
- \item Leapfrog scheme, \hyperpage{267}, \hyperpage{273}
- \item least common multiple, \hyperpage{9}
- \item least element, \hyperpage{8}
- \item Least-squares method, \hyperpage{249}
- \item least-squares method, \hyperpage{249}
- \item leave, \hyperpage{49}
- \item Lebesgue differentiation theorem, \hyperpage{298}
- \item Lebesgue integrable, \hyperpage{174}
- \item Lebesgue integral, \hyperpage{174}
- \item Lebesgue measurable, \hyperpage{292, 293}
- \item Lebesgue measure, \hyperpage{174}, \hyperpage{292}
- \item left cosets, \hyperpage{38}
- \item Left side, \hyperpage{119}
- \item left singular vectors, \hyperpage{264}
- \item Left-open interval, \hyperpage{24}
- \item left-sided limit of $f$ at $x_0$, \hyperpage{26}
- \item Legendre polynomials, \hyperpage{96}
- \item Leibnitz rule, \hyperpage{241}
- \item Leibnitz's test, \hyperpage{76}
- \item length, \hyperpage{57}, \hyperpage{140}
- \item length of the polygonal, \hyperpage{33}, \hyperpage{59},
- \hyperpage{140}
- \item level set, \hyperpage{54}
- \item leverage, \hyperpage{252}
- \item levorotation, \hyperpage{144}
- \item lexicographic degree, \hyperpage{162}
- \item lexicographic order, \hyperpage{162}
- \item Likelihood, \hyperpage{194}
- \item likelihood function, \hyperpage{194}
- \item likelihood ratio test, \hyperpage{199}
- \item Likelihood-ratio test, \hyperpage{199}
- \item Limit, \hyperpage{25}
- \item limit, \hyperpage{104}, \hyperpage{187}
- \item Limit comparison test, \hyperpage{75}
- \item limit cycle, \hyperpage{135}
- \item limit distribution, \hyperpage{328}
- \item limit inferior, \hyperpage{26}, \hyperpage{187}
- \item limit of $f$ at infinity, \hyperpage{27}
- \item limit of the function $f$ at the point $x_0$, \hyperpage{26}
- \item limit set, \hyperpage{53}
- \item limit superior, \hyperpage{26}, \hyperpage{187}
- \item line, \hyperpage{66}, \hyperpage{69}
- \item line integral, \hyperpage{60}, \hyperpage{111}
- \item line intergal, \hyperpage{158}
- \item line of curvature, \hyperpage{149}
- \item line search method, \hyperpage{263}
- \item linear, \hyperpage{121}
- \item linear $k$-step method, \hyperpage{260}
- \item linear combination, \hyperpage{15}
- \item linear convergence, \hyperpage{90}
- \item linear discrete map, \hyperpage{221}
- \item linear equation, \hyperpage{12}
- \item Linear loss function, \hyperpage{202}
- \item linear map, \hyperpage{16}
- \item Linear multistep method, \hyperpage{260}
- \item linear programming to maximize, \hyperpage{50}
- \item linear programming to minimize, \hyperpage{50}
- \item linear recurrence relation of order $k$, \hyperpage{47}
- \item linear saddles, \hyperpage{226}
- \item linear span, \hyperpage{15}
- \item Linearity, \hyperpage{75}
- \item linearization, \hyperpage{220}
- \item linearly dependent, \hyperpage{15}, \hyperpage{81}
- \item linearly independent, \hyperpage{15}, \hyperpage{81}
- \item lines, \hyperpage{62}
- \item Liouville's formula, \hyperpage{126}, \hyperpage{152}
- \item Liouville's theorem, \hyperpage{113}
- \item Lipschitz continuous, \hyperpage{54}
+ \item L'H\^opital's rule, \hyperpage{30}
+ \item lack of fit test, \hyperpage{254}
+ \item Lagrange basis polynomials, \hyperpage{93}
+ \item Lagrange multipliers theorem, \hyperpage{58}
+ \item Lagrange's interpolation problem, \hyperpage{93}
+ \item Lagrange's theorem, \hyperpage{39}
+ \item Laguerre polynomials, \hyperpage{96}
+ \item Lamé coefficients, \hyperpage{277}
+ \item Laplace equation, \hyperpage{140}, \hyperpage{288}
+ \item Laplacian, \hyperpage{61}
+ \item lattice of subgroups, \hyperpage{169}
+ \item Laurent series, \hyperpage{117}
+ \item Laurent series theorem, \hyperpage{117}
+ \item law of $X$, \hyperpage{336}
+ \item Law of the iterated logarithm, \hyperpage{333}
+ \item Law of total expectation, \hyperpage{186, 187}, \hyperpage{315}
+ \item Law of total probability, \hyperpage{174}, \hyperpage{315}
+ \item Lax theorem, \hyperpage{261}
+ \item Lax-Friedrichs scheme, \hyperpage{268}
+ \item Lax-Richtmyer equivalence theorem, \hyperpage{273}
+ \item Lax-Wendroff, \hyperpage{271}
+ \item Lax-Wendroff scheme, \hyperpage{271}
+ \item leading coefficient, \hyperpage{11}
+ \item Leapfrog scheme, \hyperpage{268}, \hyperpage{274}
+ \item least common multiple, \hyperpage{10}
+ \item least element, \hyperpage{9}
+ \item Least-squares method, \hyperpage{250}
+ \item least-squares method, \hyperpage{250}
+ \item leave, \hyperpage{50}
+ \item Lebesgue differentiation theorem, \hyperpage{299}
+ \item Lebesgue integrable, \hyperpage{175}
+ \item Lebesgue integral, \hyperpage{175}
+ \item Lebesgue measurable, \hyperpage{293, 294}
+ \item Lebesgue measure, \hyperpage{175}, \hyperpage{293}
+ \item left cosets, \hyperpage{39}
+ \item Left side, \hyperpage{120}
+ \item left singular vectors, \hyperpage{265}
+ \item Left-open interval, \hyperpage{25}
+ \item left-sided limit of $f$ at $x_0$, \hyperpage{27}
+ \item Legendre polynomials, \hyperpage{97}
+ \item Leibnitz rule, \hyperpage{243}
+ \item Leibnitz's test, \hyperpage{77}
+ \item length, \hyperpage{58}, \hyperpage{141}
+ \item length of the polygonal, \hyperpage{34}, \hyperpage{60},
+ \hyperpage{141}
+ \item level set, \hyperpage{55}
+ \item leverage, \hyperpage{253}
+ \item levorotation, \hyperpage{145}
+ \item lexicographic degree, \hyperpage{163}
+ \item lexicographic order, \hyperpage{163}
+ \item Likelihood, \hyperpage{195}
+ \item likelihood function, \hyperpage{195}
+ \item likelihood ratio test, \hyperpage{200}
+ \item Likelihood-ratio test, \hyperpage{200}
+ \item Limit, \hyperpage{26}
+ \item limit, \hyperpage{105}, \hyperpage{188}
+ \item Limit comparison test, \hyperpage{76}
+ \item limit cycle, \hyperpage{136}
+ \item limit distribution, \hyperpage{329}
+ \item limit inferior, \hyperpage{27}, \hyperpage{188}
+ \item limit of $f$ at infinity, \hyperpage{28}
+ \item limit of the function $f$ at the point $x_0$, \hyperpage{27}
+ \item limit set, \hyperpage{54}
+ \item limit superior, \hyperpage{27}, \hyperpage{188}
+ \item line, \hyperpage{67}, \hyperpage{70}
+ \item line integral, \hyperpage{61}, \hyperpage{112}
+ \item line intergal, \hyperpage{159}
+ \item line of curvature, \hyperpage{150}
+ \item line search method, \hyperpage{264}
+ \item linear, \hyperpage{122}
+ \item linear $k$-step method, \hyperpage{261}
+ \item linear combination, \hyperpage{16}
+ \item linear convergence, \hyperpage{91}
+ \item linear discrete map, \hyperpage{222}
+ \item linear equation, \hyperpage{13}
+ \item Linear loss function, \hyperpage{203}
+ \item linear map, \hyperpage{17}
+ \item Linear multistep method, \hyperpage{261}
+ \item linear programming to maximize, \hyperpage{51}
+ \item linear programming to minimize, \hyperpage{51}
+ \item linear recurrence relation of order $k$, \hyperpage{48}
+ \item linear saddles, \hyperpage{227}
+ \item linear span, \hyperpage{16}
+ \item Linearity, \hyperpage{76}
+ \item linearization, \hyperpage{221}
+ \item linearly dependent, \hyperpage{16}, \hyperpage{82}
+ \item linearly independent, \hyperpage{16}, \hyperpage{82}
+ \item lines, \hyperpage{63}
+ \item Liouville's formula, \hyperpage{127}, \hyperpage{153}
+ \item Liouville's theorem, \hyperpage{114}
+ \item Lipschitz continuous, \hyperpage{55}
\item Lipschitz continuous with respect to the second variable,
- \hyperpage{123}
- \item Lipschitz's theorem, \hyperpage{84}
- \item Little Picard's theorem, \hyperpage{117}
- \item Liénard system, \hyperpage{227}
- \item Liénard's theorem, \hyperpage{227}
- \item load vector, \hyperpage{275}
- \item Local behaviour of a holomorphic function, \hyperpage{115}
- \item local bifurcation, \hyperpage{222}
- \item local canonical form, \hyperpage{144}
- \item Local Cauchy's integral formula, \hyperpage{112}
+ \hyperpage{124}
+ \item Lipschitz's theorem, \hyperpage{85}
+ \item Little Picard's theorem, \hyperpage{118}
+ \item Liénard system, \hyperpage{228}
+ \item Liénard's theorem, \hyperpage{228}
+ \item load vector, \hyperpage{276}
+ \item Local behaviour of a holomorphic function, \hyperpage{116}
+ \item local bifurcation, \hyperpage{223}
+ \item local canonical form, \hyperpage{145}
+ \item Local Cauchy's integral formula, \hyperpage{113}
\item Local Cauchy's integral formula for derivatives,
- \hyperpage{112}
- \item Local Cauchy's integral theorem, \hyperpage{111}
- \item local conjugacy, \hyperpage{131}
- \item local diffeomorphism, \hyperpage{140}
- \item local equivalence, \hyperpage{131}
- \item local extremum, \hyperpage{29}, \hyperpage{56}
- \item Local Gau\ss -Bonnet theorem, \hyperpage{159}
- \item local isometry, \hyperpage{147}
- \item local maximum, \hyperpage{29}, \hyperpage{56}
- \item local minimum, \hyperpage{29}, \hyperpage{56}
- \item Local structure of immersions, \hyperpage{145}
- \item Local structure of submersions, \hyperpage{145}
- \item local transversal section, \hyperpage{131}
- \item local truncation error, \hyperpage{261}
- \item local truncation errors, \hyperpage{257}
- \item locally, \hyperpage{213}
- \item locally bounded, \hyperpage{120}, \hyperpage{303}
- \item locally compact, \hyperpage{213}
- \item locally connected, \hyperpage{214}
- \item locally integrable, \hyperpage{78}
+ \hyperpage{113}
+ \item Local Cauchy's integral theorem, \hyperpage{112}
+ \item local conjugacy, \hyperpage{132}
+ \item local diffeomorphism, \hyperpage{141}
+ \item local equivalence, \hyperpage{132}
+ \item local extremum, \hyperpage{30}, \hyperpage{57}
+ \item Local Gau\ss -Bonnet theorem, \hyperpage{160}
+ \item local isometry, \hyperpage{148}
+ \item local maximum, \hyperpage{30}, \hyperpage{57}
+ \item local minimum, \hyperpage{30}, \hyperpage{57}
+ \item Local structure of immersions, \hyperpage{146}
+ \item Local structure of submersions, \hyperpage{146}
+ \item local transversal section, \hyperpage{132}
+ \item local truncation error, \hyperpage{262}
+ \item local truncation errors, \hyperpage{258}
+ \item locally, \hyperpage{214}
+ \item locally bounded, \hyperpage{121}, \hyperpage{304}
+ \item locally compact, \hyperpage{214}
+ \item locally connected, \hyperpage{215}
+ \item locally integrable, \hyperpage{79}
\item locally Lipschitz continuous with respect to the second variable,
- \hyperpage{123}
- \item locally path-connected, \hyperpage{215}
- \item locally topologically conjugate, \hyperpage{131}
- \item locally topologically equivalent, \hyperpage{131}
- \item LOF test, \hyperpage{253}
- \item log-likelihood function, \hyperpage{194}
- \item log-odds, \hyperpage{256}
- \item logarithm with base $a$, \hyperpage{28}
- \item Logarithmic test, \hyperpage{75}
- \item logistic map, \hyperpage{227}
- \item logit, \hyperpage{256}
- \item loop, \hyperpage{48}, \hyperpage{214}
- \item Lorenz system, \hyperpage{227}
- \item loss function, \hyperpage{202}
- \item lower bound, \hyperpage{24}
- \item lower integral, \hyperpage{31}, \hyperpage{57}
- \item lower limit topology, \hyperpage{205}
- \item lower sum, \hyperpage{31}, \hyperpage{57}
- \item lower triangular, \hyperpage{96}
- \item LRT, \hyperpage{199}
- \item LRT test statistic, \hyperpage{199}
- \item LU decomposition, \hyperpage{101}
- \item LU descompostion, \hyperpage{101}
- \item Lyapunov central limit theorem, \hyperpage{190}
- \item Lyapunov function, \hyperpage{136}
- \item Lyapunov stable, \hyperpage{136}
- \item Lyapunov's method, \hyperpage{225}
- \item Lyapunov's theorem, \hyperpage{136}, \hyperpage{222}
- \item Lévy-Lindeberg central limit theorem, \hyperpage{190}
+ \hyperpage{124}
+ \item locally path-connected, \hyperpage{216}
+ \item locally topologically conjugate, \hyperpage{132}
+ \item locally topologically equivalent, \hyperpage{132}
+ \item LOF test, \hyperpage{254}
+ \item log-likelihood function, \hyperpage{195}
+ \item log-odds, \hyperpage{257}
+ \item logarithm with base $a$, \hyperpage{29}
+ \item Logarithmic test, \hyperpage{76}
+ \item logistic map, \hyperpage{228}
+ \item logit, \hyperpage{257}
+ \item loop, \hyperpage{49}, \hyperpage{215}
+ \item Lorenz system, \hyperpage{228}
+ \item loss function, \hyperpage{203}
+ \item lower bound, \hyperpage{25}
+ \item lower integral, \hyperpage{32}, \hyperpage{58}
+ \item lower limit topology, \hyperpage{206}
+ \item lower sum, \hyperpage{32}, \hyperpage{58}
+ \item lower triangular, \hyperpage{97}
+ \item LRT, \hyperpage{200}
+ \item LRT test statistic, \hyperpage{200}
+ \item LU decomposition, \hyperpage{102}
+ \item LU descompostion, \hyperpage{102}
+ \item Lyapunov central limit theorem, \hyperpage{192}
+ \item Lyapunov function, \hyperpage{137}
+ \item Lyapunov stable, \hyperpage{137}
+ \item Lyapunov's method, \hyperpage{226}
+ \item Lyapunov's theorem, \hyperpage{137}, \hyperpage{223}
+ \item Lévy-Lindeberg central limit theorem, \hyperpage{192}
\indexspace
- \item machine epsilon $\epsilon $, \hyperpage{88}
- \item Malgrange-Ehrenpreis theorem, \hyperpage{246}
- \item Mallow's $C_p$ statistic, \hyperpage{255}
- \item mantissa, \hyperpage{88}
- \item Marcinkiewicz interpolation theorem, \hyperpage{305}
- \item marginal pdf, \hyperpage{179}
- \item marginal pmf, \hyperpage{179}
- \item Marginal probability density functions, \hyperpage{179}
- \item marginal probability density functions, \hyperpage{179}
- \item Marginal probability mass functions, \hyperpage{179}
- \item marginal probability mass functions, \hyperpage{179}
- \item Markov chain, \hyperpage{317}
- \item Markov property, \hyperpage{317}
- \item Markov's inequality, \hyperpage{184}
- \item material derivative operator, \hyperpage{276}
- \item Matrix, \hyperpage{12}
- \item matrix, \hyperpage{12}, \hyperpage{17}
- \item matrix exponential, \hyperpage{126}
- \item matrix norm, \hyperpage{96}
- \item matrix of the bilinear form, \hyperpage{21}
- \item matrix solution, \hyperpage{126}
- \item maximal, \hyperpage{43}, \hyperpage{125}
- \item maximal element, \hyperpage{8}, \hyperpage{125}
- \item maximum likelihood estimator, \hyperpage{194}
- \item Maximum likelihood method, \hyperpage{194}
- \item Maximum metric, \hyperpage{204}
- \item Maximum modulus principle, \hyperpage{113}
