main_math.idx

\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 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}
\indexentry{Ruffini's rule|hyperpage}{12}
\indexentry{irreducible|hyperpage}{12}
\indexentry{D'Alembert theorem|hyperpage}{12}
\indexentry{linear equation|hyperpage}{13}
\indexentry{variables|hyperpage}{13}
\indexentry{unknowns|hyperpage}{13}
\indexentry{constant term|hyperpage}{13}
\indexentry{system of linear equations|hyperpage}{13}
\indexentry{solution of a system of equations|hyperpage}{13}
\indexentry{equivalent|hyperpage}{13}
\indexentry{Matrix|hyperpage}{13}
\indexentry{matrix|hyperpage}{13}
\indexentry{sum|hyperpage}{13}
\indexentry{product|hyperpage}{13}
\indexentry{Properties of addition and scalar multiplication of matrices|hyperpage}{13}
\indexentry{product|hyperpage}{13}
\indexentry{Properties of matrix product|hyperpage}{13}
\indexentry{invertible|hyperpage}{14}
\indexentry{idempotent|hyperpage}{14}
\indexentry{nilpotent|hyperpage}{14}
\indexentry{index|hyperpage}{14}
\indexentry{$i$-th pivot|hyperpage}{14}
\indexentry{Row echelon form|hyperpage}{14}
\indexentry{row echelon form|hyperpage}{14}
\indexentry{Reduced row echelon form|hyperpage}{14}
\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}
\indexentry{Rouché-Frobenius theorem|hyperpage}{14}
\indexentry{determined and consistent|hyperpage}{14}
\indexentry{indeterminate|hyperpage}{14}
\indexentry{free variables|hyperpage}{14}
\indexentry{inconsistent|hyperpage}{14}
\indexentry{Determinant|hyperpage}{14}
\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}
\indexentry{generating set|hyperpage}{16}
\indexentry{linearly independent|hyperpage}{16}
\indexentry{linearly dependent|hyperpage}{16}
\indexentry{basis|hyperpage}{16}
\indexentry{Steinitz exchange lemma|hyperpage}{16}
\indexentry{dimension|hyperpage}{16}
\indexentry{coordinates|hyperpage}{16}
\indexentry{sum|hyperpage}{16}
\indexentry{Gra\ss mann formula|hyperpage}{16}
\indexentry{Direct sum|hyperpage}{16}
\indexentry{direct|hyperpage}{16}
\indexentry{row rank|hyperpage}{16}
\indexentry{column rank|hyperpage}{16}
\indexentry{rank|hyperpage}{16}
\indexentry{minor|hyperpage}{16}
\indexentry{complementary subspace|hyperpage}{17}
\indexentry{equivalent|hyperpage}{17}
\indexentry{equivalence class|hyperpage}{17}
\indexentry{quotient space|hyperpage}{17}
\indexentry{linear map|hyperpage}{17}
\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}
\indexentry{similar|hyperpage}{20}
\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}
\indexentry{bilinear|hyperpage}{22}
\indexentry{bilinear form|hyperpage}{22}
\indexentry{symmetric|hyperpage}{22}
\indexentry{matrix of the bilinear form|hyperpage}{22}
\indexentry{orthogonal|hyperpage}{22}
\indexentry{isotropic|hyperpage}{22}
\indexentry{orthogonal|hyperpage}{22}
\indexentry{orthonormal|hyperpage}{22}
\indexentry{orthogonal complement|hyperpage}{22}
\indexentry{radical|hyperpage}{22}
\indexentry{nonsingular|hyperpage}{22}
\indexentry{orthogonal|hyperpage}{23}
\indexentry{orthogonal projection|hyperpage}{23}
\indexentry{Gram-Schmidt process|hyperpage}{23}
\indexentry{orthogonal geometry|hyperpage}{23}
\indexentry{isometry|hyperpage}{23}
\indexentry{isometric|hyperpage}{23}
\indexentry{equivalent|hyperpage}{23}
\indexentry{Sylvester's law of inertia|hyperpage}{23}
\indexentry{rank|hyperpage}{23}
\indexentry{signature|hyperpage}{23}
\indexentry{positive-definite|hyperpage}{23}
\indexentry{negative-definite|hyperpage}{23}
\indexentry{positive-semidefinite|hyperpage}{23}
\indexentry{negative-semidefinite|hyperpage}{23}
\indexentry{inner product|hyperpage}{24}
\indexentry{Euclidean vector space|hyperpage}{24}
\indexentry{Cauchy-Schwarz inequality|hyperpage}{24}
\indexentry{norm|hyperpage}{24}
\indexentry{norm associated with the inner product|hyperpage}{24}
\indexentry{angle|hyperpage}{24}
\indexentry{adjoint|hyperpage}{24}
\indexentry{auto-adjoint|hyperpage}{24}
\indexentry{orthogonal|hyperpage}{24}
\indexentry{Spectral theorem|hyperpage}{24}
\indexentry{complex conjugate|hyperpage}{24}
\indexentry{Descartes' rule of signs|hyperpage}{24}
\indexentry{ordered field|hyperpage}{25}
\indexentry{bounded from above|hyperpage}{25}
\indexentry{upper bound|hyperpage}{25}
\indexentry{bounded from below|hyperpage}{25}
\indexentry{lower bound|hyperpage}{25}
\indexentry{supremum|hyperpage}{25}
\indexentry{infimum|hyperpage}{25}
\indexentry{Supremum axiom|hyperpage}{25}
\indexentry{Archimedean property|hyperpage}{25}
\indexentry{Open interval|hyperpage}{25}
\indexentry{Right-open interval|hyperpage}{25}
\indexentry{Left-open interval|hyperpage}{25}
\indexentry{Closed interval|hyperpage}{25}
\indexentry{absolute value|hyperpage}{25}
\indexentry{Triangular inequality|hyperpage}{25}
\indexentry{neighbourhood|hyperpage}{25}
\indexentry{infinite|hyperpage}{25}
\indexentry{finite|hyperpage}{25}
\indexentry{countable|hyperpage}{25}
\indexentry{uncountable|hyperpage}{25}
\indexentry{sequence of real numbers|hyperpage}{26}
\indexentry{bounded from above|hyperpage}{26}
\indexentry{bounded from below|hyperpage}{26}
\indexentry{bounded|hyperpage}{26}
\indexentry{Limit|hyperpage}{26}
\indexentry{convergent|hyperpage}{26}
\indexentry{divergent|hyperpage}{26}
\indexentry{monotonically increasing|hyperpage}{26}
\indexentry{monotonically decreasing|hyperpage}{26}
\indexentry{monotonic|hyperpage}{26}
\indexentry{Squeeze theorem|hyperpage}{26}
\indexentry{Root test|hyperpage}{26}
\indexentry{Ratio test|hyperpage}{26}
\indexentry{Subsequence|hyperpage}{26}
\indexentry{subsequence|hyperpage}{26}
\indexentry{accumulation point|hyperpage}{26}
\indexentry{strictly increasing|hyperpage}{26}
\indexentry{strictly decreasing|hyperpage}{26}
\indexentry{Bolzano-Weierstra\ss \ theorem|hyperpage}{27}
\indexentry{limit superior|hyperpage}{27}
\indexentry{limit inferior|hyperpage}{27}
\indexentry{Cauchy sequence|hyperpage}{27}
