From bcf043b403ce7d77894f9e2e9f644cc5329748f4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?V=C3=ADctor?= Date: Mon, 18 Sep 2023 19:45:21 +0200 Subject: [PATCH] upload new files --- .github/workflows/buildpdf.yml | 24 +++++++++ .../Introduction_to_evolution_PDEs.tex | 8 +++ ...troduction_to_non_linear_elliptic_PDEs.tex | 8 +++ .../Limit_theorems_and_large_deviations.tex | 8 +++ .../Stochastic_calculus.tex | 8 +++ main_math.idx | 49 ++++++++++++++--- main_math.ilg | 6 +-- main_math.ind | 53 ++++++++++++++----- main_math.tex | 13 +++++ preamble_formulas.sty | 4 ++ 10 files changed, 158 insertions(+), 23 deletions(-) create mode 100644 Mathematics/5th/Introduction_to_evolution_PDEs/Introduction_to_evolution_PDEs.tex create mode 100644 Mathematics/5th/Introduction_to_non_linear_elliptic_PDEs/Introduction_to_non_linear_elliptic_PDEs.tex create mode 100644 Mathematics/5th/Limit_theorems_and_large_deviations/Limit_theorems_and_large_deviations.tex create mode 100644 Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex diff --git a/.github/workflows/buildpdf.yml b/.github/workflows/buildpdf.yml index 7782e47..f9f945d 100644 --- a/.github/workflows/buildpdf.yml +++ b/.github/workflows/buildpdf.yml @@ -172,6 +172,26 @@ jobs: with: root_file: Advanced_topics_in_functional_analysis_and_PDEs.tex working_directory: Mathematics/5th/Advanced_topics_in_functional_analysis_and_PDEs/ + - name: Compile - IEPDE + uses: xu-cheng/latex-action@v2 + with: + root_file: Introduction_to_evolution_PDEs.tex + working_directory: Mathematics/5th/Introduction_to_evolution_PDEs/ + - name: Compile - INEPDE + uses: xu-cheng/latex-action@v2 + with: + root_file: Introduction_to_nonlinear_elliptic_PDEs.tex + working_directory: Mathematics/5th/Introduction_to_nonlinear_elliptic_PDEs/ + - name: Compile - LTLD + uses: xu-cheng/latex-action@v2 + with: + root_file: Limit_theorems_and_large_deviations.tex + working_directory: Mathematics/5th/Limit_theorems_and_large_deviations/ + - name: Compile - SC + uses: xu-cheng/latex-action@v2 + with: + root_file: Stochastic_calculus.tex + working_directory: Mathematics/5th/Stochastic_calculus/ ########## ########## - name: Compile - main_math @@ -252,6 +272,10 @@ jobs: Mathematics/4th/Stochastic_processes/Stochastic_processes.pdf Mathematics/5th/Advanced_probability/Advanced_probability.pdf Mathematics/5th/Advanced_topics_in_functional_analysis_and_PDEs/Advanced_topics_in_functional_analysis_and_PDEs.pdf + Mathematics/5th/Introduction_to_evolution_PDEs/Introduction_to_evolution_PDEs.pdf + Mathematics/5th/Introduction_to_nonlinear_elliptic_PDEs/Introduction_to_nonlinear_elliptic_PDEs.pdf + Mathematics/5th/Limit_theorems_and_large_deviations/Limit_theorems_and_large_deviations.pdf + Mathematics/5th/Stochastic_calculus/Stochastic_calculus.pdf main_physics.pdf Physics/Basic/Electricity_and_magnetism/Electricity_and_magnetism.pdf Physics/Basic/Mechanics_and_special_relativity/Mechanics_and_special_relativity.pdf diff --git a/Mathematics/5th/Introduction_to_evolution_PDEs/Introduction_to_evolution_PDEs.tex b/Mathematics/5th/Introduction_to_evolution_PDEs/Introduction_to_evolution_PDEs.tex new file mode 100644 index 0000000..724d078 --- /dev/null +++ b/Mathematics/5th/Introduction_to_evolution_PDEs/Introduction_to_evolution_PDEs.tex @@ -0,0 +1,8 @@ +\documentclass[../../../main_math.tex]{subfiles} + +\begin{document} +\changecolor{IEPDE} +\begin{multicols}{2}[\section{Introduction to evolution PDEs}] + +\end{multicols} +\end{document} \ No newline at end of file diff --git a/Mathematics/5th/Introduction_to_non_linear_elliptic_PDEs/Introduction_to_non_linear_elliptic_PDEs.tex b/Mathematics/5th/Introduction_to_non_linear_elliptic_PDEs/Introduction_to_non_linear_elliptic_PDEs.tex new file mode 100644 index 0000000..5ad4adb --- /dev/null +++ b/Mathematics/5th/Introduction_to_non_linear_elliptic_PDEs/Introduction_to_non_linear_elliptic_PDEs.tex @@ -0,0 +1,8 @@ +\documentclass[../../../main_math.tex]{subfiles} + +\begin{document} +\changecolor{INLEPDE} +\begin{multicols}{2}[\section{Introduction to non linear elliptic PDEs}] + +\end{multicols} +\end{document} \ No newline at