- \item Maximum principle, \hyperpage{286}
- \item Maximum principle on unbounded domains, \hyperpage{286}
- \item Maxwell-Faraday equation, \hyperpage{277}
- \item mean, \hyperpage{177}
- \item mean curvature, \hyperpage{148}
- \item mean function, \hyperpage{329}
- \item mean square error, \hyperpage{250}
- \item mean squared error, \hyperpage{193}
- \item Mean value property, \hyperpage{114}
- \item Mean value theorem, \hyperpage{29}, \hyperpage{55}
- \item Mean value theorem for integrals, \hyperpage{94},
- \hyperpage{297}
- \item Mean value theorem for vector-valued functions, \hyperpage{55}
- \item mean vector, \hyperpage{180}, \hyperpage{195}
- \item measurable, \hyperpage{174}, \hyperpage{292, 293}
- \item measurable space, \hyperpage{174}
- \item Measure, \hyperpage{290}
- \item measure, \hyperpage{173}, \hyperpage{290}
- \item Melnikov's method, \hyperpage{226}
- \item memoryless, \hyperpage{176, 177}
- \item meromorphic, \hyperpage{117}
- \item Mesh, \hyperpage{274}
- \item mesh, \hyperpage{274}
- \item mesh-points, \hyperpage{257}
- \item Method of characteristics, \hyperpage{278}
- \item Method of moments, \hyperpage{193}
- \item metric, \hyperpage{204}
- \item metric space, \hyperpage{52}, \hyperpage{204}, \hyperpage{299}
- \item metrizable, \hyperpage{186}, \hyperpage{211}
- \item Meusnier's theorem, \hyperpage{149}
- \item minimal, \hyperpage{220}
- \item minimal element, \hyperpage{8}
- \item minimal polynomial, \hyperpage{19}
- \item minimal surface, \hyperpage{148}
- \item minimizer, \hyperpage{310}
- \item Minimum modulus principle, \hyperpage{113}
- \item Minimum principle, \hyperpage{286}
- \item Minimum principle on unbounded domains, \hyperpage{287}
- \item minimum-variance unbiased estimator, \hyperpage{193}
- \item Minkowski inequality, \hyperpage{81}, \hyperpage{302},
- \hyperpage{309}
- \item Minkowski's integral inequality, \hyperpage{234}
- \item minor, \hyperpage{15}
- \item mirror of the reflection, \hyperpage{70}
- \item mixed random variable, \hyperpage{178}
- \item MLE, \hyperpage{194}
- \item MLE method, \hyperpage{250}
- \item Model with interaction, \hyperpage{252}
- \item model with interaction, \hyperpage{252}
- \item Model without interaction, \hyperpage{252}
- \item modulus, \hyperpage{103}
- \item modulus of continuity, \hyperpage{54}
- \item Moment, \hyperpage{184}
- \item Moment of inertia, \hyperpage{58}
- \item moment of inertia, \hyperpage{58}
- \item Moment-generating function, \hyperpage{185}
- \item moment-generating function, \hyperpage{185}
- \item monic, \hyperpage{10}
- \item Monotone convergence theorem, \hyperpage{183}, \hyperpage{295}
- \item monotonic, \hyperpage{25}, \hyperpage{27}
- \item monotonically decreasing, \hyperpage{25}
- \item monotonically increasing, \hyperpage{25}
- \item Montel's theorem, \hyperpage{120}
- \item more efficient than, \hyperpage{193}
- \item Morera's theorem, \hyperpage{113}
- \item morphism of field extensions, \hyperpage{164}
- \item MSE, \hyperpage{193}
- \item multi-index notation, \hyperpage{56}
- \item multicollinearity, \hyperpage{254}
- \item multilinear forms, \hyperpage{154}
- \item multilinear map, \hyperpage{154}
- \item Multinomial distrbution, \hyperpage{179}
- \item multinomial distribution, \hyperpage{179}
- \item multiple, \hyperpage{9}
- \item multiple edges, \hyperpage{48}
- \item Multiple shooting method, \hyperpage{263}
- \item multiple shooting method, \hyperpage{263}
- \item multiplicative group, \hyperpage{42}
- \item multiplicity, \hyperpage{113}
- \item multistep, \hyperpage{267}
- \item multivalued function, \hyperpage{103}
- \item multivariate cdf, \hyperpage{180}
- \item multivariate cumulative distribution function, \hyperpage{180}
- \item Multivariate normal distribution, \hyperpage{180}
- \item multivariate normal distribution, \hyperpage{179},
- \hyperpage{195}
- \item multivariate standard deviation, \hyperpage{195}
- \item Multivariate standard normal distribution, \hyperpage{179}
- \item Multivariate uniform distribution, \hyperpage{179}
- \item multivariate uniform distribution, \hyperpage{179}
- \item MVUE, \hyperpage{193}
- \item Möbius band, \hyperpage{210}
- \item Möbius transformation, \hyperpage{118}
- \item Möbius transformations, \hyperpage{118}
+ \item machine epsilon $\epsilon $, \hyperpage{89}
+ \item Malgrange-Ehrenpreis theorem, \hyperpage{247}
+ \item Mallow's $C_p$ statistic, \hyperpage{256}
+ \item mantissa, \hyperpage{89}
+ \item Marcinkiewicz interpolation theorem, \hyperpage{306}
+ \item marginal pdf, \hyperpage{180}
+ \item marginal pmf, \hyperpage{180}
+ \item Marginal probability density functions, \hyperpage{180}
+ \item marginal probability density functions, \hyperpage{180}
+ \item Marginal probability mass functions, \hyperpage{180}
+ \item marginal probability mass functions, \hyperpage{180}
+ \item Markov chain, \hyperpage{318}
+ \item Markov property, \hyperpage{318}
+ \item Markov's inequality, \hyperpage{185}
+ \item material derivative operator, \hyperpage{277}
+ \item Matrix, \hyperpage{13}
+ \item matrix, \hyperpage{13}, \hyperpage{18}
+ \item matrix exponential, \hyperpage{127}
+ \item matrix norm, \hyperpage{97}
+ \item matrix of the bilinear form, \hyperpage{22}
+ \item matrix solution, \hyperpage{127}
+ \item maximal, \hyperpage{44}, \hyperpage{126}
+ \item maximal element, \hyperpage{9}, \hyperpage{126}
+ \item maximum likelihood estimator, \hyperpage{195}
+ \item Maximum likelihood method, \hyperpage{195}
+ \item Maximum metric, \hyperpage{205}
+ \item Maximum modulus principle, \hyperpage{114}
+ \item Maximum principle, \hyperpage{287}
+ \item Maximum principle on unbounded domains, \hyperpage{287}
+ \item Maxwell-Faraday equation, \hyperpage{278}
+ \item mean, \hyperpage{178}
+ \item mean curvature, \hyperpage{149}
+ \item mean function, \hyperpage{330}
+ \item mean square error, \hyperpage{251}
+ \item mean squared error, \hyperpage{194}
+ \item Mean value property, \hyperpage{115}
+ \item Mean value theorem, \hyperpage{30}, \hyperpage{56}
+ \item Mean value theorem for integrals, \hyperpage{95},
+ \hyperpage{298}
+ \item Mean value theorem for vector-valued functions, \hyperpage{56}
+ \item mean vector, \hyperpage{181}, \hyperpage{196}
+ \item measurable, \hyperpage{175}, \hyperpage{293, 294},
+ \hyperpage{335}
+ \item measurable space, \hyperpage{175}, \hyperpage{335}
+ \item Measure, \hyperpage{291}, \hyperpage{335}
+ \item measure, \hyperpage{174}, \hyperpage{291}, \hyperpage{335}
+ \item Melnikov's method, \hyperpage{227}
+ \item memoryless, \hyperpage{177, 178}
+ \item meromorphic, \hyperpage{118}
+ \item Mesh, \hyperpage{275}
+ \item mesh, \hyperpage{275}
+ \item mesh-points, \hyperpage{258}
+ \item Method of characteristics, \hyperpage{279}
+ \item Method of moments, \hyperpage{194}
+ \item metric, \hyperpage{205}
+ \item metric space, \hyperpage{53}, \hyperpage{205}, \hyperpage{300}
+ \item metrizable, \hyperpage{187}, \hyperpage{212}
+ \item Meusnier's theorem, \hyperpage{150}
+ \item minimal, \hyperpage{221}
+ \item minimal element, \hyperpage{9}
+ \item minimal polynomial, \hyperpage{20}
+ \item minimal surface, \hyperpage{149}
+ \item minimizer, \hyperpage{311}
+ \item Minimum modulus principle, \hyperpage{114}
+ \item Minimum principle, \hyperpage{287}
+ \item Minimum principle on unbounded domains, \hyperpage{288}
+ \item minimum-variance unbiased estimator, \hyperpage{194}
+ \item Minkowski inequality, \hyperpage{82}, \hyperpage{303},
+ \hyperpage{310}
+ \item Minkowski's integral inequality, \hyperpage{235}
+ \item minor, \hyperpage{16}
+ \item mirror of the reflection, \hyperpage{71}
+ \item mixed random variable, \hyperpage{179}
+ \item MLE, \hyperpage{195}
+ \item MLE method, \hyperpage{251}
+ \item Model with interaction, \hyperpage{253}
+ \item model with interaction, \hyperpage{253}
+ \item Model without interaction, \hyperpage{253}
+ \item modulus, \hyperpage{104}
+ \item modulus of continuity, \hyperpage{55}
+ \item Moment, \hyperpage{185}
+ \item Moment of inertia, \hyperpage{59}
+ \item moment of inertia, \hyperpage{59}
+ \item Moment-generating function, \hyperpage{186}
+ \item moment-generating function, \hyperpage{186}
+ \item monic, \hyperpage{11}
+ \item Monotone convergence theorem, \hyperpage{184}, \hyperpage{296},
+ \hyperpage{335}
+ \item monotonic, \hyperpage{26}, \hyperpage{28}
+ \item monotonically decreasing, \hyperpage{26}
+ \item monotonically increasing, \hyperpage{26}
+ \item Montel's theorem, \hyperpage{121}
+ \item more efficient than, \hyperpage{194}
+ \item Morera's theorem, \hyperpage{114}
+ \item morphism of field extensions, \hyperpage{165}
+ \item MSE, \hyperpage{194}
+ \item multi-index notation, \hyperpage{57}
+ \item multicollinearity, \hyperpage{255}
+ \item multilinear forms, \hyperpage{155}
+ \item multilinear map, \hyperpage{155}
+ \item Multinomial distrbution, \hyperpage{180}
+ \item multinomial distribution, \hyperpage{180}
+ \item multiple, \hyperpage{10}
+ \item multiple edges, \hyperpage{49}
+ \item Multiple shooting method, \hyperpage{264}
+ \item multiple shooting method, \hyperpage{264}
+ \item multiplicative group, \hyperpage{43}
+ \item multiplicity, \hyperpage{114}
+ \item multistep, \hyperpage{268}
+ \item multivalued function, \hyperpage{104}
+ \item multivariate cdf, \hyperpage{181}
+ \item multivariate cumulative distribution function, \hyperpage{181}
+ \item Multivariate normal distribution, \hyperpage{181}
+ \item multivariate normal distribution, \hyperpage{180},
+ \hyperpage{196}
+ \item multivariate standard deviation, \hyperpage{196}
+ \item Multivariate standard normal distribution, \hyperpage{180}
+ \item Multivariate uniform distribution, \hyperpage{180}
+ \item multivariate uniform distribution, \hyperpage{180}
+ \item MVUE, \hyperpage{194}
+ \item Möbius band, \hyperpage{211}
+ \item Möbius transformation, \hyperpage{119}
+ \item Möbius transformations, \hyperpage{119}
\indexspace
- \item Nart-Vila theorem, \hyperpage{170}
- \item Natural cubic spline, \hyperpage{93}
- \item Navier-Cauchy equation, \hyperpage{276}
- \item negation, \hyperpage{7}
- \item negative, \hyperpage{140}
- \item negative basis, \hyperpage{141}
- \item Negative binomial distribution, \hyperpage{177}
- \item negative binomial distribution, \hyperpage{177}
- \item negative part, \hyperpage{76}
- \item negative semi-orbit, \hyperpage{129}
- \item negative-definite, \hyperpage{22}
- \item negative-semidefinite, \hyperpage{22}
- \item negatively invariant, \hyperpage{130}
- \item negatively rotated, \hyperpage{226}
- \item negatively stable, \hyperpage{130}
- \item negatively-oriented, \hyperpage{141}
- \item neighbourhood, \hyperpage{24}, \hyperpage{53}, \hyperpage{206}
- \item Neumann, \hyperpage{273}
- \item Neumann series, \hyperpage{307}
- \item Neville's algorithm, \hyperpage{92}
- \item Newton method, \hyperpage{261}, \hyperpage{263}
- \item Newton's divided differences\\method, \hyperpage{92}
- \item Newton-Raphson method, \hyperpage{89}
- \item Newton-Raphson modified method, \hyperpage{89}
- \item Neyman-Pearson lemma, \hyperpage{199}
- \item Neyman-Pearson test, \hyperpage{199}
- \item Neymann-Pearson test, \hyperpage{199}
- \item nilpotent, \hyperpage{13}, \hyperpage{223}
+ \item Nart-Vila theorem, \hyperpage{171}
+ \item Natural cubic spline, \hyperpage{94}
+ \item Navier-Cauchy equation, \hyperpage{277}
+ \item negation, \hyperpage{8}
+ \item negative, \hyperpage{141}
+ \item negative basis, \hyperpage{142}
+ \item Negative binomial distribution, \hyperpage{178}
+ \item negative binomial distribution, \hyperpage{178}
+ \item negative part, \hyperpage{77}
+ \item negative semi-orbit, \hyperpage{130}
+ \item negative-definite, \hyperpage{23}
+ \item negative-semidefinite, \hyperpage{23}
+ \item negatively invariant, \hyperpage{131}
+ \item negatively rotated, \hyperpage{227}
+ \item negatively stable, \hyperpage{131}
+ \item negatively-oriented, \hyperpage{142}
+ \item neighbourhood, \hyperpage{25}, \hyperpage{54}, \hyperpage{207}
+ \item Neumann, \hyperpage{274}
+ \item Neumann series, \hyperpage{308}
+ \item Neville's algorithm, \hyperpage{93}
+ \item Newton method, \hyperpage{262}, \hyperpage{264}
+ \item Newton's divided differences\\method, \hyperpage{93}
+ \item Newton-Raphson method, \hyperpage{90}
+ \item Newton-Raphson modified method, \hyperpage{90}
+ \item Neyman-Pearson lemma, \hyperpage{200}
+ \item Neyman-Pearson test, \hyperpage{200}
+ \item Neymann-Pearson test, \hyperpage{200}
+ \item nilpotent, \hyperpage{14}, \hyperpage{224}
\item Nilpotent singular points classification theorem,
- \hyperpage{223}
- \item no-intercept, \hyperpage{251}
- \item nodal basis, \hyperpage{274}
- \item nodes, \hyperpage{274}
- \item Noetherian, \hyperpage{42}
- \item Non-Archimedean geometry, \hyperpage{65}
- \item non-autonomous, \hyperpage{121}
- \item non-degenerate, \hyperpage{73}
- \item non-degenerated, \hyperpage{226}
- \item non-Desarguesian planes, \hyperpage{67}
- \item Non-parametric bootstrap, \hyperpage{201}
- \item Non-Paschian geometry, \hyperpage{64}
- \item Non-SAS geometry, \hyperpage{65}
- \item non-singular, \hyperpage{130}
- \item noncommutative ring, \hyperpage{41}
- \item nonsingular, \hyperpage{21}
- \item norm, \hyperpage{23}, \hyperpage{52}, \hyperpage{93},
- \hyperpage{299}, \hyperpage{304}
- \item norm associated with the inner product, \hyperpage{23}
- \item normal, \hyperpage{37}, \hyperpage{120}, \hyperpage{166},
- \hyperpage{189}, \hyperpage{211}
- \item normal closure, \hyperpage{166}
- \item Normal confidence interval, \hyperpage{201}
- \item normal confidence interval, \hyperpage{201}
- \item normal curvature, \hyperpage{149}
- \item Normal distribution, \hyperpage{177}
- \item normal distribution, \hyperpage{177}
- \item normal form, \hyperpage{222}
- \item Normal plane, \hyperpage{142}
- \item Normal Q-Q plots, \hyperpage{203}
- \item normal unit field, \hyperpage{148}
- \item normalized, \hyperpage{88}, \hyperpage{217}
- \item Normalized power method, \hyperpage{100}
- \item normalized power method, \hyperpage{100}