\indexentry{Cauchy sequence|hyperpage}{27}
\indexentry{Stolz-Cesàro theorem|hyperpage}{27}
\indexentry{limit of the function $f$ at the point $x_0$|hyperpage}{27}
\indexentry{bounded|hyperpage}{27}
\indexentry{right-sided limit of $f$ at $x_0$|hyperpage}{27}
\indexentry{left-sided limit of $f$ at $x_0$|hyperpage}{27}
\indexentry{limit of $f$ at infinity|hyperpage}{28}
\indexentry{continuous at $x_0$|hyperpage}{28}
\indexentry{continuous|hyperpage}{28}
\indexentry{Weierstra\ss \ theorem|hyperpage}{28}
\indexentry{Bolzano's theorem|hyperpage}{28}
\indexentry{Intermediate value theorem|hyperpage}{28}
\indexentry{increasing|hyperpage}{28}
\indexentry{decreasing|hyperpage}{28}
\indexentry{monotonic|hyperpage}{28}
\indexentry{Removable discontinuity|hyperpage}{28}
\indexentry{Jump discontinuity|hyperpage}{28}
\indexentry{Discontinuity of the first kind|hyperpage}{28}
\indexentry{Discontinuity of the second kind|hyperpage}{28}
\indexentry{strictly increasing|hyperpage}{28}
\indexentry{strictly decreasing|hyperpage}{28}
\indexentry{exponential function with base $a$|hyperpage}{29}
\indexentry{logarithm with base $a$|hyperpage}{29}
\indexentry{differentiable at $x_0\in (a,b)$|hyperpage}{29}
\indexentry{derivative of $f$ at $x_0$|hyperpage}{29}
\indexentry{differentiable|hyperpage}{29}
\indexentry{tangent line to the graph at the point $(x_0,f(x_0))$|hyperpage}{29}
\indexentry{Chain rule|hyperpage}{29}
\indexentry{Inverse function rule|hyperpage}{30}
\indexentry{local maximum|hyperpage}{30}
\indexentry{local minimum|hyperpage}{30}
\indexentry{local extremum|hyperpage}{30}
\indexentry{Rolle's theorem|hyperpage}{30}
\indexentry{Mean value theorem|hyperpage}{30}
\indexentry{Cauchy's mean value theorem|hyperpage}{30}
\indexentry{L'H\^opital's rule|hyperpage}{30}
\indexentry{Darboux's theorem|hyperpage}{30}
\indexentry{convex|hyperpage}{30}
\indexentry{concave|hyperpage}{30}
\indexentry{strictly convex|hyperpage}{30}
\indexentry{strictly concave|hyperpage}{30}
\indexentry{two times differentiable at $a$|hyperpage}{31}
\indexentry{two times differentiable|hyperpage}{31}
\indexentry{second derivative of $f$ at $a$|hyperpage}{31}
\indexentry{inflection point|hyperpage}{31}
\indexentry{contact of order $\geq n$ at $a$|hyperpage}{31}
\indexentry{$n$-th derivative of $f$ at the point $a\in \ensuremath  {\mathbb  {R}}$|hyperpage}{31}
\indexentry{class $\mathcal  {C}^n$ at a point $a\in \ensuremath  {\mathbb  {R}}$|hyperpage}{31}
\indexentry{class $\mathcal  {C}^\infty $ at $a$|hyperpage}{31}
\indexentry{class $\mathcal  {C}^p$|hyperpage}{31}
\indexentry{Taylor polynomial of order $n$ of $f$ centered at $a$|hyperpage}{31}
\indexentry{analytic at $a$|hyperpage}{32}
\indexentry{partition|hyperpage}{32}
\indexentry{lower sum|hyperpage}{32}
\indexentry{upper sum|hyperpage}{32}
\indexentry{finer than|hyperpage}{32}
\indexentry{lower integral|hyperpage}{32}
\indexentry{upper integral|hyperpage}{32}
\indexentry{integrable|hyperpage}{32}
\indexentry{uniformly continuous|hyperpage}{33}
\indexentry{Fundamental theorem of calculus|hyperpage}{33}
\indexentry{primitive function|hyperpage}{33}
\indexentry{Integration by parts|hyperpage}{33}
\indexentry{Integration by substitution|hyperpage}{33}
\indexentry{Riemann sum|hyperpage}{34}
\indexentry{length of the polygonal|hyperpage}{34}
\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}
\indexentry{group|hyperpage}{37}
\indexentry{commutative|hyperpage}{37}
\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}
\indexentry{closed trail|hyperpage}{49}
\indexentry{cycle|hyperpage}{49}
\indexentry{connected components|hyperpage}{50}
\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}
\indexentry{linear programming to maximize|hyperpage}{51}
\indexentry{objective function|hyperpage}{51}
\indexentry{restrictions|hyperpage}{51}
\indexentry{canonical form of a linear programming to maximize|hyperpage}{51}
\indexentry{objective function|hyperpage}{51}
\indexentry{restrictions|hyperpage}{51}
\indexentry{canonical form of a linear programming to minimize|hyperpage}{51}
\indexentry{feasible region|hyperpage}{51}
\indexentry{feasible solution|hyperpage}{51}
\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}
\indexentry{complete|hyperpage}{54}
\indexentry{compact|hyperpage}{54}
\indexentry{Graph of a function|hyperpage}{55}
\indexentry{graph|hyperpage}{55}
\indexentry{level set|hyperpage}{55}
\indexentry{continuous|hyperpage}{55}
\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}
\indexentry{differential|hyperpage}{55}
\indexentry{directional derivative|hyperpage}{55}
\indexentry{partial derivative|hyperpage}{55}
\indexentry{Jacobian matrix|hyperpage}{55}
\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}
\indexentry{local extremum|hyperpage}{57}
\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{length|hyperpage}{58}
\indexentry{surface|hyperpage}{58}
\indexentry{partition|hyperpage}{58}
\indexentry{regular|hyperpage}{58}
\indexentry{finer than|hyperpage}{58}
\indexentry{lower sum|hyperpage}{58}
\indexentry{upper sum|hyperpage}{58}
\indexentry{lower integral|hyperpage}{58}
\indexentry{upper integral|hyperpage}{58}
\indexentry{Riemann-integrable|hyperpage}{58}
\indexentry{Riemann sum|hyperpage}{58}
\indexentry{Fubini's theorem|hyperpage}{59}
\indexentry{elementary region|hyperpage}{59}
\indexentry{$x$-simple|hyperpage}{59}
\indexentry{$xy$-simple|hyperpage}{59}
\indexentry{Fubini's theorem for elementary regions|hyperpage}{59}
\indexentry{$n$-dimensional volume|hyperpage}{59}
\indexentry{Cavalieri's principle|hyperpage}{59}
\indexentry{Center of mass|hyperpage}{59}
\indexentry{center of mass|hyperpage}{59}
\indexentry{Moment of inertia|hyperpage}{59}
\indexentry{moment of inertia|hyperpage}{59}
\indexentry{integrable function|hyperpage}{59}
\indexentry{Riemann-integrable function|hyperpage}{59}
\indexentry{$y$-simple|hyperpage}{59}
\indexentry{$yz$-simple|hyperpage}{59}