end of file diff --git a/Mathematics/5th/Limit_theorems_and_large_deviations/Limit_theorems_and_large_deviations.tex b/Mathematics/5th/Limit_theorems_and_large_deviations/Limit_theorems_and_large_deviations.tex new file mode 100644 index 0000000..f76ead4 --- /dev/null +++ b/Mathematics/5th/Limit_theorems_and_large_deviations/Limit_theorems_and_large_deviations.tex @@ -0,0 +1,8 @@ +\documentclass[../../../main_math.tex]{subfiles} + +\begin{document} +\changecolor{LTLD} +\begin{multicols}{2}[\section{Limit theorem and large deviations}] + +\end{multicols} +\end{document} \ No newline at end of file diff --git a/Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex b/Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex new file mode 100644 index 0000000..de89e91 --- /dev/null +++ b/Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex @@ -0,0 +1,8 @@ +\documentclass[../../../main_math.tex]{subfiles} + +\begin{document} +\changecolor{SC} +\begin{multicols}{2}[\section{Stochastic calculus}] + +\end{multicols} +\end{document} \ No newline at end of file diff --git a/main_math.idx b/main_math.idx index 31e0bbc..718f564 100644 --- a/main_math.idx +++ b/main_math.idx @@ -2887,6 +2887,7 @@ \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} @@ -2900,6 +2901,8 @@ \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} @@ -2908,7 +2911,7 @@ \indexentry{Neumann series|hyperpage}{308} \indexentry{convex functional|hyperpage}{308} \indexentry{Hahn-Banach theorem|hyperpage}{308} -\indexentry{prolongation|hyperpage}{308} +\indexentry{extension|hyperpage}{308} \indexentry{Seminorm|hyperpage}{308} \indexentry{seminorm|hyperpage}{308} \indexentry{Hahn-Banach theorem|hyperpage}{308} @@ -2923,7 +2926,7 @@ \indexentry{Baire's theorem|hyperpage}{309} \indexentry{Open mapping theorem|hyperpage}{309} \indexentry{Closed graph theorem|hyperpage}{309} -\indexentry{Banach-Steinhaus theorem|hyperpage}{309} +\indexentry{Banach-Steinhaus theorem|hyperpage}{310} \indexentry{semilinear|hyperpage}{310} \indexentry{inner product|hyperpage}{310} \indexentry{pre-Hilbert space|hyperpage}{310} @@ -2942,6 +2945,10 @@ \indexentry{Riesz representation theorem|hyperpage}{312} \indexentry{adjoint operator|hyperpage}{312} \indexentry{self-adjoint|hyperpage}{312} +\indexentry{continuous|hyperpage}{313} +\indexentry{coercive|hyperpage}{313} +\indexentry{symmetric|hyperpage}{313} +\indexentry{Lax-Milgram theorem|hyperpage}{313} \indexentry{orthogonal system|hyperpage}{313} \indexentry{orthonormal system|hyperpage}{313} \indexentry{complete|hyperpage}{313} @@ -2954,7 +2961,7 @@ \indexentry{Fourier transform|hyperpage}{313} \indexentry{Riesz-Fischer theorem|hyperpage}{313} \indexentry{Parseval identity|hyperpage}{313} -\indexentry{Spectral theorem|hyperpage}{313} +\indexentry{Spectral theorem|hyperpage}{314} \indexentry{Hilbert-Schmidt spectral representation theorem|hyperpage}{314} \indexentry{Fredholm alternative|hyperpage}{314} \indexentry{Law of total probability|hyperpage}{315} @@ -3090,7 +3097,35 @@ \indexentry{conditional expectation of $X$ given $Y$|hyperpage}{337} \indexentry{probability kernel|hyperpage}{337} \indexentry{conditional law of $X$ given $Y$|hyperpage}{337} -\indexentry{Sobolev spaces|hyperpage}{338} -\indexentry{Sobolev spaces|hyperpage}{338} -\indexentry{Poincaré's inequality|hyperpage}{338} -\indexentry{Poincaré-Wirtinger's inequality|hyperpage}{338} +\indexentry{filtration|hyperpage}{337} +\indexentry{filtered probability space|hyperpage}{337} +\indexentry{adapted|hyperpage}{337} +\indexentry{martingale|hyperpage}{337} +\indexentry{submartingale|hyperpage}{337} +\indexentry{supermartingale|hyperpage}{337} +\indexentry{stopping time|hyperpage}{337} +\indexentry{stopped process|hyperpage}{337} +\indexentry{uniformly integrable|hyperpage}{337} +\indexentry{converges weakly|hyperpage}{338} +\indexentry{converges strongly|hyperpage}{338} +\indexentry{converges weakly-*|hyperpage}{338} +\indexentry{Banach-Alaoglu theorem|hyperpage}{338} +\indexentry{strongly lower-semicontinuous|hyperpage}{338} +\indexentry{weakly lower-semicontinuity|hyperpage}{338} +\indexentry{weak-* lower-semicontinuity|hyperpage}{338} +\indexentry{support