- \item normalizer, \hyperpage{40}
- \item normed algebra, \hyperpage{306}
- \item normed vector space, \hyperpage{52}, \hyperpage{299}
- \item not integrable, \hyperpage{181}
- \item not orientation-preserving, \hyperpage{216}
- \item null hypothesis, \hyperpage{198}
- \item null recurrent, \hyperpage{323}
- \item null set, \hyperpage{173}, \hyperpage{292}
- \item number of steps, \hyperpage{267}
- \item numeric series, \hyperpage{75}
- \item numeric series of complex numbers, \hyperpage{104}
- \item numerical boundary condition, \hyperpage{271}
- \item numerically stable, \hyperpage{89}
- \item numerically unstable, \hyperpage{89}
- \item Nyquist-Shannon sampling theorem, \hyperpage{238}
+ \hyperpage{224}
+ \item no-intercept, \hyperpage{252}
+ \item nodal basis, \hyperpage{275}
+ \item nodes, \hyperpage{275}
+ \item Noetherian, \hyperpage{43}
+ \item Non-Archimedean geometry, \hyperpage{66}
+ \item non-autonomous, \hyperpage{122}
+ \item non-degenerate, \hyperpage{74}
+ \item non-degenerated, \hyperpage{227}
+ \item non-Desarguesian planes, \hyperpage{68}
+ \item Non-parametric bootstrap, \hyperpage{202}
+ \item Non-Paschian geometry, \hyperpage{65}
+ \item Non-SAS geometry, \hyperpage{66}
+ \item non-singular, \hyperpage{131}
+ \item noncommutative ring, \hyperpage{42}
+ \item nonsingular, \hyperpage{22}
+ \item norm, \hyperpage{24}, \hyperpage{53}, \hyperpage{94},
+ \hyperpage{300}, \hyperpage{305}
+ \item norm associated with the inner product, \hyperpage{24}
+ \item normal, \hyperpage{38}, \hyperpage{121}, \hyperpage{167},
+ \hyperpage{191}, \hyperpage{212}
+ \item normal closure, \hyperpage{167}
+ \item Normal confidence interval, \hyperpage{202}
+ \item normal confidence interval, \hyperpage{202}
+ \item normal curvature, \hyperpage{150}
+ \item Normal distribution, \hyperpage{178}
+ \item normal distribution, \hyperpage{178}
+ \item normal form, \hyperpage{223}
+ \item Normal plane, \hyperpage{143}
+ \item Normal Q-Q plots, \hyperpage{204}
+ \item normal unit field, \hyperpage{149}
+ \item normalized, \hyperpage{89}, \hyperpage{218}
+ \item Normalized power method, \hyperpage{101}
+ \item normalized power method, \hyperpage{101}
+ \item normalizer, \hyperpage{41}
+ \item normed algebra, \hyperpage{307}
+ \item normed vector space, \hyperpage{53}, \hyperpage{300}
+ \item not integrable, \hyperpage{182}
+ \item not orientation-preserving, \hyperpage{217}
+ \item null hypothesis, \hyperpage{199}
+ \item null recurrent, \hyperpage{324}
+ \item null set, \hyperpage{174}, \hyperpage{293}
+ \item number of steps, \hyperpage{268}
+ \item numeric series, \hyperpage{76}
+ \item numeric series of complex numbers, \hyperpage{105}
+ \item numerical boundary condition, \hyperpage{272}
+ \item numerically stable, \hyperpage{90}
+ \item numerically unstable, \hyperpage{90}
+ \item Nyquist-Shannon sampling theorem, \hyperpage{239}
\indexspace
- \item objective function, \hyperpage{50}
- \item observed information, \hyperpage{194}
- \item odd extension, \hyperpage{83}
- \item odd periodic extension, \hyperpage{282}
- \item odds, \hyperpage{256}
- \item ode, \hyperpage{121}
- \item Olinde Rodrigues' theorem, \hyperpage{149}
- \item one-parameter family of rotated vector fields, \hyperpage{226}
- \item One-point compactification, \hyperpage{213}
- \item one-point compactification, \hyperpage{213}
- \item one-sided left tail test, \hyperpage{198}
- \item one-sided right tail test, \hyperpage{198}
- \item one-step, \hyperpage{267}
- \item one-step method, \hyperpage{257}
- \item open, \hyperpage{53}, \hyperpage{204}, \hyperpage{207}
- \item open ball, \hyperpage{53}
- \item open cover, \hyperpage{212}
- \item Open function, \hyperpage{207}
- \item Open interval, \hyperpage{24}
- \item Open mapping theorem, \hyperpage{115}, \hyperpage{308}
- \item open sets, \hyperpage{204}
- \item operator, \hyperpage{123}, \hyperpage{304}
- \item opposite orientations, \hyperpage{141}, \hyperpage{216}
- \item orbit, \hyperpage{7}, \hyperpage{39}, \hyperpage{129}
- \item Orbit linear structure, \hyperpage{7}
- \item Orbit structure, \hyperpage{7}
- \item Orbit-stabilizer theorem, \hyperpage{39}
- \item Orbits formula, \hyperpage{39}
- \item order, \hyperpage{7}, \hyperpage{36}, \hyperpage{48},
- \hyperpage{115}, \hyperpage{258}
- \item Order axioms, \hyperpage{62}
- \item order of accuracy, \hyperpage{258}, \hyperpage{261}
- \item order of consistency, \hyperpage{258}, \hyperpage{261}
- \item Order of convergence, \hyperpage{90}
- \item order of convergence, \hyperpage{90}, \hyperpage{258}
- \item order of convergence at least $p$, \hyperpage{90}
- \item order relation, \hyperpage{62}
- \item order statistic, \hyperpage{195}
- \item order statistics, \hyperpage{195}
- \item ordered field, \hyperpage{24}, \hyperpage{63}
- \item ordinary differential equation, \hyperpage{121}
- \item ordinary generating function, \hyperpage{47}
- \item orientable, \hyperpage{148}, \hyperpage{157}, \hyperpage{216}
- \item orientation, \hyperpage{119}, \hyperpage{141}, \hyperpage{148},
- \hyperpage{216}
- \item orientation induced by $M$, \hyperpage{157}
- \item Orientation principle, \hyperpage{119}
- \item orientation-preserving, \hyperpage{141}, \hyperpage{216}
- \item oriented vector space, \hyperpage{141}, \hyperpage{216}
- \item origin, \hyperpage{69}
- \item orthogonal, \hyperpage{21--23}, \hyperpage{71}, \hyperpage{81},
- \hyperpage{147}, \hyperpage{309}
- \item orthogonal basis, \hyperpage{95}
- \item orthogonal complement, \hyperpage{21}, \hyperpage{309}
- \item orthogonal coordinates, \hyperpage{147}
- \item orthogonal geometry, \hyperpage{22}
- \item orthogonal group, \hyperpage{144}
- \item Orthogonal polynomials, \hyperpage{95}
- \item orthogonal projection, \hyperpage{22}
- \item orthogonal projection on $F$, \hyperpage{310}
- \item orthogonal reflections, \hyperpage{72}
- \item orthogonal system, \hyperpage{311}
+ \item objective function, \hyperpage{51}
+ \item observed information, \hyperpage{195}
+ \item odd extension, \hyperpage{84}
+ \item odd periodic extension, \hyperpage{283}
+ \item odds, \hyperpage{257}
+ \item ode, \hyperpage{122}
+ \item Olinde Rodrigues' theorem, \hyperpage{150}
+ \item one-parameter family of rotated vector fields, \hyperpage{227}
+ \item One-point compactification, \hyperpage{214}
+ \item one-point compactification, \hyperpage{214}
+ \item one-sided left tail test, \hyperpage{199}
+ \item one-sided right tail test, \hyperpage{199}
+ \item one-step, \hyperpage{268}
+ \item one-step method, \hyperpage{258}
+ \item open, \hyperpage{54}, \hyperpage{205}, \hyperpage{208}
+ \item open ball, \hyperpage{54}
+ \item open cover, \hyperpage{213}
+ \item Open function, \hyperpage{208}
+ \item Open interval, \hyperpage{25}
+ \item Open mapping theorem, \hyperpage{116}, \hyperpage{309}
+ \item open sets, \hyperpage{205}
+ \item operator, \hyperpage{124}, \hyperpage{305}
+ \item opposite orientations, \hyperpage{142}, \hyperpage{217}
+ \item orbit, \hyperpage{8}, \hyperpage{40}, \hyperpage{130}
+ \item Orbit linear structure, \hyperpage{8}
+ \item Orbit structure, \hyperpage{8}
+ \item Orbit-stabilizer theorem, \hyperpage{40}
+ \item Orbits formula, \hyperpage{40}
+ \item order, \hyperpage{8}, \hyperpage{37}, \hyperpage{49},
+ \hyperpage{116}, \hyperpage{259}
+ \item Order axioms, \hyperpage{63}
+ \item order of accuracy, \hyperpage{259}, \hyperpage{262}
+ \item order of consistency, \hyperpage{259}, \hyperpage{262}
+ \item Order of convergence, \hyperpage{91}
+ \item order of convergence, \hyperpage{91}, \hyperpage{259}
+ \item order of convergence at least $p$, \hyperpage{91}
+ \item order relation, \hyperpage{63}
+ \item order statistic, \hyperpage{196}
+ \item order statistics, \hyperpage{196}
+ \item ordered field, \hyperpage{25}, \hyperpage{64}
+ \item ordinary differential equation, \hyperpage{122}
+ \item ordinary generating function, \hyperpage{48}
+ \item orientable, \hyperpage{149}, \hyperpage{158}, \hyperpage{217}
+ \item orientation, \hyperpage{120}, \hyperpage{142}, \hyperpage{149},
+ \hyperpage{217}
+ \item orientation induced by $M$, \hyperpage{158}
+ \item Orientation principle, \hyperpage{120}
+ \item orientation-preserving, \hyperpage{142}, \hyperpage{217}
+ \item oriented vector space, \hyperpage{142}, \hyperpage{217}
+ \item origin, \hyperpage{70}
+ \item orthogonal, \hyperpage{22--24}, \hyperpage{72}, \hyperpage{82},
+ \hyperpage{148}, \hyperpage{310}
+ \item orthogonal basis, \hyperpage{96}
+ \item orthogonal complement, \hyperpage{22}, \hyperpage{310}
+ \item orthogonal coordinates, \hyperpage{148}
+ \item orthogonal geometry, \hyperpage{23}
+ \item orthogonal group, \hyperpage{145}
+ \item Orthogonal polynomials, \hyperpage{96}
+ \item orthogonal projection, \hyperpage{23}
+ \item orthogonal projection on $F$, \hyperpage{311}
+ \item orthogonal reflections, \hyperpage{73}
+ \item orthogonal system, \hyperpage{313}
\item orthogonal with respect to the weight $\omega (x)$,
- \hyperpage{95}
- \item orthonormal, \hyperpage{21}, \hyperpage{81}
- \item orthonormal system, \hyperpage{81}, \hyperpage{311}
- \item orthonormalization, \hyperpage{312}
- \item osculating circle, \hyperpage{143}
- \item Osculating plane, \hyperpage{142}
- \item osculating sphere, \hyperpage{143}
- \item Outer measure, \hyperpage{291}
- \item outer measure, \hyperpage{291}
- \item outliars, \hyperpage{254}
- \item Over-relaxation methods, \hyperpage{99}
+ \hyperpage{96}
+ \item orthonormal, \hyperpage{22}, \hyperpage{82}
+ \item orthonormal system, \hyperpage{82}, \hyperpage{313}
+ \item orthonormalization, \hyperpage{313}
+ \item osculating circle, \hyperpage{144}
+ \item Osculating plane, \hyperpage{143}
+ \item osculating sphere, \hyperpage{144}
+ \item Outer measure, \hyperpage{292}
+ \item outer measure, \hyperpage{292}
+ \item outliars, \hyperpage{255}
+ \item Over-relaxation methods, \hyperpage{100}
\indexspace
- \item Paley-Wiener-Zygmund theorem, \hyperpage{330}
- \item Pappus configuration, \hyperpage{67}
- \item PAQ reduction theorem, \hyperpage{13}
- \item parabolic, \hyperpage{272}
- \item parabolic boundary, \hyperpage{286}
- \item parabolic cylinder, \hyperpage{286}
- \item parabolic point, \hyperpage{149}
- \item parallel, \hyperpage{69}, \hyperpage{151}
- \item parallel transport, \hyperpage{151}
- \item Parallelogram law, \hyperpage{52}, \hyperpage{309}
- \item parameter set, \hyperpage{315}
- \item parameter space, \hyperpage{192}
- \item parametric, \hyperpage{192}
- \item Parametric bootstrap, \hyperpage{201}
- \item parametric bootstrap distribution, \hyperpage{201}
- \item parametric equations, \hyperpage{69}
- \item parametrization, \hyperpage{140}, \hyperpage{146}
- \item parametrized surface, \hyperpage{60}
- \item Parseval identity, \hyperpage{312}
- \item Parseval's identity, \hyperpage{86}
- \item partial derivative, \hyperpage{54}
- \item partial derivative of order $k$, \hyperpage{55}
- \item partial differential equation, \hyperpage{138}
- \item Partial fraction decomposition theorem, \hyperpage{116}
- \item partial inverse Fourier transform, \hyperpage{232}
- \item partial order relation, \hyperpage{8}
- \item Partial pivoting, \hyperpage{101}
- \item partially ordered set, \hyperpage{8}
- \item Particular point topology, \hyperpage{205}
- \item partition, \hyperpage{31}, \hyperpage{57}, \hyperpage{173}
- \item partition of unity, \hyperpage{157}
- \item Pasch's axiom, \hyperpage{62}
+ \item Paley-Wiener-Zygmund theorem, \hyperpage{331}
+ \item Pappus configuration, \hyperpage{68}
+ \item PAQ reduction theorem, \hyperpage{14}
+ \item parabolic, \hyperpage{273}
+ \item parabolic boundary, \hyperpage{287}
+ \item parabolic cylinder, \hyperpage{287}
+ \item parabolic point, \hyperpage{150}
+ \item parallel, \hyperpage{70}, \hyperpage{152}
+ \item parallel transport, \hyperpage{152}
+ \item Parallelogram law, \hyperpage{53}, \hyperpage{311}
+ \item parameter set, \hyperpage{316}
+ \item parameter space, \hyperpage{193}
+ \item parametric, \hyperpage{193}
+ \item Parametric bootstrap, \hyperpage{202}
+ \item parametric bootstrap distribution, \hyperpage{202}
+ \item parametric equations, \hyperpage{70}
+ \item parametrization, \hyperpage{141}, \hyperpage{147}
+ \item parametrized surface, \hyperpage{61}
+ \item Parseval identity, \hyperpage{313}
+ \item Parseval's identity, \hyperpage{87}
+ \item partial derivative, \hyperpage{55}
+ \item partial derivative of order $k$, \hyperpage{56}
+ \item partial differential equation, \hyperpage{139}
+ \item Partial fraction decomposition theorem, \hyperpage{117}
+ \item partial inverse Fourier transform, \hyperpage{233}
+ \item partial order relation, \hyperpage{9}
+ \item Partial pivoting, \hyperpage{102}
+ \item partially ordered set, \hyperpage{9}
+ \item Particular point topology, \hyperpage{206}
+ \item partition, \hyperpage{32}, \hyperpage{58}, \hyperpage{174}
+ \item partition of unity, \hyperpage{158}
+ \item Pasch's axiom, \hyperpage{63}
\item Passage from the affine plane to the projective plane,
- \hyperpage{65}
+ \hyperpage{66}
\item Passage from the projective plane to the affine plane,
- \hyperpage{65}
- \item path, \hyperpage{48}, \hyperpage{214}
- \item path from $x$ to $y$, \hyperpage{214}
- \item path-connected, \hyperpage{214, 215}
- \item path-connected components, \hyperpage{215}
- \item pde, \hyperpage{138}
- \item pdf, \hyperpage{177}
- \item Peano axioms, \hyperpage{5}
- \item Peano theorem, \hyperpage{124}
- \item Pearson correlation coefficient, \hyperpage{184}
- \item Percentile confidence interval, \hyperpage{201}
- \item percentile confidence interval, \hyperpage{201}
- \item perfect, \hyperpage{165}
- \item Perfect fields, \hyperpage{165}
- \item period, \hyperpage{319}
- \item Period three theorem, \hyperpage{228}
- \item Period-doubling bifurcation, \hyperpage{228}
- \item period-doubling bifurcation, \hyperpage{228}
- \item period-doubling cascade, \hyperpage{228}
- \item period-halving bifurcation, \hyperpage{228}
- \item periodic, \hyperpage{130}
- \item periodic orbit of period $T$, \hyperpage{220}