\indexentry{$xz$-simple|hyperpage}{59}
\indexentry{Change of variable theorem|hyperpage}{60}
\indexentry{Integral in polar coordinates|hyperpage}{60}
\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}
\indexentry{rectifiable|hyperpage}{60}
\indexentry{reparametrization|hyperpage}{60}
\indexentry{arc length parameter|hyperpage}{60}
\indexentry{vector field|hyperpage}{60}
\indexentry{curvature|hyperpage}{61}
\indexentry{line integral|hyperpage}{61}
\indexentry{line integral|hyperpage}{61}
\indexentry{circulation|hyperpage}{61}
\indexentry{Jordan arc|hyperpage}{61}
\indexentry{Jordan closed curve|hyperpage}{61}
\indexentry{conservative|hyperpage}{61}
\indexentry{gradient vector field|hyperpage}{61}
\indexentry{potential|hyperpage}{61}
\indexentry{divergence|hyperpage}{61}
\indexentry{curl|hyperpage}{61}
\indexentry{Laplacian|hyperpage}{61}
\indexentry{parametrized surface|hyperpage}{61}
\indexentry{surface integral|hyperpage}{61}
\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{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{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{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{Runge's phenomenon|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{divergent|hyperpage}{105}
\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{converges uniformly|hyperpage}{106}
\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}
\indexentry{differential system|hyperpage}{122}
\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}
\indexentry{positively stable|hyperpage}{131}
\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}
\indexentry{invariant algebraic curve|hyperpage}{135}
\indexentry{cofactor|hyperpage}{136}
\indexentry{Poincaré map|hyperpage}{136}
\indexentry{Poincaré map|hyperpage}{136}
\indexentry{limit cycle|hyperpage}{136}
\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{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}
\indexentry{differentiable|hyperpage}{147}
\indexentry{differentiable|hyperpage}{147}
\indexentry{tangent vector|hyperpage}{147}
\indexentry{tangent space|hyperpage}{147}
\indexentry{tangent plane|hyperpage}{147}
\indexentry{tangent function|hyperpage}{148}
\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}
\indexentry{second fundamental form|hyperpage}{150}
\indexentry{normal curvature|hyperpage}{150}
\indexentry{Meusnier's theorem|hyperpage}{150}
\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}
\indexentry{vector field|hyperpage}{152}
\indexentry{differentiable|hyperpage}{152}
\indexentry{parallel|hyperpage}{152}
\indexentry{parallel transport|hyperpage}{152}
\indexentry{geodesic|hyperpage}{153}
\indexentry{algebraic value|hyperpage}{153}
\indexentry{geodesic curvature|hyperpage}{153}
\indexentry{Liouville's formula|hyperpage}{153}
\indexentry{vector field|hyperpage}{154}
\indexentry{differentiable|hyperpage}{154}
\indexentry{differentiable|hyperpage}{154}
\indexentry{integral curve|hyperpage}{154}
\indexentry{first integral|hyperpage}{154}
\indexentry{vector field|hyperpage}{154}
\indexentry{differentiable|hyperpage}{154}
\indexentry{tangent|hyperpage}{154}
\indexentry{multilinear map|hyperpage}{155}
\indexentry{$k$-linear map|hyperpage}{155}
\indexentry{degree|hyperpage}{155}
\indexentry{alternating|hyperpage}{155}
\indexentry{multilinear forms|hyperpage}{155}
\indexentry{exterior product|hyperpage}{155}
\indexentry{differential $k$-form|hyperpage}{155}
\indexentry{differential|hyperpage}{155}
\indexentry{pull-back|hyperpage}{156}
\indexentry{pull-back|hyperpage}{156}
\indexentry{interior product|hyperpage}{156}
\indexentry{volume element|hyperpage}{156}
\indexentry{exterior differential|hyperpage}{156}
\indexentry{closed|hyperpage}{156}
\indexentry{exact|hyperpage}{156}
\indexentry{tangent vector|hyperpage}{156}
\indexentry{tangent space|hyperpage}{156}
\indexentry{vector field|hyperpage}{156}
\indexentry{differentiable|hyperpage}{156}
\indexentry{differentiable|hyperpage}{156}
\indexentry{tangent|hyperpage}{156}
\indexentry{differential $\ell $-form|hyperpage}{156}
\indexentry{exterior differential|hyperpage}{157}
\indexentry{differentiable|hyperpage}{157}
\indexentry{differential|hyperpage}{157}
\indexentry{submanifold with boundary|hyperpage}{157}
\indexentry{interior point|hyperpage}{157}
\indexentry{boundary|hyperpage}{157}
\indexentry{tangent space|hyperpage}{157}
\indexentry{set of interior vectors|hyperpage}{157}
\indexentry{exterior vectors|hyperpage}{157}
\indexentry{orientable|hyperpage}{158}
\indexentry{compatible|hyperpage}{158}
\indexentry{volume element|hyperpage}{158}
\indexentry{unit normal exterior vector field|hyperpage}{158}
\indexentry{positive|hyperpage}{158}
\indexentry{orientation induced by $M$|hyperpage}{158}
\indexentry{integral|hyperpage}{158}
\indexentry{integral|hyperpage}{158}
\indexentry{integral|hyperpage}{158}
\indexentry{partition of unity|hyperpage}{158}
\indexentry{integral|hyperpage}{159}
\indexentry{Change of variables|hyperpage}{159}
\indexentry{Stokes theorem|hyperpage}{159}
\indexentry{Green's formula|hyperpage}{159}
\indexentry{line intergal|hyperpage}{159}
\indexentry{circulation|hyperpage}{159}
\indexentry{surface intergal|hyperpage}{159}
\indexentry{flux|hyperpage}{159}
\indexentry{Curl theorem|hyperpage}{159}
\indexentry{Divergence theorem on $\ensuremath  {\mathbb  {R}}^3$|hyperpage}{160}
\indexentry{Divergence theorem|hyperpage}{160}
\indexentry{simple region|hyperpage}{160}
\indexentry{edges|hyperpage}{160}
\indexentry{vertices|hyperpage}{160}
\indexentry{exterior angle|hyperpage}{160}
\indexentry{Local Gau\ss -Bonnet theorem|hyperpage}{160}
\indexentry{triangle|hyperpage}{160}
\indexentry{regular region|hyperpage}{160}
\indexentry{Global Gau\ss -Bonnet theorem|hyperpage}{160}
\indexentry{singular point|hyperpage}{160}
\indexentry{isolated singular point|hyperpage}{160}
\indexentry{isolated singularity|hyperpage}{160}