- \item periodic point, \hyperpage{227}
- \item periodic with period $T$, \hyperpage{80}
- \item permutation matrix, \hyperpage{101}
- \item Perron-Frobenius theorem, \hyperpage{100}
- \item perspectivity, \hyperpage{68}
- \item pgf, \hyperpage{315}
- \item phase portrait, \hyperpage{129}
- \item phase space, \hyperpage{129}
- \item Picard iteration process, \hyperpage{124}
- \item Picard theorem, \hyperpage{124}
- \item PID, \hyperpage{43}
- \item piecewise linear manifold, \hyperpage{215}
- \item Pigeonhole principle, \hyperpage{9}
- \item Pitchfork bifurcation, \hyperpage{222}
- \item pitchfork bifurcation, \hyperpage{222}
- \item pivot, \hyperpage{197}
- \item Plancherel theorem, \hyperpage{235}, \hyperpage{237, 238}
- \item plane curve, \hyperpage{140}
- \item plane point, \hyperpage{149}
- \item Playfair's axiom, \hyperpage{62}
- \item Plücker coordinates, \hyperpage{68}
- \item pmf, \hyperpage{175}
- \item Poincaré compactification, \hyperpage{137}
- \item Poincaré disk, \hyperpage{137}
- \item Poincaré index formula, \hyperpage{138}
- \item Poincaré inequality, \hyperpage{288}
- \item Poincaré map, \hyperpage{135}
- \item Poincaré's method, \hyperpage{225}
- \item Poincaré-Bendixson theorem, \hyperpage{135}
- \item Poincaré-Hopf theorem, \hyperpage{138}, \hyperpage{160}
- \item Poincaré-Hopf theorem on $S^2$, \hyperpage{138}
- \item points, \hyperpage{62}, \hyperpage{204}
- \item points of the quadric, \hyperpage{72}
- \item pointwise bounded, \hyperpage{124}, \hyperpage{303}
- \item pointwise equicontinuous, \hyperpage{124}, \hyperpage{303}
- \item Poisson distribution, \hyperpage{176}
- \item Poisson equation, \hyperpage{276}
- \item Poisson kernel, \hyperpage{230}, \hyperpage{233}
- \item Poisson process, \hyperpage{325}
- \item Poisson summation formula, \hyperpage{237}, \hyperpage{239}
- \item Polar form, \hyperpage{107}
- \item polar form, \hyperpage{107}
- \item Polarization identity, \hyperpage{309}
- \item Pole, \hyperpage{115}
- \item pole, \hyperpage{115}
+ \hyperpage{66}
+ \item path, \hyperpage{49}, \hyperpage{215}
+ \item path from $x$ to $y$, \hyperpage{215}
+ \item path-connected, \hyperpage{215, 216}
+ \item path-connected components, \hyperpage{216}
+ \item pde, \hyperpage{139}
+ \item pdf, \hyperpage{178}
+ \item Peano axioms, \hyperpage{6}
+ \item Peano theorem, \hyperpage{125}
+ \item Pearson correlation coefficient, \hyperpage{185}
+ \item Percentile confidence interval, \hyperpage{202}
+ \item percentile confidence interval, \hyperpage{202}
+ \item perfect, \hyperpage{166}
+ \item Perfect fields, \hyperpage{166}
+ \item period, \hyperpage{320}
+ \item Period three theorem, \hyperpage{229}
+ \item Period-doubling bifurcation, \hyperpage{229}
+ \item period-doubling bifurcation, \hyperpage{229}
+ \item period-doubling cascade, \hyperpage{229}
+ \item period-halving bifurcation, \hyperpage{229}
+ \item periodic, \hyperpage{131}
+ \item periodic orbit of period $T$, \hyperpage{221}
+ \item periodic point, \hyperpage{228}
+ \item periodic with period $T$, \hyperpage{81}
+ \item permutation matrix, \hyperpage{102}
+ \item Perron-Frobenius theorem, \hyperpage{101}
+ \item perspectivity, \hyperpage{69}
+ \item pgf, \hyperpage{316}
+ \item phase portrait, \hyperpage{130}
+ \item phase space, \hyperpage{130}
+ \item Picard iteration process, \hyperpage{125}
+ \item Picard theorem, \hyperpage{125}
+ \item PID, \hyperpage{44}
+ \item piecewise linear manifold, \hyperpage{216}
+ \item Pigeonhole principle, \hyperpage{10}
+ \item Pitchfork bifurcation, \hyperpage{223}
+ \item pitchfork bifurcation, \hyperpage{223}
+ \item pivot, \hyperpage{198}
+ \item Plancherel theorem, \hyperpage{236}, \hyperpage{238},
+ \hyperpage{240}
+ \item plane curve, \hyperpage{141}
+ \item plane point, \hyperpage{150}
+ \item Playfair's axiom, \hyperpage{63}
+ \item Plücker coordinates, \hyperpage{69}
+ \item pmf, \hyperpage{176}
+ \item Poincaré compactification, \hyperpage{138}
+ \item Poincaré disk, \hyperpage{138}
+ \item Poincaré index formula, \hyperpage{139}
+ \item Poincaré inequality, \hyperpage{289}
+ \item Poincaré map, \hyperpage{136}
+ \item Poincaré's inequality, \hyperpage{338}
+ \item Poincaré's method, \hyperpage{226}
+ \item Poincaré-Bendixson theorem, \hyperpage{136}
+ \item Poincaré-Hopf theorem, \hyperpage{139}, \hyperpage{161}
+ \item Poincaré-Hopf theorem on $S^2$, \hyperpage{139}
+ \item Poincaré-Wirtinger's inequality, \hyperpage{338}
+ \item points, \hyperpage{63}, \hyperpage{205}
+ \item points of the quadric, \hyperpage{73}
+ \item pointwise bounded, \hyperpage{125}, \hyperpage{304}
+ \item pointwise equicontinuous, \hyperpage{125}, \hyperpage{304}
+ \item Poisson distribution, \hyperpage{177}
+ \item Poisson equation, \hyperpage{277}
+ \item Poisson kernel, \hyperpage{231}, \hyperpage{234}
+ \item Poisson process, \hyperpage{326}
+ \item Poisson summation formula, \hyperpage{238}, \hyperpage{240}
+ \item Polar form, \hyperpage{108}
+ \item polar form, \hyperpage{108}
+ \item Polarization identity, \hyperpage{310}
+ \item Pole, \hyperpage{116}
+ \item pole, \hyperpage{116}
\item Polya's theorem on $\ensuremath {\mathbb {Z}}$,
- \hyperpage{323}
+ \hyperpage{324}
\item Polya's theorem on $\ensuremath {\mathbb {Z}}^2$,
- \hyperpage{323}
+ \hyperpage{324}
\item Polya's theorem on $\ensuremath {\mathbb {Z}}^3$,
- \hyperpage{323}
- \item polyhedron, \hyperpage{50}
- \item polynomial, \hyperpage{10}
- \item polynomial ring, \hyperpage{161}
- \item polynomial system, \hyperpage{134}
- \item polynomial vector field, \hyperpage{134}
- \item polytope, \hyperpage{50}
- \item poset, \hyperpage{8}
- \item positive, \hyperpage{140}, \hyperpage{157}
- \item positive basis, \hyperpage{141}
- \item positive part, \hyperpage{76}
- \item positive recurrent, \hyperpage{323}
- \item positive semi-orbit, \hyperpage{129}
- \item positive-definite, \hyperpage{22}
- \item positive-semidefinite, \hyperpage{22}
- \item positively invariant, \hyperpage{130}
- \item positively oriented, \hyperpage{141}
- \item positively rotated, \hyperpage{226}
- \item positively stable, \hyperpage{130}
- \item posterior, \hyperpage{201}
- \item posterior distribution, \hyperpage{201}
- \item posterior mean, \hyperpage{202}
- \item posterior median, \hyperpage{202}
- \item posterior mode, \hyperpage{202}
- \item potential, \hyperpage{60}, \hyperpage{276}
- \item power, \hyperpage{198}
- \item power function, \hyperpage{198}
- \item Power method, \hyperpage{100}
- \item power method, \hyperpage{100}
- \item power series, \hyperpage{77}
- \item power set, \hyperpage{5}
- \item pre-Hilbert space, \hyperpage{309}
- \item predicate, \hyperpage{5}
- \item prediction, \hyperpage{252}
- \item prediction band, \hyperpage{253}
- \item preditions, \hyperpage{249}
- \item preimage, \hyperpage{6}
- \item primal, \hyperpage{50}
- \item prime, \hyperpage{9}, \hyperpage{11}, \hyperpage{43}
- \item Prime number theorem, \hyperpage{9}
- \item prime period, \hyperpage{227}
- \item primitive element, \hyperpage{163}
- \item Primitive element theorem, \hyperpage{167}
- \item primitive function, \hyperpage{32}
- \item primitive polynomial, \hyperpage{46}
- \item principal argument, \hyperpage{103}
- \item principal curvatures, \hyperpage{148}
- \item principal directons, \hyperpage{148}
- \item Principal ideal, \hyperpage{42}
- \item principal ideal, \hyperpage{42}
- \item principal ideal domain, \hyperpage{43}
- \item principal value, \hyperpage{107}
- \item Principle of least action, \hyperpage{278}
- \item prior, \hyperpage{201}
- \item prior distribution, \hyperpage{201}
- \item probability, \hyperpage{172}
- \item probability density function, \hyperpage{177}
- \item Probability mass function, \hyperpage{175}
- \item probability mass function, \hyperpage{175}
- \item probability space, \hyperpage{172}
- \item probability-generating function, \hyperpage{315}
- \item product, \hyperpage{10}, \hyperpage{12}, \hyperpage{105}
- \item product topology, \hyperpage{208}
- \item products of group subsets, \hyperpage{39}
- \item projection, \hyperpage{70}
- \item Projection theorem, \hyperpage{310}
- \item Projections, \hyperpage{70}
- \item Projective axiom, \hyperpage{65}
- \item projective frame, \hyperpage{66}
- \item projective plane, \hyperpage{65}
- \item projective subvariety, \hyperpage{65}
- \item projectivity, \hyperpage{68}
- \item prolongation, \hyperpage{307}
- \item Propagation of absolute errors, \hyperpage{88}
- \item Propagation of relative errors, \hyperpage{88}
- \item proper, \hyperpage{36}
- \item proper subspace of $T$, \hyperpage{308}
+ \hyperpage{324}
+ \item polyhedron, \hyperpage{51}
+ \item polynomial, \hyperpage{11}
+ \item polynomial ring, \hyperpage{162}
+ \item polynomial system, \hyperpage{135}
+ \item polynomial vector field, \hyperpage{135}
+ \item polytope, \hyperpage{51}
+ \item poset, \hyperpage{9}
+ \item positive, \hyperpage{141}, \hyperpage{158}
+ \item positive basis, \hyperpage{142}
+ \item positive part, \hyperpage{77}
+ \item positive recurrent, \hyperpage{324}
+ \item positive semi-orbit, \hyperpage{130}
+ \item positive-definite, \hyperpage{23}
+ \item positive-semidefinite, \hyperpage{23}
+ \item positively invariant, \hyperpage{131}
+ \item positively oriented, \hyperpage{142}
+ \item positively rotated, \hyperpage{227}
+ \item positively stable, \hyperpage{131}
+ \item posterior, \hyperpage{202}
+ \item posterior distribution, \hyperpage{202}
+ \item posterior mean, \hyperpage{203}
+ \item posterior median, \hyperpage{203}
+ \item posterior mode, \hyperpage{203}
+ \item potential, \hyperpage{61}, \hyperpage{277}
+ \item power, \hyperpage{199}
+ \item power function, \hyperpage{199}
+ \item Power method, \hyperpage{101}
+ \item power method, \hyperpage{101}
+ \item power series, \hyperpage{78}
+ \item power set, \hyperpage{6}
+ \item pre-Hilbert space, \hyperpage{310}
+ \item predicate, \hyperpage{6}
+ \item prediction, \hyperpage{253}
+ \item prediction band, \hyperpage{254}
+ \item preditions, \hyperpage{250}
+ \item preimage, \hyperpage{7}
+ \item primal, \hyperpage{51}
+ \item prime, \hyperpage{10}, \hyperpage{12}, \hyperpage{44}
+ \item Prime number theorem, \hyperpage{10}
+ \item prime period, \hyperpage{228}
+ \item primitive element, \hyperpage{164}
+ \item Primitive element theorem, \hyperpage{168}
+ \item primitive function, \hyperpage{33}
+ \item primitive polynomial, \hyperpage{47}
+ \item principal argument, \hyperpage{104}
+ \item principal curvatures, \hyperpage{149}
+ \item principal directons, \hyperpage{149}
+ \item Principal ideal, \hyperpage{43}
+ \item principal ideal, \hyperpage{43}
+ \item principal ideal domain, \hyperpage{44}
+ \item principal value, \hyperpage{108}
+ \item Principle of least action, \hyperpage{279}
+ \item prior, \hyperpage{202}
+ \item prior distribution, \hyperpage{202}
+ \item probability, \hyperpage{173}
+ \item probability density function, \hyperpage{178}
+ \item probability kernel, \hyperpage{337}
+ \item Probability mass function, \hyperpage{176}
+ \item probability mass function, \hyperpage{176}
+ \item probability space, \hyperpage{173}, \hyperpage{336}
+ \item probability-generating function, \hyperpage{316}
+ \item product, \hyperpage{11}, \hyperpage{13}, \hyperpage{106}
+ \item Product measure, \hyperpage{335}
+ \item product measure, \hyperpage{335}
+ \item product topology, \hyperpage{209}
+ \item products of group subsets, \hyperpage{40}
+ \item projection, \hyperpage{71}
+ \item Projection theorem, \hyperpage{311}
+ \item Projections, \hyperpage{71}
+ \item Projective axiom, \hyperpage{66}
+ \item projective frame, \hyperpage{67}
+ \item projective plane, \hyperpage{66}
+ \item projective subvariety, \hyperpage{66}
+ \item projectivity, \hyperpage{69}
+ \item prolongation, \hyperpage{308}
+ \item Propagation of absolute errors, \hyperpage{89}
+ \item Propagation of relative errors, \hyperpage{89}
+ \item proper, \hyperpage{37}
+ \item proper subspace of $T$, \hyperpage{309}
\item Properties of addition and scalar multiplication of matrices,
- \hyperpage{12}
- \item Properties of homotheties, \hyperpage{71}
- \item Properties of matrix norms, \hyperpage{97}
- \item Properties of matrix product, \hyperpage{12}
- \item Properties of projections, \hyperpage{70}
- \item Properties of reflections, \hyperpage{70}
- \item Properties of translations, \hyperpage{70}
- \item Proximity theorem, \hyperpage{228}
- \item pull-back, \hyperpage{155}
- \item pure birth process, \hyperpage{328}
- \item pure death process, \hyperpage{328}
- \item purely inseparable, \hyperpage{167}
- \item purely transcendental, \hyperpage{164}
- \item Pythagorean, \hyperpage{63}
- \item Pythagorean plane, \hyperpage{63}
- \item Pythagorean theorem, \hyperpage{71}, \hyperpage{309}
+ \hyperpage{13}
+ \item Properties of homotheties, \hyperpage{72}
+ \item Properties of matrix norms, \hyperpage{98}
+ \item Properties of matrix product, \hyperpage{13}
+ \item Properties of projections, \hyperpage{71}
+ \item Properties of reflections, \hyperpage{71}
+ \item Properties of translations, \hyperpage{71}
+ \item Proximity theorem, \hyperpage{229}
+ \item pull-back, \hyperpage{156}
+ \item pure birth process, \hyperpage{329}
+ \item pure death process, \hyperpage{329}
+ \item purely inseparable, \hyperpage{168}
+ \item purely transcendental, \hyperpage{165}
+ \item Pythagorean, \hyperpage{64}
+ \item Pythagorean plane, \hyperpage{64}
+ \item Pythagorean theorem, \hyperpage{72}, \hyperpage{310}
\indexspace
- \item Q-Q plots, \hyperpage{203}
- \item QR decomposition, \hyperpage{266}
- \item QR descompostion, \hyperpage{266}
- \item quadratic convergence, \hyperpage{90}
- \item quadratic form, \hyperpage{73}
- \item Quadratic loss function, \hyperpage{202}
- \item quadratic polynomial, \hyperpage{161}
- \item quadratic space, \hyperpage{73}
- \item quadrature formula, \hyperpage{94}
- \item quadrature formula with weight $\omega (x)$, \hyperpage{96}
- \item quadric, \hyperpage{72}
- \item Quantile, \hyperpage{195}
- \item Quantile-Quantile plot, \hyperpage{203}
- \item quartic polynomial, \hyperpage{161}
- \item quasi-Newton method, \hyperpage{262}
- \item quasilinear pde, \hyperpage{139}
- \item quaternion group, \hyperpage{41}
- \item Quotient group, \hyperpage{38}
- \item quotient group, \hyperpage{38}
- \item quotient map, \hyperpage{209}
- \item quotient space, \hyperpage{16}, \hyperpage{209},
- \hyperpage{301}
- \item quotient space of collapsing a set to a point, \hyperpage{210}
- \item quotient topology, \hyperpage{209}
+ \item Q-Q plots, \hyperpage{204}
+ \item QR decomposition, \hyperpage{267}
+ \item QR descompostion, \hyperpage{267}
+ \item quadratic convergence, \hyperpage{91}
+ \item quadratic form, \hyperpage{74}
+ \item Quadratic loss function, \hyperpage{203}
+ \item quadratic polynomial, \hyperpage{162}
+ \item quadratic space, \hyperpage{74}
+ \item quadrature formula, \hyperpage{95}
+ \item quadrature formula with weight $\omega (x)$, \hyperpage{97}
+ \item quadric, \hyperpage{73}
+ \item Quantile, \hyperpage{196}
+ \item Quantile-Quantile plot, \hyperpage{204}
+ \item quartic polynomial, \hyperpage{162}
+ \item quasi-Newton method, \hyperpage{263}
+ \item quasilinear pde, \hyperpage{140}
+ \item quaternion group, \hyperpage{42}
+ \item Quotient group, \hyperpage{39}
+ \item quotient group, \hyperpage{39}
+ \item quotient map, \hyperpage{210}
+ \item quotient space, \hyperpage{17}, \hyperpage{210},
+ \hyperpage{302}
+ \item quotient space of collapsing a set to a point, \hyperpage{211}
+ \item quotient topology, \hyperpage{210}
\indexspace
- \item Raabe's test, \hyperpage{75}
- \item radical, \hyperpage{21}, \hyperpage{169}
- \item radical tower, \hyperpage{169}
- \item radius of convergence, \hyperpage{107}
- \item radius of convergence of the power series, \hyperpage{78}
- \item radius of curvature, \hyperpage{143}
- \item radix-2 decimation-in-time (DIT) FFT, \hyperpage{239}
- \item Radix-2 DIT Cooley-Tukey FFT algorithm, \hyperpage{239}
- \item Radó theorem, \hyperpage{217}
- \item random sample, \hyperpage{192}
- \item random variable, \hyperpage{174}
- \item random vector, \hyperpage{178}
- \item Random walk, \hyperpage{318}
- \item random walk, \hyperpage{318}
- \item Rank, \hyperpage{13}
- \item rank, \hyperpage{13}, \hyperpage{15}, \hyperpage{22},
- \hyperpage{73}
- \item Rankine-Hugoniot equation, \hyperpage{279}
- \item rate, \hyperpage{178}
- \item rate of convergence, \hyperpage{98}
- \item Ratio test, \hyperpage{25}, \hyperpage{75}
- \item ray, \hyperpage{62}
- \item Rayleigh quotient, \hyperpage{100}
- \item RC, \hyperpage{63}
- \item reachable, \hyperpage{319}
- \item real function, \hyperpage{293}
- \item real part, \hyperpage{103}
- \item real random variable, \hyperpage{174}
- \item realizable, \hyperpage{66}
- \item realization, \hyperpage{192}
- \item rearrangement of the sequence, \hyperpage{76}
- \item rearrangement of the series, \hyperpage{76}
- \item rectangle, \hyperpage{57}
- \item rectifiable, \hyperpage{33}, \hyperpage{59}, \hyperpage{140}
- \item Rectifying plane, \hyperpage{142}
- \item recurrence relation of order $k$, \hyperpage{47}
- \item recurrent, \hyperpage{47}, \hyperpage{321}, \hyperpage{323}
- \item Reduced row echelon form, \hyperpage{13}
- \item reduced row echelon form, \hyperpage{13}
- \item reducible, \hyperpage{99}
- \item Reducible linear ode of second order, \hyperpage{122}
- \item reflection, \hyperpage{70}, \hyperpage{119}
- \item Reflections, \hyperpage{70}
- \item reflexive, \hyperpage{307}
- \item refractive index, \hyperpage{277}
- \item region, \hyperpage{114}, \hyperpage{147}, \hyperpage{203}
- \item regression axis, \hyperpage{150}
- \item regression coefficients, \hyperpage{249}
- \item regression sum of squares, \hyperpage{251}
- \item regressor coefficients, \hyperpage{249}
- \item Regula falsi method, \hyperpage{89}
- \item regular, \hyperpage{48}, \hyperpage{57}, \hyperpage{130},
- \hyperpage{140}, \hyperpage{194, 195}, \hyperpage{211},
- \hyperpage{327}
- \item regular distributions, \hyperpage{240}
- \item regular domain, \hyperpage{147}
- \item regular region, \hyperpage{159}
- \item regular surface, \hyperpage{146}
- \item Related samples with unknown variances, \hyperpage{198}
- \item relative condition numbers, \hyperpage{89}
- \item relative error, \hyperpage{88}
- \item relatively compact, \hyperpage{120}
- \item relatively prime, \hyperpage{9, 10}
- \item relaxation factor, \hyperpage{99}
- \item Removable discontinuity, \hyperpage{27}
- \item Removable singularity, \hyperpage{115}
- \item removable singularity, \hyperpage{115}
- \item reordering, \hyperpage{105}
- \item reparametrization, \hyperpage{59}, \hyperpage{140}
- \item repelling, \hyperpage{130}
- \item repelling parabolic sector, \hyperpage{132}
- \item repulsor fixed point, \hyperpage{90}
- \item residuals, \hyperpage{249}
- \item residue, \hyperpage{115}
- \item Residues theorem, \hyperpage{116}
- \item response, \hyperpage{252}
- \item restrictions, \hyperpage{50}
- \item Reuter criterion, \hyperpage{329}
- \item Riccati differential equation, \hyperpage{122}
- \item Richardson extrapolation, \hyperpage{94}, \hyperpage{259}
- \item Riemann conformal representation theorem, \hyperpage{120}
- \item Riemann sum, \hyperpage{33}, \hyperpage{57}
- \item Riemann's theorem, \hyperpage{76}
- \item Riemann's theorem on removable singularities, \hyperpage{115}
- \item Riemann-integrable, \hyperpage{57}
- \item Riemann-integrable function, \hyperpage{58}
- \item Riemann-Lebesgue lemma, \hyperpage{84}, \hyperpage{231},
- \hyperpage{237}
- \item Riesz representation theorem, \hyperpage{311}
- \item Riesz theorem, \hyperpage{246}
- \item Riesz transform, \hyperpage{247}
- \item Riesz's theorem, \hyperpage{305}
- \item Riesz-Fischer theorem, \hyperpage{312}
- \item right cosets, \hyperpage{38}
- \item Right side, \hyperpage{119}
- \item right singular vectors, \hyperpage{264}
- \item Right-open interval, \hyperpage{24}
- \item right-sided limit of $f$ at $x_0$, \hyperpage{26}
- \item Ring, \hyperpage{41}
- \item ring, \hyperpage{41}
- \item Ring morphism, \hyperpage{42}
- \item ring morphism, \hyperpage{42}
- \item RK methods, \hyperpage{259}
- \item Robin, \hyperpage{273}
- \item Rolle's theorem, \hyperpage{29}
- \item Romberg method, \hyperpage{95}
- \item root, \hyperpage{11}
- \item root condition, \hyperpage{261}
- \item root of the reflection, \hyperpage{70}
- \item Root test, \hyperpage{25}, \hyperpage{75}
- \item rotation, \hyperpage{118}
- \item Rouché's theorem, \hyperpage{118}
- \item Rouché-Frobenius theorem, \hyperpage{13}
- \item Routh-Hurwitz stability criterion, \hyperpage{226}
- \item Row echelon form, \hyperpage{13}
- \item row echelon form, \hyperpage{13}
- \item row rank, \hyperpage{15}
- \item Ruffini's rule, \hyperpage{11}
- \item ruled surface, \hyperpage{150}
- \item Runge-Kutta-Fehlberg method, \hyperpage{259}
+ \item Raabe's test, \hyperpage{76}
+ \item radical, \hyperpage{22}, \hyperpage{170}
+ \item radical tower, \hyperpage{170}
+ \item radius of convergence, \hyperpage{108}
+ \item radius of convergence of the power series, \hyperpage{79}
+ \item radius of curvature, \hyperpage{144}
+ \item radix-2 decimation-in-time (DIT) FFT, \hyperpage{240}
+ \item Radix-2 DIT Cooley-Tukey FFT algorithm, \hyperpage{240}
+ \item Radon-Nikodym, \hyperpage{336}
+ \item Radó theorem, \hyperpage{218}
+ \item random sample, \hyperpage{193}
+ \item Random variable, \hyperpage{336}
+ \item random variable, \hyperpage{175}
+ \item random vector, \hyperpage{179}
+ \item Random walk, \hyperpage{319}
+ \item random walk, \hyperpage{319}
+ \item Rank, \hyperpage{14}
+ \item rank, \hyperpage{14}, \hyperpage{16}, \hyperpage{23},
+ \hyperpage{74}
+ \item Rankine-Hugoniot equation, \hyperpage{280}
+ \item rate, \hyperpage{179}
+ \item rate of convergence, \hyperpage{99}
+ \item Ratio test, \hyperpage{26}, \hyperpage{76}
+ \item ray, \hyperpage{63}
+ \item Rayleigh quotient, \hyperpage{101}
+ \item RC, \hyperpage{64}
+ \item reachable, \hyperpage{320}
+ \item real function, \hyperpage{294}
+ \item real part, \hyperpage{104}
+ \item real random variable, \hyperpage{175}
+ \item realizable, \hyperpage{67}
+ \item realization, \hyperpage{193}
+ \item rearrangement of the sequence, \hyperpage{77}
+ \item rearrangement of the series, \hyperpage{77}
+ \item rectangle, \hyperpage{58}
+ \item rectifiable, \hyperpage{34}, \hyperpage{60}, \hyperpage{141}
+ \item Rectifying plane, \hyperpage{143}
+ \item recurrence relation of order $k$, \hyperpage{48}
+ \item recurrent, \hyperpage{48}, \hyperpage{322}, \hyperpage{324}
+ \item Reduced row echelon form, \hyperpage{14}
+ \item reduced row echelon form, \hyperpage{14}
+ \item reducible, \hyperpage{100}
+ \item Reducible linear ode of second order, \hyperpage{123}
+ \item reflection, \hyperpage{71}, \hyperpage{120}
+ \item Reflections, \hyperpage{71}
+ \item reflexive, \hyperpage{308}
+ \item refractive index, \hyperpage{278}
+ \item region, \hyperpage{115}, \hyperpage{148}, \hyperpage{204}
+ \item regression axis, \hyperpage{151}
+ \item regression coefficients, \hyperpage{250}
+ \item regression sum of squares, \hyperpage{252}
+ \item regressor coefficients, \hyperpage{250}
+ \item Regula falsi method, \hyperpage{90}
+ \item regular, \hyperpage{49}, \hyperpage{58}, \hyperpage{131},
+ \hyperpage{141}, \hyperpage{195, 196}, \hyperpage{212},
+ \hyperpage{328}
+ \item regular distributions, \hyperpage{241}
+ \item regular domain, \hyperpage{148}
+ \item regular region, \hyperpage{160}
+ \item regular surface, \hyperpage{147}
+ \item Related samples with unknown variances, \hyperpage{199}
+ \item relative condition numbers, \hyperpage{90}
+ \item relative error, \hyperpage{89}
+ \item relatively compact, \hyperpage{121}
+ \item relatively prime, \hyperpage{10, 11}
+ \item relaxation factor, \hyperpage{100}
+ \item Removable discontinuity, \hyperpage{28}
+ \item Removable singularity, \hyperpage{116}
+ \item removable singularity, \hyperpage{116}
+ \item reordering, \hyperpage{106}
+ \item reparametrization, \hyperpage{60}, \hyperpage{141}
+ \item repelling, \hyperpage{131}
+ \item repelling parabolic sector, \hyperpage{133}
+ \item repulsor fixed point, \hyperpage{91}
+ \item residuals, \hyperpage{250}
+ \item residue, \hyperpage{116}
+ \item Residues theorem, \hyperpage{117}
+ \item response, \hyperpage{253}
+ \item restrictions, \hyperpage{51}
+ \item Reuter criterion, \hyperpage{330}
+ \item Riccati differential equation, \hyperpage{123}
+ \item Richardson extrapolation, \hyperpage{95}, \hyperpage{260}
+ \item Riemann conformal representation theorem, \hyperpage{121}
+ \item Riemann sum, \hyperpage{34}, \hyperpage{58}
+ \item Riemann's theorem, \hyperpage{77}
+ \item Riemann's theorem on removable singularities, \hyperpage{116}
+ \item Riemann-integrable, \hyperpage{58}
+ \item Riemann-integrable function, \hyperpage{59}
+ \item Riemann-Lebesgue lemma, \hyperpage{85}, \hyperpage{232},
+ \hyperpage{238}
+ \item Riesz representation theorem, \hyperpage{312}
+ \item Riesz theorem, \hyperpage{248}
+ \item Riesz transform, \hyperpage{248}
+ \item Riesz's theorem, \hyperpage{306}
+ \item Riesz-Fischer theorem, \hyperpage{313}
+ \item right cosets, \hyperpage{39}
+ \item Right side, \hyperpage{120}
+ \item right singular vectors, \hyperpage{265}
+ \item Right-open interval, \hyperpage{25}
+ \item right-sided limit of $f$ at $x_0$, \hyperpage{27}
+ \item Ring, \hyperpage{42}
+ \item ring, \hyperpage{42}
+ \item Ring morphism, \hyperpage{43}
+ \item ring morphism, \hyperpage{43}
+ \item RK methods, \hyperpage{260}
+ \item Robin, \hyperpage{274}
+ \item Rolle's theorem, \hyperpage{30}
+ \item Romberg method, \hyperpage{96}
+ \item root, \hyperpage{12}
+ \item root condition, \hyperpage{262}
+ \item root of the reflection, \hyperpage{71}
+ \item Root test, \hyperpage{26}, \hyperpage{76}
+ \item rotation, \hyperpage{119}
+ \item Rouché's theorem, \hyperpage{119}
+ \item Rouché-Frobenius theorem, \hyperpage{14}
+ \item Routh-Hurwitz stability criterion, \hyperpage{227}
+ \item Row echelon form, \hyperpage{14}
+ \item row echelon form, \hyperpage{14}
+ \item row rank, \hyperpage{16}
+ \item Ruffini's rule, \hyperpage{12}
+ \item ruled surface, \hyperpage{151}
+ \item Runge-Kutta-Fehlberg method, \hyperpage{260}
\indexspace
- \item SAA criterion, \hyperpage{63}
- \item Saccheri-Legendre theorem, \hyperpage{63}
- \item saddle point, \hyperpage{56}, \hyperpage{132}
- \item saddle separatrices, \hyperpage{132}
- \item saddle-node, \hyperpage{223}
- \item Saddle-node bifurcation, \hyperpage{222}
- \item saddle-node bifurcation, \hyperpage{222}
- \item same orientation, \hyperpage{141}, \hyperpage{216}
- \item sample correlation coefficient, \hyperpage{248}
- \item sample covariance, \hyperpage{248}
- \item sample mean, \hyperpage{190}, \hyperpage{192}
- \item sample quantiles, \hyperpage{203}
- \item Sample space, \hyperpage{172}
- \item sample space, \hyperpage{172}, \hyperpage{192}
- \item sample variance, \hyperpage{192}, \hyperpage{248}
- \item Sample variance and covariance, \hyperpage{248}
- \item SAS criterion, \hyperpage{62, 63}
- \item scalars, \hyperpage{14}
- \item scale, \hyperpage{178}
- \item Schrödinger equation, \hyperpage{278}
- \item Schwartz space, \hyperpage{242}
- \item Schwarz lemma, \hyperpage{119}
- \item Schwarz theorem, \hyperpage{241}
- \item Schwarz's theorem, \hyperpage{56}
- \item Schwarz-Pick lemma, \hyperpage{120}
- \item score function, \hyperpage{194}
- \item Score test, \hyperpage{201}
- \item score test, \hyperpage{201}
- \item Secant method, \hyperpage{89}
- \item secant-like method, \hyperpage{262}
- \item Second Borel-Cantelli lemma, \hyperpage{187}
- \item second derivative of $f$ at $a$, \hyperpage{30}
- \item second fundamental form, \hyperpage{149}
- \item Second isomorphism theorem, \hyperpage{17}, \hyperpage{39},
- \hyperpage{43}
- \item Second Sylow theorem, \hyperpage{40}
- \item section, \hyperpage{298}
- \item sectorial decomposition, \hyperpage{132}
- \item segment, \hyperpage{71}
- \item Segmented regression, \hyperpage{252}