\indexentry{index|hyperpage}{160}
\indexentry{Poincaré-Hopf theorem|hyperpage}{161}
\indexentry{quadratic polynomial|hyperpage}{162}
\indexentry{cubic polynomial|hyperpage}{162}
\indexentry{quartic polynomial|hyperpage}{162}
\indexentry{depressed equation|hyperpage}{162}
\indexentry{field morphism|hyperpage}{162}
\indexentry{characteristic|hyperpage}{162}
\indexentry{polynomial ring|hyperpage}{162}
\indexentry{Universal property of polynomials in several variables|hyperpage}{162}
\indexentry{evaluation|hyperpage}{162}
\indexentry{Universal property of the field of fractions|hyperpage}{163}
\indexentry{field of fractions|hyperpage}{163}
\indexentry{field of rational functions|hyperpage}{163}
\indexentry{subring generated|hyperpage}{163}
\indexentry{subfield generated|hyperpage}{163}
\indexentry{Symmetric polynomials|hyperpage}{163}
\indexentry{symmetric polynomial|hyperpage}{163}
\indexentry{elementary symmetric polynomials|hyperpage}{163}
\indexentry{lexicographic order|hyperpage}{163}
\indexentry{lexicographic degree|hyperpage}{163}
\indexentry{Waring's method|hyperpage}{164}
\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{irreducible polynomial|hyperpage}{164}
\indexentry{transcendental|hyperpage}{164}
\indexentry{simple|hyperpage}{164}
\indexentry{primitive element|hyperpage}{164}
\indexentry{Steinitz's theorem|hyperpage}{164}
\indexentry{Tower formula|hyperpage}{165}
\indexentry{tower of fields|hyperpage}{165}
\indexentry{finitely generated|hyperpage}{165}
\indexentry{compositum|hyperpage}{165}
\indexentry{algebraic|hyperpage}{165}
\indexentry{purely transcendental|hyperpage}{165}
\indexentry{morphism of field extensions|hyperpage}{165}
\indexentry{$K$-field morphism|hyperpage}{165}
\indexentry{Galois group|hyperpage}{166}
\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 $-additivity|hyperpage}{173}
\indexentry{event|hyperpage}{173}
\indexentry{probability space|hyperpage}{173}
\indexentry{Finite subadditivity|hyperpage}{173}
\indexentry{Continuity from below|hyperpage}{173}
\indexentry{Continuity from above|hyperpage}{173}
\indexentry{Countable subadditivity|hyperpage}{173}
\indexentry{conditional probability|hyperpage}{174}
\indexentry{Compound probability formula|hyperpage}{174}
\indexentry{Generalized compound probability formula|hyperpage}{174}
\indexentry{partition|hyperpage}{174}
\indexentry{Law of total probability|hyperpage}{174}
\indexentry{Bayes' formula|hyperpage}{174}
\indexentry{independent events|hyperpage}{174}
\indexentry{independent events|hyperpage}{174}
\indexentry{independent events|hyperpage}{174}
\indexentry{null set|hyperpage}{174}
\indexentry{set of zero-content|hyperpage}{174}
\indexentry{measure|hyperpage}{174}
\indexentry{measure space|hyperpage}{175}
\indexentry{$\sigma $-algebra of all Lebesgue measurable sets in $\ensuremath  {\mathbb  {R}}^n$|hyperpage}{175}
\indexentry{Lebesgue measure|hyperpage}{175}
\indexentry{volume|hyperpage}{175}
\indexentry{measurable|hyperpage}{175}
\indexentry{Lebesgue integral|hyperpage}{175}
\indexentry{Lebesgue integrable|hyperpage}{175}
\indexentry{Tonelli's theorem|hyperpage}{175}
\indexentry{Fubini's theorem|hyperpage}{175}
\indexentry{real random variable|hyperpage}{175}
\indexentry{random variable|hyperpage}{175}
\indexentry{distribution|hyperpage}{176}
\indexentry{equal in distribution|hyperpage}{176}
\indexentry{equal almost surely|hyperpage}{176}
\indexentry{Cumulative distribution function|hyperpage}{176}
\indexentry{cumulative distribution function|hyperpage}{176}
\indexentry{cdf|hyperpage}{176}
\indexentry{càdlàg|hyperpage}{176}
\indexentry{discrete|hyperpage}{176}
\indexentry{support|hyperpage}{176}
\indexentry{Probability mass function|hyperpage}{176}
\indexentry{probability mass function|hyperpage}{176}
\indexentry{pmf|hyperpage}{176}
\indexentry{distribution functions|hyperpage}{176}
\indexentry{Degenerated distribution|hyperpage}{177}
\indexentry{degenerated distribution|hyperpage}{177}
\indexentry{Bernoulli distribution|hyperpage}{177}
\indexentry{Bernoulli distribution|hyperpage}{177}
\indexentry{Discrete uniform distribution|hyperpage}{177}
\indexentry{discrete uniform distribution|hyperpage}{177}
\indexentry{equiprobable space|hyperpage}{177}
\indexentry{Binomial distribution|hyperpage}{177}
\indexentry{binomial distribution|hyperpage}{177}
\indexentry{Poisson distribution|hyperpage}{177}
\indexentry{Poisson distribution|hyperpage}{177}
\indexentry{Geometric distribution|hyperpage}{177}
\indexentry{geometric distribution|hyperpage}{177}
\indexentry{Discrete memorylessness property|hyperpage}{177}
\indexentry{memoryless|hyperpage}{177}
\indexentry{Hypergeometric distribution|hyperpage}{177}
\indexentry{hypergeometric distribution|hyperpage}{177}
\indexentry{success|hyperpage}{177}
\indexentry{true|hyperpage}{177}
\indexentry{failure|hyperpage}{177}
\indexentry{false|hyperpage}{177}
\indexentry{Negative binomial distribution|hyperpage}{178}
\indexentry{negative binomial distribution|hyperpage}{178}
\indexentry{absolutely continuous|hyperpage}{178}
\indexentry{probability density function|hyperpage}{178}
\indexentry{pdf|hyperpage}{178}
\indexentry{density function|hyperpage}{178}
\indexentry{Continuous uniform distribution|hyperpage}{178}
\indexentry{continuous uniform distribution|hyperpage}{178}
\indexentry{Exponential distribution|hyperpage}{178}
\indexentry{exponential distribution|hyperpage}{178}
\indexentry{Continuous memorylessness property|hyperpage}{178}
\indexentry{memoryless|hyperpage}{178}
\indexentry{Standard normal distribution|hyperpage}{178}
\indexentry{standard normal distribution|hyperpage}{178}
\indexentry{Normal distribution|hyperpage}{178}
\indexentry{normal distribution|hyperpage}{178}
\indexentry{mean|hyperpage}{178}
\indexentry{expectation|hyperpage}{178}
\indexentry{variance|hyperpage}{178}
\indexentry{standard deviation|hyperpage}{178}