- \item self-adjoint, \hyperpage{311}
- \item self-conjugate, \hyperpage{303}
- \item self-similar, \hyperpage{283}
+ \item SAA criterion, \hyperpage{64}
+ \item Saccheri-Legendre theorem, \hyperpage{64}
+ \item saddle point, \hyperpage{57}, \hyperpage{133}
+ \item saddle separatrices, \hyperpage{133}
+ \item saddle-node, \hyperpage{224}
+ \item Saddle-node bifurcation, \hyperpage{223}
+ \item saddle-node bifurcation, \hyperpage{223}
+ \item same orientation, \hyperpage{142}, \hyperpage{217}
+ \item sample correlation coefficient, \hyperpage{249}
+ \item sample covariance, \hyperpage{249}
+ \item sample mean, \hyperpage{192, 193}
+ \item sample quantiles, \hyperpage{204}
+ \item Sample space, \hyperpage{173}
+ \item sample space, \hyperpage{173}, \hyperpage{193}
+ \item sample variance, \hyperpage{193}, \hyperpage{249}
+ \item Sample variance and covariance, \hyperpage{249}
+ \item SAS criterion, \hyperpage{63, 64}
+ \item scalars, \hyperpage{15}
+ \item scale, \hyperpage{179}
+ \item Schrödinger equation, \hyperpage{279}
+ \item Schwartz space, \hyperpage{243}
+ \item Schwarz lemma, \hyperpage{120}
+ \item Schwarz theorem, \hyperpage{243}
+ \item Schwarz's theorem, \hyperpage{57}
+ \item Schwarz-Pick lemma, \hyperpage{121}
+ \item score function, \hyperpage{195}
+ \item Score test, \hyperpage{202}
+ \item score test, \hyperpage{202}
+ \item Secant method, \hyperpage{90}
+ \item secant-like method, \hyperpage{263}
+ \item Second Borel-Cantelli lemma, \hyperpage{189}
+ \item second derivative of $f$ at $a$, \hyperpage{31}
+ \item second fundamental form, \hyperpage{150}
+ \item Second isomorphism theorem, \hyperpage{18}, \hyperpage{40},
+ \hyperpage{44}
+ \item Second Sylow theorem, \hyperpage{41}
+ \item section, \hyperpage{299}
+ \item sectorial decomposition, \hyperpage{133}
+ \item segment, \hyperpage{72}
+ \item Segmented regression, \hyperpage{253}
+ \item self-adjoint, \hyperpage{312}
+ \item self-conjugate, \hyperpage{304}
+ \item self-similar, \hyperpage{284}
\item Semi-hyperbolic singular points classification theorem,
- \hyperpage{222}
- \item semi-stable, \hyperpage{135}
- \item semiaffinity, \hyperpage{69}
- \item Semidiscrete Fourier transform, \hyperpage{269}
- \item semidiscrete Fourier transform, \hyperpage{269}
- \item Semidiscrete Parseval identity, \hyperpage{269}
- \item semidynamical system, \hyperpage{129}
- \item semilinear, \hyperpage{309}
- \item semilinear isomorphism, \hyperpage{66}
- \item Seminorm, \hyperpage{307}
- \item seminorm, \hyperpage{93}, \hyperpage{307}
- \item sensitive dependence on initial conditions, \hyperpage{229}
- \item Separability theorem, \hyperpage{167}
- \item separable, \hyperpage{167}, \hyperpage{300}
- \item Separable extension, \hyperpage{167}
- \item separate the points, \hyperpage{302}
- \item separated, \hyperpage{206}
- \item separated by closed neighbourhoods, \hyperpage{206}
- \item separating set, \hyperpage{302}
- \item Separation of variables, \hyperpage{122}, \hyperpage{282}
- \item separation of variables, \hyperpage{282}
- \item sequence, \hyperpage{53}
- \item sequence of complex functions, \hyperpage{105}
- \item sequence of complex numbers, \hyperpage{104}
- \item sequence of real functions, \hyperpage{76}
- \item sequence of real numbers, \hyperpage{25}
- \item series of functions, \hyperpage{77}, \hyperpage{106}
- \item set, \hyperpage{5}
- \item set difference, \hyperpage{5}
- \item set of interior vectors, \hyperpage{156}
- \item set of left cosets, \hyperpage{38}
- \item set of periodic points, \hyperpage{227}
- \item set of periods, \hyperpage{227}
- \item set of polynomials, \hyperpage{41}
- \item set of right cosets, \hyperpage{38}
- \item set of zero-content, \hyperpage{173}
- \item shape, \hyperpage{178}
- \item Sharkovskii's order, \hyperpage{228}
- \item Sharkovskii's theorem, \hyperpage{228}
- \item Shift map, \hyperpage{228}
- \item shift map, \hyperpage{228}
- \item Shooting method, \hyperpage{263}
- \item shooting method, \hyperpage{263}
- \item Sierpiński topology, \hyperpage{205}
- \item sign, \hyperpage{7}, \hyperpage{88}
- \item signature, \hyperpage{22}
- \item signed curvature, \hyperpage{144}
- \item significance level, \hyperpage{197, 198}
- \item significant, \hyperpage{88}
- \item similar, \hyperpage{19}, \hyperpage{70}
- \item similitude ratio of the homothety, \hyperpage{71}
- \item simple, \hyperpage{48}, \hyperpage{89}, \hyperpage{115},
- \hyperpage{163}, \hyperpage{169}, \hyperpage{198}
- \item simple curve, \hyperpage{217}
- \item simple function, \hyperpage{294}
- \item Simple model, \hyperpage{249}
- \item simple random sample, \hyperpage{192}
- \item simple random variable, \hyperpage{181}
- \item simple random walk, \hyperpage{318}
- \item Simple ratio, \hyperpage{71}
- \item simple ratio, \hyperpage{71}
- \item simple region, \hyperpage{159}
- \item Simplex method: Phase I, \hyperpage{50}
- \item Simplex method: Phase II, \hyperpage{50}
- \item simply connected, \hyperpage{115}, \hyperpage{215}
- \item simply normal, \hyperpage{189}
- \item Simpson's rule, \hyperpage{94}
- \item singular point, \hyperpage{130}, \hyperpage{159}
- \item Singular value, \hyperpage{264}
- \item Singular value decomposition, \hyperpage{264}
- \item singular value decomposition, \hyperpage{264}
- \item singular values, \hyperpage{264}
- \item sink, \hyperpage{132}
- \item size, \hyperpage{48}, \hyperpage{198}
- \item Skorokhod's representation theorem, \hyperpage{189}
- \item Slutsky's theorem, \hyperpage{189}
- \item small change, \hyperpage{278}
- \item Sobolev space, \hyperpage{288}
- \item solution, \hyperpage{89}, \hyperpage{138}
- \item solution of a system of equations, \hyperpage{12}
- \item solution of the ode, \hyperpage{121}
- \item solvable, \hyperpage{40}, \hyperpage{169}
- \item solvable by radicals, \hyperpage{169}
- \item SOR, \hyperpage{99}
- \item source, \hyperpage{132}
- \item space of rapidly decreasing functions, \hyperpage{242}
- \item special orthogonal group, \hyperpage{144}
- \item specific heat capacity, \hyperpage{277}
- \item spectral radius, \hyperpage{97}
- \item Spectral theorem, \hyperpage{23}, \hyperpage{312}
- \item spectral values, \hyperpage{308}
- \item spectrum, \hyperpage{96}, \hyperpage{308}
- \item sphere, \hyperpage{53}
- \item Spline, \hyperpage{93}
- \item spline, \hyperpage{93}
- \item splits into linear factors, \hyperpage{166}
- \item Splitting field, \hyperpage{166}
- \item splitting field, \hyperpage{166}
- \item Squeeze theorem, \hyperpage{25}
- \item SSS criterion, \hyperpage{63}
- \item stability function, \hyperpage{260}
- \item stability number, \hyperpage{133}
- \item stability region, \hyperpage{260}, \hyperpage{267}
- \item stabilizer, \hyperpage{39}
- \item stable, \hyperpage{135}, \hyperpage{260}, \hyperpage{268},
- \hyperpage{273}, \hyperpage{327}
- \item stable degenerated node, \hyperpage{132}
- \item stable focus, \hyperpage{132}
- \item stable manifold, \hyperpage{221}
- \item stable node, \hyperpage{132}
- \item stable star, \hyperpage{132}
- \item standard, \hyperpage{329}
- \item standard $n$-simplex, \hyperpage{217}
- \item Standard deviation, \hyperpage{184}
- \item standard deviation, \hyperpage{177}, \hyperpage{184}
- \item standard error, \hyperpage{184}
- \item standard form, \hyperpage{50}
- \item Standard normal distribution, \hyperpage{177}
- \item standard normal distribution, \hyperpage{177}
- \item standardized form, \hyperpage{178}
- \item star domain, \hyperpage{114}
- \item state space, \hyperpage{315}, \hyperpage{317}
- \item states, \hyperpage{317}
- \item stationary distribution, \hyperpage{324}, \hyperpage{328}
- \item stationary increments, \hyperpage{325}
- \item Statistic, \hyperpage{192}
- \item statistic, \hyperpage{192}
- \item statistical model, \hyperpage{192}
- \item Steepest descent, \hyperpage{263}
- \item Steffensen's method, \hyperpage{91}
- \item Steinitz exchange lemma, \hyperpage{15}
- \item Steinitz's theorem, \hyperpage{163}
- \item step size, \hyperpage{257}, \hyperpage{263}
- \item Stereographic projection, \hyperpage{104}
- \item stereographic projection, \hyperpage{104}
- \item stiff equations, \hyperpage{260}
- \item stiffness matrix, \hyperpage{275}
- \item Stirling's formula, \hyperpage{80}
- \item Stochastic matrix, \hyperpage{317}
- \item stochastic matrix, \hyperpage{317}
- \item Stochastic process, \hyperpage{315}
- \item stochastic process, \hyperpage{315}
- \item stochastically equivalent, \hyperpage{330}
- \item Stokes theorem, \hyperpage{158}
- \item Stokes' theorem, \hyperpage{61}
- \item Stolz-Cesàro theorem, \hyperpage{26}
- \item Stone-Weierstra\ss \ theorem, \hyperpage{303}
- \item stopping time, \hyperpage{320}
- \item strict Lyapunov function, \hyperpage{136}
- \item strictly concave, \hyperpage{29}
- \item strictly convex, \hyperpage{29}
- \item strictly decreasing, \hyperpage{25}, \hyperpage{27}
- \item strictly diagonally dominant by columns, \hyperpage{98}
- \item strictly diagonally dominant by rows, \hyperpage{98}
- \item strictly increasing, \hyperpage{25}, \hyperpage{27}
- \item Strong duality theorem, \hyperpage{51}
- \item Strong law, \hyperpage{189}
- \item Strong Markov property, \hyperpage{320, 321}
- \item strongly consistent estimator, \hyperpage{193}
- \item Strum's sequence, \hyperpage{91}
+ \hyperpage{223}
+ \item semi-stable, \hyperpage{136}
+ \item semiaffinity, \hyperpage{70}
+ \item Semidiscrete Fourier transform, \hyperpage{270}
+ \item semidiscrete Fourier transform, \hyperpage{270}
+ \item Semidiscrete Parseval identity, \hyperpage{270}
+ \item semidynamical system, \hyperpage{130}
+ \item semilinear, \hyperpage{310}
+ \item semilinear isomorphism, \hyperpage{67}
+ \item Seminorm, \hyperpage{308}
+ \item seminorm, \hyperpage{94}, \hyperpage{308}
+ \item sensitive dependence on initial conditions, \hyperpage{230}
+ \item Separability theorem, \hyperpage{168}
+ \item separable, \hyperpage{168}, \hyperpage{301}
+ \item Separable extension, \hyperpage{168}
+ \item separate the points, \hyperpage{303}
+ \item separated, \hyperpage{207}
+ \item separated by closed neighbourhoods, \hyperpage{207}
+ \item separating set, \hyperpage{303}
+ \item Separation of variables, \hyperpage{123}, \hyperpage{283}
+ \item separation of variables, \hyperpage{283}
+ \item sequence, \hyperpage{54}
+ \item sequence of complex functions, \hyperpage{106}
+ \item sequence of complex numbers, \hyperpage{105}
+ \item sequence of real functions, \hyperpage{77}
+ \item sequence of real numbers, \hyperpage{26}
+ \item series of functions, \hyperpage{78}, \hyperpage{107}
+ \item set, \hyperpage{6}
+ \item set difference, \hyperpage{6}
+ \item set of interior vectors, \hyperpage{157}
+ \item set of left cosets, \hyperpage{39}
+ \item set of periodic points, \hyperpage{228}
+ \item set of periods, \hyperpage{228}
+ \item set of polynomials, \hyperpage{42}
+ \item set of right cosets, \hyperpage{39}
+ \item set of zero-content, \hyperpage{174}
+ \item shape, \hyperpage{179}
+ \item Sharkovskii's order, \hyperpage{229}
+ \item Sharkovskii's theorem, \hyperpage{229}
+ \item Shift map, \hyperpage{229}
+ \item shift map, \hyperpage{229}
+ \item Shooting method, \hyperpage{264}
+ \item shooting method, \hyperpage{264}
+ \item Sierpiński topology, \hyperpage{206}
+ \item sign, \hyperpage{8}, \hyperpage{89}
+ \item signature, \hyperpage{23}
+ \item signed curvature, \hyperpage{145}
+ \item significance level, \hyperpage{198, 199}
+ \item significant, \hyperpage{89}
+ \item similar, \hyperpage{20}, \hyperpage{71}
+ \item similitude ratio of the homothety, \hyperpage{72}
+ \item simple, \hyperpage{49}, \hyperpage{90}, \hyperpage{116},
+ \hyperpage{164}, \hyperpage{170}, \hyperpage{199}
+ \item simple curve, \hyperpage{218}
+ \item simple function, \hyperpage{295}
+ \item Simple model, \hyperpage{250}
+ \item simple random sample, \hyperpage{193}
+ \item simple random variable, \hyperpage{182}
+ \item simple random walk, \hyperpage{319}
+ \item Simple ratio, \hyperpage{72}
+ \item simple ratio, \hyperpage{72}
+ \item simple region, \hyperpage{160}
+ \item Simplex method: Phase I, \hyperpage{51}
+ \item Simplex method: Phase II, \hyperpage{51}
+ \item simply connected, \hyperpage{116}, \hyperpage{216}
+ \item simply normal, \hyperpage{191}
+ \item Simpson's rule, \hyperpage{95}
+ \item singular point, \hyperpage{131}, \hyperpage{160}
+ \item Singular value, \hyperpage{265}
+ \item Singular value decomposition, \hyperpage{265}
+ \item singular value decomposition, \hyperpage{265}
+ \item singular values, \hyperpage{265}
+ \item sink, \hyperpage{133}
+ \item size, \hyperpage{49}, \hyperpage{199}
+ \item Skorokhod's representation theorem, \hyperpage{190}
+ \item Slutsky's theorem, \hyperpage{190}
+ \item small change, \hyperpage{279}
+ \item Sobolev space, \hyperpage{289}
+ \item Sobolev spaces, \hyperpage{338}
+ \item solution, \hyperpage{90}, \hyperpage{139}
+ \item solution of a system of equations, \hyperpage{13}
+ \item solution of the ode, \hyperpage{122}
+ \item solvable, \hyperpage{41}, \hyperpage{170}
+ \item solvable by radicals, \hyperpage{170}
+ \item SOR, \hyperpage{100}
+ \item source, \hyperpage{133}
+ \item space of rapidly decreasing functions, \hyperpage{243}
+ \item special orthogonal group, \hyperpage{145}
+ \item specific heat capacity, \hyperpage{278}
+ \item spectral radius, \hyperpage{98}
+ \item Spectral theorem, \hyperpage{24}, \hyperpage{313}
+ \item spectral values, \hyperpage{309}
+ \item spectrum, \hyperpage{97}, \hyperpage{309}
+ \item sphere, \hyperpage{54}
+ \item Spline, \hyperpage{94}
+ \item spline, \hyperpage{94}
+ \item splits into linear factors, \hyperpage{167}
+ \item Splitting field, \hyperpage{167}
+ \item splitting field, \hyperpage{167}
+ \item Squeeze theorem, \hyperpage{26}
+ \item SSS criterion, \hyperpage{64}
+ \item stability function, \hyperpage{261}
+ \item stability number, \hyperpage{134}
+ \item stability region, \hyperpage{261}, \hyperpage{268}
+ \item stabilizer, \hyperpage{40}
+ \item stable, \hyperpage{136}, \hyperpage{261}, \hyperpage{269},