\indexentry{standardized form|hyperpage}{179}
\indexentry{Gamma distribution|hyperpage}{179}
\indexentry{gamma distribution|hyperpage}{179}
\indexentry{shape|hyperpage}{179}
\indexentry{rate|hyperpage}{179}
\indexentry{scale|hyperpage}{179}
\indexentry{beta function|hyperpage}{179}
\indexentry{Beta distribution|hyperpage}{179}
\indexentry{beta distribution|hyperpage}{179}
\indexentry{Cauchy distribution|hyperpage}{179}
\indexentry{Cauchy distribution|hyperpage}{179}
\indexentry{mixed random variable|hyperpage}{179}
\indexentry{random vector|hyperpage}{179}
\indexentry{distribution|hyperpage}{180}
\indexentry{discrete|hyperpage}{180}
\indexentry{support|hyperpage}{180}
\indexentry{Joint probability mass function|hyperpage}{180}
\indexentry{joint probability mass function|hyperpage}{180}
\indexentry{joint pmf|hyperpage}{180}
\indexentry{Marginal probability mass functions|hyperpage}{180}
\indexentry{marginal probability mass functions|hyperpage}{180}
\indexentry{marginal pmf|hyperpage}{180}
\indexentry{Multinomial distrbution|hyperpage}{180}
\indexentry{multinomial distribution|hyperpage}{180}
\indexentry{absolutely continuous|hyperpage}{180}
\indexentry{joint probability density function|hyperpage}{180}
\indexentry{joint pdf|hyperpage}{180}
\indexentry{Marginal probability density functions|hyperpage}{180}
\indexentry{marginal probability density functions|hyperpage}{180}
\indexentry{marginal pdf|hyperpage}{180}
\indexentry{Multivariate standard normal distribution|hyperpage}{180}
\indexentry{multivariate normal distribution|hyperpage}{180}
\indexentry{Multivariate uniform distribution|hyperpage}{180}
\indexentry{multivariate uniform distribution|hyperpage}{180}
\indexentry{multivariate cumulative distribution function|hyperpage}{181}
\indexentry{multivariate cdf|hyperpage}{181}
\indexentry{Borel measurable|hyperpage}{181}
\indexentry{Multivariate normal distribution|hyperpage}{181}
\indexentry{mean vector|hyperpage}{181}
\indexentry{covariance matrix|hyperpage}{181}
\indexentry{independent|hyperpage}{181}
\indexentry{independent and identically distributed|hyperpage}{181}
\indexentry{i.i.d.|hyperpage}{181}
\indexentry{increment|hyperpage}{181}
\indexentry{increasing|hyperpage}{181}
\indexentry{conditional probability mass function|hyperpage}{182}
\indexentry{conditional probability density function|hyperpage}{182}
\indexentry{simple random variable|hyperpage}{182}
\indexentry{finite expectation|hyperpage}{182}
\indexentry{integrable|hyperpage}{182}
\indexentry{expectation|hyperpage}{182}
\indexentry{not integrable|hyperpage}{182}
\indexentry{Expectation|hyperpage}{183}
\indexentry{finite expectation|hyperpage}{183}
\indexentry{integrable|hyperpage}{183}
\indexentry{expectation|hyperpage}{183}
\indexentry{Comparison test|hyperpage}{183}
\indexentry{dyadic partition of order $n$|hyperpage}{183}
\indexentry{Monotone convergence theorem|hyperpage}{184}
\indexentry{Dominated convergence theorem|hyperpage}{184}
\indexentry{Fatou's lemma|hyperpage}{184}
\indexentry{finite expectation|hyperpage}{184}
\indexentry{expectation|hyperpage}{184}
\indexentry{Moment|hyperpage}{185}
\indexentry{finite moment of order $k$|hyperpage}{185}
\indexentry{finite $k$-th moment|hyperpage}{185}
\indexentry{Cauchy-Schwarz inequality|hyperpage}{185}
\indexentry{Variance|hyperpage}{185}
\indexentry{variance|hyperpage}{185}
\indexentry{Standard deviation|hyperpage}{185}
\indexentry{standard deviation|hyperpage}{185}
\indexentry{standard error|hyperpage}{185}
\indexentry{Covariance|hyperpage}{185}
\indexentry{covariance|hyperpage}{185}
\indexentry{uncorrelated|hyperpage}{185}
\indexentry{Pearson correlation coefficient|hyperpage}{185}
\indexentry{Pearson correlation coefficient|hyperpage}{185}
\indexentry{correlation coefficient|hyperpage}{185}
\indexentry{Markov's inequality|hyperpage}{185}
\indexentry{Chebyshev's inequality|hyperpage}{186}
\indexentry{Moment-generating function|hyperpage}{186}
\indexentry{moment-generating function|hyperpage}{186}
\indexentry{conditional expectation|hyperpage}{186}
\indexentry{Law of total expectation|hyperpage}{186}
\indexentry{conditional expectation|hyperpage}{186}
\indexentry{Law of total expectation|hyperpage}{187}
\indexentry{converges in probability|hyperpage}{187}
\indexentry{metrizable|hyperpage}{187}
\indexentry{Cauchy condition in probability|hyperpage}{187}
\indexentry{Cauchy in probability|hyperpage}{187}
\indexentry{converges almost surely|hyperpage}{188}
\indexentry{limit superior|hyperpage}{188}
\indexentry{limit inferior|hyperpage}{188}
\indexentry{limit|hyperpage}{188}
\indexentry{First Borel-Cantelli lemma|hyperpage}{188}
\indexentry{Second Borel-Cantelli lemma|hyperpage}{189}
\indexentry{converges in the $p$-th mean|hyperpage}{189}
\indexentry{Dominated convergence theorem|hyperpage}{189}
\indexentry{Cauchy condition in $p$-th mean|hyperpage}{189}
\indexentry{Cauchy in $p$-th mean|hyperpage}{189}
\indexentry{converges in distribution|hyperpage}{190}
\indexentry{Skorokhod's representation theorem|hyperpage}{190}
\indexentry{Slutsky's theorem|hyperpage}{190}
\indexentry{Weak law of large numbers|hyperpage}{190}
\indexentry{Weak law of large numbers|hyperpage}{190}
\indexentry{Kolmogorov's strong law of large numbers|hyperpage}{191}
\indexentry{Strong law of large numbers|hyperpage}{191}
\indexentry{simply normal|hyperpage}{191}
\indexentry{normal|hyperpage}{191}
\indexentry{Borel's theorem|hyperpage}{191}
\indexentry{complex random variable|hyperpage}{191}
\indexentry{Characteristic function|hyperpage}{191}
\indexentry{characteristic function|hyperpage}{191}
\indexentry{Lévy-Lindeberg central limit theorem|hyperpage}{192}
\indexentry{Lyapunov central limit theorem|hyperpage}{192}
\indexentry{sample mean|hyperpage}{192}
\indexentry{De Moivre-Laplace theorem|hyperpage}{192}
\indexentry{Continuity correction|hyperpage}{192}
\indexentry{continuity correction|hyperpage}{192}
\indexentry{statistical model|hyperpage}{193}
\indexentry{sample space|hyperpage}{193}
\indexentry{parameter space|hyperpage}{193}
\indexentry{random sample|hyperpage}{193}
\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}
\indexentry{estimator|hyperpage}{193}
\indexentry{Bias|hyperpage}{193}
\indexentry{bias|hyperpage}{193}
\indexentry{unbiased estimator|hyperpage}{193}
\indexentry{biased estimator|hyperpage}{193}
\indexentry{mean squared error|hyperpage}{194}
\indexentry{MSE|hyperpage}{194}
\indexentry{more efficient than|hyperpage}{194}
\indexentry{minimum-variance unbiased estimator|hyperpage}{194}
\indexentry{MVUE|hyperpage}{194}
\indexentry{sufficient|hyperpage}{194}
\indexentry{Fisher-Neyman factorization theorem|hyperpage}{194}
\indexentry{weakly consistent estimator|hyperpage}{194}
\indexentry{strongly consistent estimator|hyperpage}{194}
\indexentry{consistent estimator in $L^2$|hyperpage}{194}
\indexentry{asymptotically unbiased estimator|hyperpage}{194}
\indexentry{an asymptotically normal estimator|hyperpage}{194}
\indexentry{Method of moments|hyperpage}{194}
\indexentry{Likelihood|hyperpage}{195}
\indexentry{likelihood function|hyperpage}{195}
\indexentry{likelihood function|hyperpage}{195}
\indexentry{Maximum likelihood method|hyperpage}{195}
\indexentry{maximum likelihood estimator|hyperpage}{195}
\indexentry{MLE|hyperpage}{195}
\indexentry{log-likelihood function|hyperpage}{195}
\indexentry{score function|hyperpage}{195}
\indexentry{Invariance of the MLE|hyperpage}{195}
\indexentry{regular|hyperpage}{195}
\indexentry{observed information|hyperpage}{195}
\indexentry{Fisher information|hyperpage}{195}
\indexentry{regular|hyperpage}{196}
\indexentry{Cramér-Rao bound|hyperpage}{196}
\indexentry{efficient estimator|hyperpage}{196}
\indexentry{asymptotic efficient estimator|hyperpage}{196}
\indexentry{Delta method|hyperpage}{196}
\indexentry{order statistic|hyperpage}{196}
\indexentry{order statistics|hyperpage}{196}
\indexentry{Quantile|hyperpage}{196}
\indexentry{multivariate normal distribution|hyperpage}{196}
\indexentry{mean vector|hyperpage}{196}
\indexentry{covariance matrix|hyperpage}{196}
\indexentry{multivariate standard deviation|hyperpage}{196}
\indexentry{chi-squared distribution with $n$ degrees of freedom|hyperpage}{197}
\indexentry{Student's $t$-distribution with $n$ degrees of freedom|hyperpage}{197}
\indexentry{Fisher's theorem|hyperpage}{197}
\indexentry{confidence region|hyperpage}{198}
\indexentry{confidence level|hyperpage}{198}
\indexentry{confidence intervals|hyperpage}{198}
\indexentry{significance level|hyperpage}{198}
\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|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{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{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{relatively compact|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{bidual space|hyperpage}{307}
\indexentry{reflexive|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{extension|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}{310}
\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{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{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{shift map|hyperpage}{335}
\indexentry{expansion map|hyperpage}{335}
\indexentry{hyperbolicity|hyperpage}{336}
\indexentry{mixing|hyperpage}{336}
\indexentry{$\mathcal  {C}^0$-close|hyperpage}{336}
\indexentry{$\mathcal  {C}^1$-close|hyperpage}{336}
\indexentry{Structal stability|hyperpage}{336}
\indexentry{conjugacy equation|hyperpage}{336}
\indexentry{sensitive dependence on initial conditions|hyperpage}{336}
\indexentry{Lyapunov exponent|hyperpage}{336}
\indexentry{chaotic|hyperpage}{337}
\indexentry{Hamiltonian vector field|hyperpage}{337}
\indexentry{circle|hyperpage}{337}
\indexentry{Existence of a lift|hyperpage}{337}
\indexentry{lift|hyperpage}{337}
\indexentry{preserves orientation|hyperpage}{337}
\indexentry{Arnold family|hyperpage}{337}
\indexentry{subadditive|hyperpage}{338}
\indexentry{superadditive|hyperpage}{338}
\indexentry{Existence of the rotation number|hyperpage}{338}
\indexentry{rotation number|hyperpage}{338}
\indexentry{rotation number|hyperpage}{338}
\indexentry{semi-conjugate|hyperpage}{338}
\indexentry{conjugate|hyperpage}{338}
\indexentry{measure on $\mathcal  {C}(\ensuremath  {\mathbb  {T}}^1)$|hyperpage}{339}
\indexentry{probability measure|hyperpage}{339}
\indexentry{push-forward measure|hyperpage}{339}
\indexentry{invariant|hyperpage}{339}
\indexentry{$F$-invariant|hyperpage}{339}
\indexentry{orbit|hyperpage}{339}
\indexentry{positive orbit|hyperpage}{339}
\indexentry{negative orbit|hyperpage}{339}
\indexentry{positively invariant|hyperpage}{340}
\indexentry{negatively invariant|hyperpage}{340}
\indexentry{invariant|hyperpage}{340}
\indexentry{positively recurrent points|hyperpage}{340}
\indexentry{negatively recurrent points|hyperpage}{340}
\indexentry{wandering point|hyperpage}{340}
\indexentry{wandering domain|hyperpage}{340}
\indexentry{non-wandering|hyperpage}{340}
\indexentry{minimal|hyperpage}{340}
\indexentry{minimal|hyperpage}{340}
\indexentry{measure of $U$|hyperpage}{340}
\indexentry{measure of $A$|hyperpage}{340}
\indexentry{support of $\mu $|hyperpage}{340}
\indexentry{Cantor set|hyperpage}{341}
\indexentry{uniquely ergodic|hyperpage}{341}
\indexentry{bounded variation|hyperpage}{342}
\indexentry{Denjoy-Koksma inequality|hyperpage}{342}
\indexentry{Denjoy theorem|hyperpage}{343}
\indexentry{$\sigma $-algebra|hyperpage}{344}
\indexentry{$\sigma $-algebra|hyperpage}{344}
\indexentry{measurable space|hyperpage}{344}
\indexentry{$\sigma $-algebra generated by $\mathcal  {F}$|hyperpage}{344}
\indexentry{measurable|hyperpage}{344}
\indexentry{Measure|hyperpage}{344}
\indexentry{measure|hyperpage}{344}
\indexentry{measure space|hyperpage}{344}