+ \hyperpage{274}, \hyperpage{328}
+ \item stable degenerated node, \hyperpage{133}
+ \item stable focus, \hyperpage{133}
+ \item stable manifold, \hyperpage{222}
+ \item stable node, \hyperpage{133}
+ \item stable star, \hyperpage{133}
+ \item standard, \hyperpage{330}
+ \item standard $n$-simplex, \hyperpage{218}
+ \item Standard deviation, \hyperpage{185}
+ \item standard deviation, \hyperpage{178}, \hyperpage{185}
+ \item standard error, \hyperpage{185}
+ \item standard form, \hyperpage{51}
+ \item Standard normal distribution, \hyperpage{178}
+ \item standard normal distribution, \hyperpage{178}
+ \item standardized form, \hyperpage{179}
+ \item star domain, \hyperpage{115}
+ \item state space, \hyperpage{316}, \hyperpage{318}
+ \item states, \hyperpage{318}
+ \item stationary distribution, \hyperpage{325}, \hyperpage{329}
+ \item stationary increments, \hyperpage{326}
+ \item Statistic, \hyperpage{193}
+ \item statistic, \hyperpage{193}
+ \item statistical model, \hyperpage{193}
+ \item Steepest descent, \hyperpage{264}
+ \item Steffensen's method, \hyperpage{92}
+ \item Steinitz exchange lemma, \hyperpage{16}
+ \item Steinitz's theorem, \hyperpage{164}
+ \item step size, \hyperpage{258}, \hyperpage{264}
+ \item Stereographic projection, \hyperpage{105}
+ \item stereographic projection, \hyperpage{105}
+ \item stiff equations, \hyperpage{261}
+ \item stiffness matrix, \hyperpage{276}
+ \item Stirling's formula, \hyperpage{81}
+ \item Stochastic matrix, \hyperpage{318}
+ \item stochastic matrix, \hyperpage{318}
+ \item Stochastic process, \hyperpage{316}
+ \item stochastic process, \hyperpage{316}
+ \item stochastically equivalent, \hyperpage{331}
+ \item Stokes theorem, \hyperpage{159}
+ \item Stokes' theorem, \hyperpage{62}
+ \item Stolz-Cesàro theorem, \hyperpage{27}
+ \item Stone-Weierstra\ss \ theorem, \hyperpage{304}
+ \item stopping time, \hyperpage{321}
+ \item strict Lyapunov function, \hyperpage{137}
+ \item strictly concave, \hyperpage{30}
+ \item strictly convex, \hyperpage{30}
+ \item strictly decreasing, \hyperpage{26}, \hyperpage{28}
+ \item strictly diagonally dominant by columns, \hyperpage{99}
+ \item strictly diagonally dominant by rows, \hyperpage{99}
+ \item strictly increasing, \hyperpage{26}, \hyperpage{28}
+ \item Strong duality theorem, \hyperpage{52}
+ \item Strong law, \hyperpage{191}
+ \item Strong Markov property, \hyperpage{321, 322}
+ \item strongly consistent estimator, \hyperpage{194}
+ \item Strum's sequence, \hyperpage{92}
\item Student's $t$-distribution with $n$ degrees of freedom,
- \hyperpage{196}
- \item Sturm's sequence, \hyperpage{91}
- \item Sturm's theorem, \hyperpage{91}
- \item Sturm-Picone comparison theorem, \hyperpage{282}
- \item sub-multiplicativity, \hyperpage{96}
- \item subalgebra, \hyperpage{302}
- \item subbasis, \hyperpage{205}
- \item subcover, \hyperpage{212}
- \item subfield generated, \hyperpage{162}
- \item Subgroup, \hyperpage{36}
- \item subgroup, \hyperpage{36}
- \item subgroup generated, \hyperpage{36}
- \item sublinear, \hyperpage{305}
- \item submanifold, \hyperpage{145}
- \item submanifold with boundary, \hyperpage{156}
- \item Submersion, \hyperpage{145}
- \item submersion, \hyperpage{145}
- \item subordinated matrix norm, \hyperpage{96}
- \item Subring, \hyperpage{41}
- \item subring, \hyperpage{41}
- \item subring generated, \hyperpage{162}
- \item Subsequence, \hyperpage{25}
- \item subsequence, \hyperpage{25}
- \item subset, \hyperpage{5}
- \item subspace topology, \hyperpage{207}
- \item Substitution principle, \hyperpage{314}
- \item success, \hyperpage{176}
- \item Successive over-relaxation \\method, \hyperpage{99}
- \item Successive over-relaxation method, \hyperpage{99}
- \item sufficient, \hyperpage{193}
- \item sum, \hyperpage{10}, \hyperpage{12}, \hyperpage{15},
- \hyperpage{69}
- \item sum of the series, \hyperpage{75}, \hyperpage{105}
- \item sum of the series in a pointwise sense, \hyperpage{77},
- \hyperpage{106}
- \item sum of the series in an uniform sense, \hyperpage{77},
- \hyperpage{106}
- \item support, \hyperpage{7}, \hyperpage{78}, \hyperpage{145},
- \hyperpage{175}, \hyperpage{179}, \hyperpage{241}
- \item support points, \hyperpage{92}
- \item supremum, \hyperpage{24}
- \item Supremum axiom, \hyperpage{24}
- \item supremum norm, \hyperpage{302}
- \item surface, \hyperpage{57}, \hyperpage{146}, \hyperpage{216}
- \item surface integral, \hyperpage{60, 61}
- \item surface intergal, \hyperpage{158}
- \item Surface of revolution, \hyperpage{33}
- \item surface of revolution, \hyperpage{146}
- \item surjective, \hyperpage{6}, \hyperpage{120}
- \item SVD, \hyperpage{264}
- \item Sylow $p$-subgroup, \hyperpage{40}
- \item Sylvester's criterion, \hyperpage{57}
- \item Sylvester's law of inertia, \hyperpage{22}
- \item symmetric, \hyperpage{21}, \hyperpage{61}
- \item Symmetric difference formula of order 1, \hyperpage{94}
- \item Symmetric difference formula of order 2, \hyperpage{94}
- \item symmetric group, \hyperpage{7}, \hyperpage{37}
- \item symmetric polynomial, \hyperpage{162}
- \item Symmetric polynomials, \hyperpage{162}
- \item symmetric with respect to the $x$-axis, \hyperpage{220}
- \item symmetric with respect to the $y$-axis, \hyperpage{220}
- \item Symmetry principle, \hyperpage{119}
- \item system of linear differential equations, \hyperpage{125}
- \item system of linear equations, \hyperpage{12}
- \item system of ordinary differential equations, \hyperpage{121}
+ \hyperpage{197}
+ \item Sturm's sequence, \hyperpage{92}
+ \item Sturm's theorem, \hyperpage{92}
+ \item Sturm-Picone comparison theorem, \hyperpage{283}
+ \item sub-multiplicativity, \hyperpage{97}
+ \item subalgebra, \hyperpage{303}
+ \item subbasis, \hyperpage{206}
+ \item subcover, \hyperpage{213}
+ \item subfield generated, \hyperpage{163}
+ \item Subgroup, \hyperpage{37}
+ \item subgroup, \hyperpage{37}
+ \item subgroup generated, \hyperpage{37}
+ \item sublinear, \hyperpage{306}
+ \item submanifold, \hyperpage{146}
+ \item submanifold with boundary, \hyperpage{157}
+ \item Submersion, \hyperpage{146}
+ \item submersion, \hyperpage{146}
+ \item subordinated matrix norm, \hyperpage{97}
+ \item Subring, \hyperpage{42}
+ \item subring, \hyperpage{42}
+ \item subring generated, \hyperpage{163}
+ \item Subsequence, \hyperpage{26}
+ \item subsequence, \hyperpage{26}
+ \item subset, \hyperpage{6}
+ \item subspace topology, \hyperpage{208}
+ \item Substitution principle, \hyperpage{315}
+ \item success, \hyperpage{177}
+ \item Successive over-relaxation \\method, \hyperpage{100}
+ \item Successive over-relaxation method, \hyperpage{100}
+ \item sufficient, \hyperpage{194}
+ \item sum, \hyperpage{11}, \hyperpage{13}, \hyperpage{16},
+ \hyperpage{70}
+ \item sum of the series, \hyperpage{76}, \hyperpage{106}
+ \item sum of the series in a pointwise sense, \hyperpage{78},
+ \hyperpage{107}
+ \item sum of the series in an uniform sense, \hyperpage{78},
+ \hyperpage{107}
+ \item support, \hyperpage{8}, \hyperpage{79}, \hyperpage{146},
+ \hyperpage{176}, \hyperpage{180}, \hyperpage{242}
+ \item support points, \hyperpage{93}
+ \item supremum, \hyperpage{25}
+ \item Supremum axiom, \hyperpage{25}
+ \item supremum norm, \hyperpage{303}
+ \item surface, \hyperpage{58}, \hyperpage{147}, \hyperpage{217}
+ \item surface integral, \hyperpage{61, 62}
+ \item surface intergal, \hyperpage{159}
+ \item Surface of revolution, \hyperpage{34}
+ \item surface of revolution, \hyperpage{147}
+ \item surjective, \hyperpage{7}, \hyperpage{121}
+ \item SVD, \hyperpage{265}
+ \item Sylow $p$-subgroup, \hyperpage{41}
+ \item Sylvester's criterion, \hyperpage{58}
+ \item Sylvester's law of inertia, \hyperpage{23}
+ \item symmetric, \hyperpage{22}, \hyperpage{62}
+ \item Symmetric difference formula of order 1, \hyperpage{95}
+ \item Symmetric difference formula of order 2, \hyperpage{95}
+ \item symmetric group, \hyperpage{8}, \hyperpage{38}
+ \item symmetric polynomial, \hyperpage{163}
+ \item Symmetric polynomials, \hyperpage{163}
+ \item symmetric with respect to the $x$-axis, \hyperpage{221}
+ \item symmetric with respect to the $y$-axis, \hyperpage{221}
+ \item Symmetry principle, \hyperpage{120}
+ \item system of linear differential equations, \hyperpage{126}
+ \item system of linear equations, \hyperpage{13}
+ \item system of ordinary differential equations, \hyperpage{122}
\indexspace
- \item tangent, \hyperpage{153}, \hyperpage{155}
- \item tangent function, \hyperpage{147}
- \item tangent line, \hyperpage{140}, \hyperpage{143}
+ \item tangent, \hyperpage{154}, \hyperpage{156}
+ \item tangent function, \hyperpage{148}
+ \item tangent line, \hyperpage{141}, \hyperpage{144}
\item tangent line to the graph at the point $(x_0,f(x_0))$,
- \hyperpage{28}
- \item tangent plane, \hyperpage{146}
- \item tangent space, \hyperpage{146}, \hyperpage{155, 156}
- \item tangent vector, \hyperpage{140}, \hyperpage{146},
- \hyperpage{155}
- \item tangent vector field, \hyperpage{138}
- \item Taxicab metric, \hyperpage{204}
- \item Taylor method, \hyperpage{258}
- \item Taylor method of order $r$, \hyperpage{258}
+ \hyperpage{29}
+ \item tangent plane, \hyperpage{147}
+ \item tangent space, \hyperpage{147}, \hyperpage{156, 157}
+ \item tangent vector, \hyperpage{141}, \hyperpage{147},
+ \hyperpage{156}
+ \item tangent vector field, \hyperpage{139}
+ \item Taxicab metric, \hyperpage{205}
+ \item Taylor method, \hyperpage{259}
+ \item Taylor method of order $r$, \hyperpage{259}
\item Taylor polynomial of order $n$ of $f$ centered at $a$,
- \hyperpage{30}
- \item Taylor's theorem, \hyperpage{56}
- \item tempered distribution, \hyperpage{242}
- \item tends to the boundary, \hyperpage{125}
- \item terminal point, \hyperpage{214}
- \item test, \hyperpage{199}
- \item test functions, \hyperpage{239}
- \item Test of homogenity, \hyperpage{200}
- \item Test of independence, \hyperpage{200}
- \item test problem, \hyperpage{260}
- \item test statistic, \hyperpage{198}
- \item the Best Linear Unbiased Estimator, \hyperpage{250}
- \item The center manifold theorem, \hyperpage{222}
- \item The stable manifold theorem, \hyperpage{221}
- \item theorem, \hyperpage{66}
- \item theoretical quantiles, \hyperpage{203}
- \item thermal conductivity, \hyperpage{277}
- \item thermal diffusivity, \hyperpage{277}
- \item thin QR decomposition, \hyperpage{266}
- \item Third isomorphism theorem, \hyperpage{17}, \hyperpage{39},
- \hyperpage{43}
- \item Third Sylow theorem, \hyperpage{40}
- \item Tietze extension theorem, \hyperpage{211}
- \item time-homogeneous Markov chain, \hyperpage{317}
- \item TNB frame, \hyperpage{142}
- \item tolerance, \hyperpage{254}
- \item Tonelli's theorem, \hyperpage{174}, \hyperpage{298}
- \item topological embedding, \hyperpage{213}
- \item topological homeomorphism, \hyperpage{305}
- \item Topological manifold, \hyperpage{215}
- \item topological manifold, \hyperpage{215}
- \item topological property, \hyperpage{212}
- \item Topological space, \hyperpage{204}
- \item topological space, \hyperpage{204}
- \item topological subspace, \hyperpage{207}
- \item topologically conjugate, \hyperpage{131}
- \item topologically equivalent, \hyperpage{130}
- \item topologically transitive, \hyperpage{229}
- \item topology, \hyperpage{204}
- \item topology generated, \hyperpage{205}
- \item Topology induced from the metric, \hyperpage{204}
- \item torsion, \hyperpage{142}
- \item Torus, \hyperpage{209}
- \item torus, \hyperpage{209}
- \item total mean of squares, \hyperpage{251}
- \item total order relation, \hyperpage{8}
- \item total subset, \hyperpage{300}
- \item total sum of squares, \hyperpage{251}
- \item totally disconnected, \hyperpage{214}
- \item totally isotropic, \hyperpage{73}
- \item Tower formula, \hyperpage{164}
- \item tower of fields, \hyperpage{164}
- \item trace, \hyperpage{140}, \hyperpage{288}
- \item Trace theorem, \hyperpage{288}
- \item Traffic flow equation, \hyperpage{279}
- \item trail, \hyperpage{48}
- \item trajectories, \hyperpage{325}
- \item transcendental, \hyperpage{163}
- \item Transcritical bifurcation, \hyperpage{222}
- \item transcritical bifurcation, \hyperpage{222}
- \item transient, \hyperpage{321}, \hyperpage{323}
- \item transition functions, \hyperpage{215}
- \item transition matrix, \hyperpage{317}
- \item transition probabilities, \hyperpage{317}, \hyperpage{325}
- \item transitive, \hyperpage{168}
- \item translation, \hyperpage{70}, \hyperpage{118}
- \item Translations, \hyperpage{70}
- \item transpose, \hyperpage{13}
- \item Transposition, \hyperpage{13}
- \item transposition, \hyperpage{7}
- \item transversal section, \hyperpage{131}
- \item Trapezoidal method, \hyperpage{258}
- \item Trapezoidal rule, \hyperpage{94}
- \item traversable, \hyperpage{49}
- \item tree, \hyperpage{49}
- \item triangle, \hyperpage{159}
- \item Triangular inequality, \hyperpage{24}, \hyperpage{71}
- \item triangular inequality, \hyperpage{52}, \hyperpage{204},
- \hyperpage{299}
- \item triangular system, \hyperpage{96}
- \item triangularization, \hyperpage{217}
- \item triple, \hyperpage{89}
- \item trivial $\sigma $-algebra, \hyperpage{171}
- \item Trivial topology, \hyperpage{205}
- \item true, \hyperpage{176}
- \item truncated, \hyperpage{265}
- \item truncated Hilbert transform, \hyperpage{246}
- \item truncated singular value decomposition, \hyperpage{265}
- \item TSVD, \hyperpage{265}
- \item two times differentiable, \hyperpage{30}
- \item two times differentiable at $a$, \hyperpage{30}
- \item two-sided test, \hyperpage{199}
- \item Tychonoff's theorem, \hyperpage{212}
+ \hyperpage{31}
+ \item Taylor's theorem, \hyperpage{57}
+ \item tempered distribution, \hyperpage{244}
+ \item tends to the boundary, \hyperpage{126}
+ \item terminal point, \hyperpage{215}
+ \item test, \hyperpage{200}
+ \item test functions, \hyperpage{240}
+ \item Test of homogenity, \hyperpage{201}
+ \item Test of independence, \hyperpage{201}
+ \item test problem, \hyperpage{261}
+ \item test statistic, \hyperpage{199}