\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{344}
\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{344}
\indexentry{Monotone convergence theorem|hyperpage}{344}
\indexentry{Fatou's lemma|hyperpage}{344}
\indexentry{Dominated convergence theorem|hyperpage}{344}
\indexentry{Product measure|hyperpage}{344}
\indexentry{product measure|hyperpage}{344}
\indexentry{$\sigma $-finite|hyperpage}{344}
\indexentry{Fubini|hyperpage}{344}
\indexentry{density|hyperpage}{345}
\indexentry{absolutely continuous|hyperpage}{345}
\indexentry{Radon-Nikodym|hyperpage}{345}
\indexentry{probability space|hyperpage}{345}
\indexentry{events|hyperpage}{345}
\indexentry{Random variable|hyperpage}{345}
\indexentry{$E$-valued random variable|hyperpage}{345}
\indexentry{Expectation|hyperpage}{345}
\indexentry{expectation of $X$|hyperpage}{345}
\indexentry{law of $X$|hyperpage}{345}
\indexentry{$\sigma $-algebra generated by $X$|hyperpage}{345}
\indexentry{Jensen's inequality|hyperpage}{345}
\indexentry{conditional expectation of $X$ given $\mathcal  {G}$|hyperpage}{345}
\indexentry{Tower property|hyperpage}{346}
\indexentry{conditional expectation of $X$ given $Y$|hyperpage}{346}
\indexentry{probability kernel|hyperpage}{346}
\indexentry{conditional law of $X$ given $Y$|hyperpage}{346}
\indexentry{filtration|hyperpage}{346}
\indexentry{filtered probability space|hyperpage}{346}
\indexentry{adapted|hyperpage}{346}
\indexentry{martingale|hyperpage}{346}
\indexentry{submartingale|hyperpage}{346}
\indexentry{supermartingale|hyperpage}{346}
\indexentry{stopping time|hyperpage}{346}
\indexentry{stopped process|hyperpage}{346}
\indexentry{uniformly integrable|hyperpage}{346}
\indexentry{converges weakly|hyperpage}{347}
\indexentry{converges strongly|hyperpage}{347}
\indexentry{converges weakly-*|hyperpage}{347}
\indexentry{Banach-Alaoglu theorem|hyperpage}{347}
\indexentry{strongly lower-semicontinuous|hyperpage}{347}
\indexentry{weakly lower-semicontinuity|hyperpage}{347}
\indexentry{weak-* lower-semicontinuity|hyperpage}{347}
\indexentry{support plane|hyperpage}{347}
\indexentry{Sobolev spaces|hyperpage}{348}
\indexentry{Sobolev spaces|hyperpage}{348}
\indexentry{Poincaré's inequality|hyperpage}{348}
\indexentry{Poincaré-Wirtinger's inequality|hyperpage}{348}
\indexentry{embedded|hyperpage}{349}
\indexentry{compactly embedded|hyperpage}{349}
\indexentry{Gagliardo, Nirengerg and Sobolev's inequality|hyperpage}{349}
\indexentry{Hölder continuity|hyperpage}{349}
\indexentry{$\mathcal  {C}^{k,\theta }$-Hölder continuous|hyperpage}{349}
\indexentry{Morrey's embedding|hyperpage}{349}
\indexentry{extension|hyperpage}{349}
\indexentry{extension operator|hyperpage}{349}
\indexentry{first order reflection|hyperpage}{350}
\indexentry{Reillich-Kondrachov's compactness theorem|hyperpage}{350}
\indexentry{trace operator|hyperpage}{350}
\indexentry{Gradient descent algorithm|hyperpage}{351}
\indexentry{gradient descent algorithm|hyperpage}{351}
\indexentry{Armijo-type rule|hyperpage}{351}
\indexentry{Frank-Wolfe-type method|hyperpage}{351}
\indexentry{$L$-co-coercive|hyperpage}{351}
\indexentry{firmly non-expansive|hyperpage}{351}
\indexentry{Baillon-Haddad|hyperpage}{351}
\indexentry{strongly convex|hyperpage}{351}
\indexentry{$\gamma $-convex|hyperpage}{351}
\indexentry{Newton method|hyperpage}{352}
\indexentry{Newton method|hyperpage}{352}
\indexentry{multistep method|hyperpage}{352}
\indexentry{Heavy ball method|hyperpage}{352}
\indexentry{Conjugate gradient|hyperpage}{352}
\indexentry{conjugate gradient method|hyperpage}{352}
\indexentry{Nesterov's accelerated gradient method|hyperpage}{352}
\indexentry{Nesterov's method|hyperpage}{352}
\indexentry{subgradient descent method|hyperpage}{352}
\indexentry{implicit descent|hyperpage}{352}
\indexentry{nonexpansive|hyperpage}{352}
\indexentry{avergaed|hyperpage}{352}
\indexentry{Opial's lemma|hyperpage}{352}
\indexentry{Krasnoselskii-Mann's convergence theorem|hyperpage}{353}
\indexentry{linear second-order PDE|hyperpage}{354}
\indexentry{non-divergence form|hyperpage}{354}
\indexentry{divergence form|hyperpage}{354}
\indexentry{Dirichlet boundary condition|hyperpage}{354}
\indexentry{homogeneous|hyperpage}{354}
\indexentry{Neumann boundary condition|hyperpage}{354}
\indexentry{homogeneous|hyperpage}{354}
\indexentry{uniformly elliptic|hyperpage}{354}
\indexentry{weak formulation|hyperpage}{354}
\indexentry{variational formulation|hyperpage}{354}
\indexentry{weak solution|hyperpage}{354}
\indexentry{strong solution|hyperpage}{354}
\indexentry{classical solution|hyperpage}{354}
\indexentry{continuous|hyperpage}{354}
\indexentry{coercive|hyperpage}{354}
\indexentry{symmetric|hyperpage}{354}
\indexentry{Lax-Milgram theorem|hyperpage}{355}
\indexentry{Abstract Fredholm alternative|hyperpage}{356}
\indexentry{formal adjoint|hyperpage}{356}
\indexentry{homogeneous adjoint problem|hyperpage}{356}
\indexentry{resolvent set|hyperpage}{356}
\indexentry{spectrum|hyperpage}{356}
\indexentry{Inner regularity|hyperpage}{357}
\indexentry{Regularity up to the boundary|hyperpage}{357}
\indexentry{Weak maximum principle|hyperpage}{357}
\indexentry{Weak maximum principle|hyperpage}{358}
\indexentry{Weak maximum principle|hyperpage}{358}
\indexentry{Hopf's lemma|hyperpage}{358}
\indexentry{interior ball condition|hyperpage}{358}
\indexentry{Strong maximum principle|hyperpage}{358}
\indexentry{Continuation method|hyperpage}{359}
\indexentry{Brower fixed point|hyperpage}{359}
\indexentry{Schauder fixed point|hyperpage}{359}
\indexentry{Schaefer fixed point|hyperpage}{359}
\indexentry{Montecarlo estimator|hyperpage}{360}
\indexentry{seed|hyperpage}{360}
\indexentry{Mersenne Twister algorithm|hyperpage}{360}
\indexentry{Acceptance-rejection method|hyperpage}{360}
\indexentry{Box-Muller method|hyperpage}{361}
\indexentry{Polar method|hyperpage}{361}
\indexentry{antithetic method|hyperpage}{361}
\indexentry{control variate|hyperpage}{361}
\indexentry{multiple control variate estimator|hyperpage}{362}
\indexentry{equivalent|hyperpage}{362}
\indexentry{importance sampling estimator|hyperpage}{362}
\indexentry{Euler method|hyperpage}{363}
\indexentry{continuous Euler scheme|hyperpage}{363}
\indexentry{Strong error of the Euler scheme|hyperpage}{363}
\indexentry{Weak error of the Euler scheme|hyperpage}{363}
\indexentry{Romberg Extrapolation|hyperpage}{363}
\indexentry{Romberg Extrapolation|hyperpage}{363}
\indexentry{finite difference estimator|hyperpage}{364}
\indexentry{Black-Scholes model|hyperpage}{364}
\indexentry{tangent process|hyperpage}{364}
\indexentry{price of an American option|hyperpage}{365}
\indexentry{risk-free interest rate|hyperpage}{365}
\indexentry{discretization method|hyperpage}{365}
\indexentry{naive approach|hyperpage}{365}
\indexentry{Tsitsiklis-Van Roy method|hyperpage}{365}
\indexentry{Tsitsiklis-Van Roy method|hyperpage}{365}
\indexentry{Longstaff-Schwartz method|hyperpage}{366}
\indexentry{Longstaff-Schwartz method|hyperpage}{366}
\indexentry{Rogers's lemma|hyperpage}{366}
\indexentry{Dirichlet boundary conditions|hyperpage}{367}
\indexentry{Neumann boundary conditions|hyperpage}{367}
\indexentry{Robin boundary conditions|hyperpage}{367}
\indexentry{conforming Galerkin method|hyperpage}{367}
\indexentry{Céa's lemma|hyperpage}{367}
\indexentry{finite element|hyperpage}{367}
\indexentry{basis functions|hyperpage}{368}
\indexentry{local interpolant|hyperpage}{368}
\indexentry{subdivision|hyperpage}{368}
\indexentry{global interpolant|hyperpage}{368}
\indexentry{triangulation|hyperpage}{368}
\indexentry{affinely equivalent|hyperpage}{368}
\indexentry{Bramble-Hilbert lemma|hyperpage}{368}
\indexentry{diameter|hyperpage}{368}
\indexentry{insphere diameter|hyperpage}{368}
\indexentry{condition number|hyperpage}{368}
\indexentry{Local interpolation error|hyperpage}{369}
\indexentry{regular|hyperpage}{369}
\indexentry{Global interpolation error|hyperpage}{369}
\indexentry{spectral methods|hyperpage}{369}
\indexentry{trial functions|hyperpage}{369}
\indexentry{globally smooth|hyperpage}{369}
\indexentry{Galerkin methods|hyperpage}{369}
\indexentry{Collocation methods|hyperpage}{369}
\indexentry{collocation points|hyperpage}{369}
\indexentry{$\tau $ methods|hyperpage}{369}
\indexentry{interpolant|hyperpage}{369}
\indexentry{interpolant|hyperpage}{370}
\indexentry{jointly Gaussian|hyperpage}{371}
\indexentry{Brownian motion|hyperpage}{371}
\indexentry{Strong law of large numbers for Brownian motion|hyperpage}{371}
\indexentry{Markov property for Brownian motion|hyperpage}{371}
\indexentry{natural filtration|hyperpage}{371}
\indexentry{Martingale|hyperpage}{371}
\indexentry{martingale|hyperpage}{371}
\indexentry{adapted|hyperpage}{371}
\indexentry{sub-martingale|hyperpage}{371}
\indexentry{super-martingale|hyperpage}{371}
\indexentry{hitting time|hyperpage}{372}
\indexentry{Doob's optional sampling theorem|hyperpage}{372}
\indexentry{stopped process|hyperpage}{372}
\indexentry{Orthogonality of martingales|hyperpage}{372}
\indexentry{Doob's maximal inequality|hyperpage}{372}
\indexentry{absoulte variation|hyperpage}{372}
\indexentry{finite variation|hyperpage}{372}
\indexentry{Quadratic variation|hyperpage}{372}
\indexentry{mesh|hyperpage}{372}
\indexentry{continuous local martingale|hyperpage}{373}
\indexentry{localizing sequence|hyperpage}{373}
\indexentry{Doob's optional sampling theorem for local martingales|hyperpage}{373}
\indexentry{Levy's characterization of Brownian motion|hyperpage}{374}
\indexentry{isometry|hyperpage}{374}
\indexentry{partial isometry|hyperpage}{374}
\indexentry{Wiener integral|hyperpage}{374}
\indexentry{Wiener isometry|hyperpage}{374}
\indexentry{Wiener integral|hyperpage}{374}
\indexentry{Wiener integral|hyperpage}{374}
\indexentry{Chasles relation|hyperpage}{374}
\indexentry{progressive|hyperpage}{375}
\indexentry{Itô integral|hyperpage}{376}
\indexentry{Itô isometry|hyperpage}{376}
\indexentry{Itô integral|hyperpage}{376}
\indexentry{generalized Itô integral|hyperpage}{376}
\indexentry{Stochastic dominated convergence theorem|hyperpage}{376}
\indexentry{Itô process|hyperpage}{377}
\indexentry{martingale term|hyperpage}{377}
\indexentry{drift term|hyperpage}{377}
\indexentry{stochastic differential|hyperpage}{377}
\indexentry{quadratic variation|hyperpage}{377}
\indexentry{Stochastic integration by parts|hyperpage}{378}
\indexentry{Itô term|hyperpage}{378}
\indexentry{Itô's formula|hyperpage}{378}
\indexentry{Doléans-Dade exponential|hyperpage}{378}
\indexentry{Novikov's condition|hyperpage}{378}
\indexentry{Giranov's theorem|hyperpage}{379}
\indexentry{drift|hyperpage}{379}
\indexentry{diffusion|hyperpage}{379}
\indexentry{stochastic differential equation|hyperpage}{379}
\indexentry{SDE|hyperpage}{379}
\indexentry{solution of the SDE|hyperpage}{379}
\indexentry{Gronwall's lemma|hyperpage}{379}
\indexentry{Existence and uniqueness of solutions of SDEs|hyperpage}{379}
\indexentry{Langevin equation|hyperpage}{379}
\indexentry{Geometric Brownian motion|hyperpage}{380}
\indexentry{Black-Scholes process|hyperpage}{380}
\indexentry{homogeneous SDE|hyperpage}{380}
\indexentry{diffusions|hyperpage}{380}
\indexentry{Invariance under time shift|hyperpage}{380}
\indexentry{Generator|hyperpage}{380}
\indexentry{generator|hyperpage}{380}
\indexentry{Kolmogorov's equation|hyperpage}{380}
\indexentry{Feynman-Kac's formula|hyperpage}{381}
\indexentry{Itô's formula|hyperpage}{382}
\indexentry{Flow property|hyperpage}{382}
\indexentry{Dynamic programming principle|hyperpage}{382}
\indexentry{Fokker-Planck equation|hyperpage}{382}
\indexentry{control parameter|hyperpage}{383}
\indexentry{Finite horizon problem|hyperpage}{383}
\indexentry{running cost|hyperpage}{383}
\indexentry{terminal cost|hyperpage}{383}
\indexentry{Infinte horizon problem|hyperpage}{383}