+ \item the Best Linear Unbiased Estimator, \hyperpage{251}
+ \item The center manifold theorem, \hyperpage{223}
+ \item The stable manifold theorem, \hyperpage{222}
+ \item theorem, \hyperpage{67}
+ \item theoretical quantiles, \hyperpage{204}
+ \item thermal conductivity, \hyperpage{278}
+ \item thermal diffusivity, \hyperpage{278}
+ \item thin QR decomposition, \hyperpage{267}
+ \item Third isomorphism theorem, \hyperpage{18}, \hyperpage{40},
+ \hyperpage{44}
+ \item Third Sylow theorem, \hyperpage{41}
+ \item Tietze extension theorem, \hyperpage{212}
+ \item time-homogeneous Markov chain, \hyperpage{318}
+ \item TNB frame, \hyperpage{143}
+ \item tolerance, \hyperpage{255}
+ \item Tonelli's theorem, \hyperpage{175}, \hyperpage{299}
+ \item topological embedding, \hyperpage{214}
+ \item topological homeomorphism, \hyperpage{306}
+ \item Topological manifold, \hyperpage{216}
+ \item topological manifold, \hyperpage{216}
+ \item topological property, \hyperpage{213}
+ \item Topological space, \hyperpage{205}
+ \item topological space, \hyperpage{205}
+ \item topological subspace, \hyperpage{208}
+ \item topologically conjugate, \hyperpage{132}
+ \item topologically equivalent, \hyperpage{131}
+ \item topologically transitive, \hyperpage{230}
+ \item topology, \hyperpage{205}
+ \item topology generated, \hyperpage{206}
+ \item Topology induced from the metric, \hyperpage{205}
+ \item torsion, \hyperpage{143}
+ \item Torus, \hyperpage{210}
+ \item torus, \hyperpage{210}
+ \item total mean of squares, \hyperpage{252}
+ \item total order relation, \hyperpage{9}
+ \item total subset, \hyperpage{301}
+ \item total sum of squares, \hyperpage{252}
+ \item totally disconnected, \hyperpage{215}
+ \item totally isotropic, \hyperpage{74}
+ \item Tower formula, \hyperpage{165}
+ \item tower of fields, \hyperpage{165}
+ \item Tower property, \hyperpage{337}
+ \item trace, \hyperpage{141}, \hyperpage{289}
+ \item Trace theorem, \hyperpage{289}
+ \item Traffic flow equation, \hyperpage{280}
+ \item trail, \hyperpage{49}
+ \item trajectories, \hyperpage{326}
+ \item transcendental, \hyperpage{164}
+ \item Transcritical bifurcation, \hyperpage{223}
+ \item transcritical bifurcation, \hyperpage{223}
+ \item transient, \hyperpage{322}, \hyperpage{324}
+ \item transition functions, \hyperpage{216}
+ \item transition matrix, \hyperpage{318}
+ \item transition probabilities, \hyperpage{318}, \hyperpage{326}
+ \item transitive, \hyperpage{169}
+ \item translation, \hyperpage{71}, \hyperpage{119}
+ \item Translations, \hyperpage{71}
+ \item transpose, \hyperpage{14}
+ \item Transposition, \hyperpage{14}
+ \item transposition, \hyperpage{8}
+ \item transversal section, \hyperpage{132}
+ \item Trapezoidal method, \hyperpage{259}
+ \item Trapezoidal rule, \hyperpage{95}
+ \item traversable, \hyperpage{50}
+ \item tree, \hyperpage{50}
+ \item triangle, \hyperpage{160}
+ \item Triangular inequality, \hyperpage{25}, \hyperpage{72}
+ \item triangular inequality, \hyperpage{53}, \hyperpage{205},
+ \hyperpage{300}
+ \item triangular system, \hyperpage{97}
+ \item triangularization, \hyperpage{218}
+ \item triple, \hyperpage{90}
+ \item trivial $\sigma $-algebra, \hyperpage{172}
+ \item Trivial topology, \hyperpage{206}
+ \item true, \hyperpage{177}
+ \item truncated, \hyperpage{266}
+ \item truncated Hilbert transform, \hyperpage{247}
+ \item truncated singular value decomposition, \hyperpage{266}
+ \item TSVD, \hyperpage{266}
+ \item two times differentiable, \hyperpage{31}
+ \item two times differentiable at $a$, \hyperpage{31}
+ \item two-sided test, \hyperpage{200}
+ \item Tychonoff's theorem, \hyperpage{213}
\indexspace
- \item UFD, \hyperpage{44}
- \item umbilic point, \hyperpage{148}
- \item UMP, \hyperpage{199}
- \item unbiased estimator, \hyperpage{192}
- \item Uncertainty principle, \hyperpage{237}
+ \item UFD, \hyperpage{45}
+ \item umbilic point, \hyperpage{149}
+ \item UMP, \hyperpage{200}
+ \item unbiased estimator, \hyperpage{193}
+ \item Uncertainty principle, \hyperpage{238}
\item Uncertainty principle in $\ensuremath {\mathbb {R}}^n$,
- \hyperpage{237}
- \item unconditionally absolutely stable, \hyperpage{260}
- \item unconditionally convergent, \hyperpage{267}
- \item uncorrelated, \hyperpage{184}
- \item uncountable, \hyperpage{24}
- \item Unicity of the splitting field, \hyperpage{166}
- \item uniform norm, \hyperpage{300}, \hyperpage{302}
- \item uniformly bounded, \hyperpage{124}, \hyperpage{303}
- \item uniformly continuous, \hyperpage{32}, \hyperpage{54}
- \item uniformly convergent, \hyperpage{116}
- \item uniformly equicontinuous, \hyperpage{124}, \hyperpage{303}
- \item uniformly most powerful, \hyperpage{199}
- \item union, \hyperpage{5}
- \item unique factorization domain, \hyperpage{44}
- \item Uniqueness of Dirichlet problem, \hyperpage{287}
- \item Uniqueness of the heat equation, \hyperpage{286}
+ \hyperpage{238}
+ \item unconditionally absolutely stable, \hyperpage{261}
+ \item unconditionally convergent, \hyperpage{268}
+ \item uncorrelated, \hyperpage{185}
+ \item uncountable, \hyperpage{25}
+ \item Unicity of the splitting field, \hyperpage{167}
+ \item uniform norm, \hyperpage{301}, \hyperpage{303}
+ \item uniformly bounded, \hyperpage{125}, \hyperpage{304}
+ \item uniformly continuous, \hyperpage{33}, \hyperpage{55}
+ \item uniformly convergent, \hyperpage{117}
+ \item uniformly equicontinuous, \hyperpage{125}, \hyperpage{304}
+ \item uniformly most powerful, \hyperpage{200}
+ \item union, \hyperpage{6}
+ \item unique factorization domain, \hyperpage{45}
+ \item Uniqueness of Dirichlet problem, \hyperpage{288}
+ \item Uniqueness of the heat equation, \hyperpage{287}
\item Uniqueness of the heat equation on the unbounded domains,
- \hyperpage{287}
- \item unit, \hyperpage{42}
- \item unit normal exterior vector field, \hyperpage{157}
- \item unit normal vector, \hyperpage{142}
- \item unit-speed parametrization, \hyperpage{140}
- \item Universal property of polynomials, \hyperpage{44}
+ \hyperpage{288}
+ \item unit, \hyperpage{43}
+ \item unit normal exterior vector field, \hyperpage{158}
+ \item unit normal vector, \hyperpage{143}
+ \item unit-speed parametrization, \hyperpage{141}
+ \item Universal property of polynomials, \hyperpage{45}
\item Universal property of polynomials in several variables,
- \hyperpage{44}, \hyperpage{161}
- \item Universal property of the field of fractions, \hyperpage{162}
- \item unknowns, \hyperpage{12}
- \item unoriented vector space, \hyperpage{141}, \hyperpage{216}
- \item unstable, \hyperpage{135}
- \item unstable degenerated node, \hyperpage{132}
- \item unstable focus, \hyperpage{132}
- \item unstable manifold, \hyperpage{221}
- \item unstable node, \hyperpage{132}
- \item unstable star, \hyperpage{132}
- \item upper bound, \hyperpage{24}, \hyperpage{125}
- \item upper integral, \hyperpage{31}, \hyperpage{57}
- \item upper sum, \hyperpage{31}, \hyperpage{57}
- \item upper triangular, \hyperpage{96}
- \item upwind condition, \hyperpage{268}
- \item Urysohn's lemma, \hyperpage{211}
- \item Urysohn's metrization theorem, \hyperpage{211}
+ \hyperpage{45}, \hyperpage{162}
+ \item Universal property of the field of fractions, \hyperpage{163}
+ \item unknowns, \hyperpage{13}
+ \item unoriented vector space, \hyperpage{142}, \hyperpage{217}
+ \item unstable, \hyperpage{136}
+ \item unstable degenerated node, \hyperpage{133}
+ \item unstable focus, \hyperpage{133}
+ \item unstable manifold, \hyperpage{222}
+ \item unstable node, \hyperpage{133}
+ \item unstable star, \hyperpage{133}
+ \item upper bound, \hyperpage{25}, \hyperpage{126}
+ \item upper integral, \hyperpage{32}, \hyperpage{58}
+ \item upper sum, \hyperpage{32}, \hyperpage{58}
+ \item upper triangular, \hyperpage{97}
+ \item upwind condition, \hyperpage{269}
+ \item Urysohn's lemma, \hyperpage{212}
+ \item Urysohn's metrization theorem, \hyperpage{212}
\indexspace
- \item Van der Pol oscillator, \hyperpage{227}
- \item vanishes nowhere, \hyperpage{302}
- \item variable, \hyperpage{10}
- \item variables, \hyperpage{12}
- \item Variacions with repetition, \hyperpage{9}
- \item Variance, \hyperpage{184}
- \item variance, \hyperpage{177}, \hyperpage{184}
- \item variance inflation factor, \hyperpage{254}
- \item Variation of constants, \hyperpage{122}
- \item variational equations, \hyperpage{128}
- \item variational formulation, \hyperpage{274}
- \item Variations without repetition, \hyperpage{9}
- \item vector field, \hyperpage{59}, \hyperpage{151}, \hyperpage{153},
- \hyperpage{155}
- \item vector space, \hyperpage{14}
+ \item Van der Pol oscillator, \hyperpage{228}
+ \item vanishes nowhere, \hyperpage{304}
+ \item variable, \hyperpage{11}
+ \item variables, \hyperpage{13}
+ \item Variacions with repetition, \hyperpage{10}
+ \item Variance, \hyperpage{185}
+ \item variance, \hyperpage{178}, \hyperpage{185}
+ \item variance inflation factor, \hyperpage{255}
+ \item Variation of constants, \hyperpage{123}
+ \item variational equations, \hyperpage{129}
+ \item variational formulation, \hyperpage{275}
+ \item Variations without repetition, \hyperpage{10}
+ \item vector field, \hyperpage{60}, \hyperpage{152}, \hyperpage{154},
+ \hyperpage{156}
+ \item vector space, \hyperpage{15}
\item vector space of polynomials with real coefficients and degree less than or equal to $n$,
- \hyperpage{92}
- \item vector subspace, \hyperpage{15}
- \item vectors, \hyperpage{14}
- \item version, \hyperpage{330}
- \item vertices, \hyperpage{159}
- \item VIF, \hyperpage{254}
- \item Viscid flow, \hyperpage{276}
- \item Volterra operator with kernel $K$, \hyperpage{306}
- \item volume, \hyperpage{174}, \hyperpage{290}
- \item volume element, \hyperpage{155}, \hyperpage{157}
- \item Volume of revolution, \hyperpage{33}
+ \hyperpage{93}
+ \item vector subspace, \hyperpage{16}
+ \item vectors, \hyperpage{15}
+ \item version, \hyperpage{331}
+ \item vertices, \hyperpage{160}
+ \item VIF, \hyperpage{255}
+ \item Viscid flow, \hyperpage{277}
+ \item Volterra operator with kernel $K$, \hyperpage{307}
+ \item volume, \hyperpage{175}, \hyperpage{291}
+ \item volume element, \hyperpage{156}, \hyperpage{158}
+ \item Volume of revolution, \hyperpage{34}
\indexspace
- \item Wald test, \hyperpage{200}
- \item Wald theorem, \hyperpage{314}
- \item walk, \hyperpage{48}
- \item Waring's method, \hyperpage{163}
- \item Wave equation, \hyperpage{139}, \hyperpage{276}
- \item wave equation, \hyperpage{139}
- \item wave function, \hyperpage{278}
- \item Weak duality theorem, \hyperpage{50}
- \item weak formulation, \hyperpage{274}
- \item Weak law, \hyperpage{189}
- \item weakly consistent estimator, \hyperpage{193}
- \item Weierstra\ss ' theorem, \hyperpage{54}, \hyperpage{113},
- \hyperpage{213}
- \item Weierstra\ss \ approximation theorem, \hyperpage{78}
- \item Weierstra\ss \ kernel, \hyperpage{233}
- \item Weierstra\ss \ M-test, \hyperpage{77}, \hyperpage{106}
- \item Weierstra\ss \ theorem, \hyperpage{27}
- \item Weingarten endomorphsim, \hyperpage{148}
- \item well-conditioned, \hyperpage{89}
- \item well-order relation, \hyperpage{8}
- \item well-ordered set, \hyperpage{8}
- \item well-posed, \hyperpage{257}
- \item well-posed in the Hadamard sense, \hyperpage{257}
- \item Wiener process, \hyperpage{329}
- \item winding number, \hyperpage{112}
- \item Wintner lemma, \hyperpage{125}
- \item Wirtinger operators, \hyperpage{110}
- \item Wirtinger's inequality, \hyperpage{86, 87}
- \item Witt's theorem, \hyperpage{73}
+ \item Wald test, \hyperpage{201}
+ \item Wald theorem, \hyperpage{315}
+ \item walk, \hyperpage{49}
+ \item Waring's method, \hyperpage{164}
+ \item Wave equation, \hyperpage{140}, \hyperpage{277}
+ \item wave equation, \hyperpage{140}
+ \item wave function, \hyperpage{279}
+ \item Weak duality theorem, \hyperpage{51}
+ \item weak formulation, \hyperpage{275}
+ \item Weak law, \hyperpage{190}
+ \item weakly consistent estimator, \hyperpage{194}
+ \item Weierstra\ss ' theorem, \hyperpage{55}, \hyperpage{114},
+ \hyperpage{214}
+ \item Weierstra\ss \ approximation theorem, \hyperpage{79}
+ \item Weierstra\ss \ kernel, \hyperpage{234}
+ \item Weierstra\ss \ M-test, \hyperpage{78}, \hyperpage{107}
+ \item Weierstra\ss \ theorem, \hyperpage{28}
+ \item Weingarten endomorphsim, \hyperpage{149}
+ \item well-conditioned, \hyperpage{90}
+ \item well-order relation, \hyperpage{9}
+ \item well-ordered set, \hyperpage{9}
+ \item well-posed, \hyperpage{258}
+ \item well-posed in the Hadamard sense, \hyperpage{258}
+ \item Wiener process, \hyperpage{330}
+ \item winding number, \hyperpage{113}
+ \item Wintner lemma, \hyperpage{126}
+ \item Wirtinger operators, \hyperpage{111}
+ \item Wirtinger's inequality, \hyperpage{87, 88}
+ \item Witt's theorem, \hyperpage{74}
\indexspace
- \item Young's convolution inequality, \hyperpage{236}
- \item Young's inequality for products, \hyperpage{301}
+ \item Young's convolution inequality, \hyperpage{237}
+ \item Young's inequality for products, \hyperpage{302}
\indexspace
- \item zero, \hyperpage{89}
- \item zero divisor, \hyperpage{43}
+ \item zero, \hyperpage{90}
+ \item zero divisor, \hyperpage{44}
\item zero of multiplicity $m\in \ensuremath {\mathbb {N}}$,
- \hyperpage{89}
- \item Zero-one loss function, \hyperpage{202}
- \item zero-stable, \hyperpage{261}
- \item Zorn's lemma, \hyperpage{125}
+ \hyperpage{90}
+ \item Zero-one loss function, \hyperpage{203}
+ \item zero-stable, \hyperpage{262}
+ \item Zorn's lemma, \hyperpage{126}
\end{theindex}
diff --git a/main_math.tex b/main_math.tex
index 087600f..8618a04 100644
--- a/main_math.tex
+++ b/main_math.tex
@@ -97,6 +97,16 @@ \chapter{Fourth year}
\subfile{Mathematics/4th/Stochastic_processes/Stochastic_processes.tex}
\cleardoublepage
+
+\chapter{Fourth year}
+\newpage
+
+\subfile{Mathematics/5th/Advanced_probability/Advanced_probability.tex}
+\cleardoublepage
+
+\subfile{Mathematics/5th/Advanced_topics_in_functional_analysis_and_PDEs/Advanced_topics_in_functional_analysis_and_PDEs.tex}
+\cleardoublepage
+
\printindex
\end{document}