plane|hyperpage}{338} +\indexentry{Sobolev spaces|hyperpage}{339} +\indexentry{Sobolev spaces|hyperpage}{339} +\indexentry{Poincaré's inequality|hyperpage}{339} +\indexentry{Poincaré-Wirtinger's inequality|hyperpage}{339} +\indexentry{embedded|hyperpage}{340} +\indexentry{compactly embedded|hyperpage}{340} +\indexentry{Gagliardo, Nirengerg and Sobolev's inequality|hyperpage}{340} +\indexentry{Hölder continuity|hyperpage}{340} +\indexentry{$\mathcal {C}^{k,\theta }$-Hölder continuous|hyperpage}{340} +\indexentry{Morrey's embedding|hyperpage}{340} +\indexentry{extension|hyperpage}{340} +\indexentry{extension operator|hyperpage}{340} +\indexentry{first order reflection|hyperpage}{341} +\indexentry{Reillich-Kondrachov's compactness theorem|hyperpage}{341} +\indexentry{trace operator|hyperpage}{341} diff --git a/main_math.ilg b/main_math.ilg index ce7d395..62ab4f1 100644 --- a/main_math.ilg +++ b/main_math.ilg @@ -1,6 +1,6 @@ This is makeindex, version 2.17 [TeX Live 2023] (kpathsea + Thai support). -Scanning input file main_math.idx.......done (3096 entries accepted, 0 rejected). -Sorting entries..............................done (40266 comparisons). -Generating output file main_math.ind......done (2638 lines written, 0 warnings). +Scanning input file main_math.idx.......done (3131 entries accepted, 0 rejected). +Sorting entries..............................done (39644 comparisons). +Generating output file main_math.ind......done (2665 lines written, 0 warnings). Output written in main_math.ind. Transcript written in main_math.ilg. diff --git a/main_math.ind b/main_math.ind index a53789b..bcc3526 100644 --- a/main_math.ind +++ b/main_math.ind @@ -23,6 +23,7 @@ \item $\alpha $-limit set, \hyperpage{131} \item $\ensuremath {\mathbb {C}}$-differentiable, \hyperpage{109} \item $\ensuremath {\mathbb {R}}$-differentiable, \hyperpage{110} + \item $\mathcal {C}^{k,\theta }$-Hölder continuous, \hyperpage{340} \item $\omega $-limit point, \hyperpage{131} \item $\omega $-limit set, \hyperpage{131} \item $\sigma $-additivity, \hyperpage{173}, \hyperpage{291} @@ -97,6 +98,7 @@ \item Adams method, \hyperpage{262} \item Adams-Bashforth method, \hyperpage{262} \item Adams-Moulton method, \hyperpage{262} + \item adapted, \hyperpage{337} \item adherence, \hyperpage{54} \item adherent point, \hyperpage{54}, \hyperpage{207} \item adjacency matrix, \hyperpage{50} @@ -194,7 +196,8 @@ \item ball, \hyperpage{205} \item Banach fixed-point theorem, \hyperpage{125} \item Banach space, \hyperpage{301} - \item Banach-Steinhaus theorem, \hyperpage{309} + \item Banach-Alaoglu theorem, \hyperpage{338} + \item Banach-Steinhaus theorem, \hyperpage{310} \item bandlimited, \hyperpage{239} \item Barrow's law, \hyperpage{298} \item barycenter, \hyperpage{69} @@ -223,6 +226,7 @@ \item Bias on the estimations, \hyperpage{255} \item Bias on the predictions, \hyperpage{255} \item biased estimator, \hyperpage{193} + \item bidual space, \hyperpage{307} \item bijective, \hyperpage{7} \item bilinear, \hyperpage{22} \item bilinear form, \hyperpage{22} @@ -401,6 +405,7 @@ \item codimension, \hyperpage{223} \item coefficient of determination, \hyperpage{252} \item coefficients, \hyperpage{11} + \item coercive, \hyperpage{313} \item cofactor, \hyperpage{136} \item cofactor matrix, \hyperpage{15} \item Cofinite topology, \hyperpage{206} @@ -415,6 +420,7 @@ \item Compact space, \hyperpage{213} \item compact subset, \hyperpage{213} \item compact support, \hyperpage{79} + \item compactly embedded, \hyperpage{340} \item compactness, \hyperpage{213} \item Comparison test, \hyperpage{76}, \hyperpage{80}, \hyperpage{183} @@ -509,7 +515,7 @@ \item Continuity from above, \hyperpage{173} \item Continuity from below, \hyperpage{173} \item continuous, \hyperpage{28}, \hyperpage{55}, \hyperpage{106}, - \hyperpage{130} + \hyperpage{130}, \hyperpage{313} \item continuous at $x_0$, \hyperpage{28} \item Continuous equation, \hyperpage{277} \item continuous equation, \hyperpage{277} @@ -534,7 +540,10 @@ \item converges in probability, \hyperpage{187} \item converges in the $p$-th mean, \hyperpage{189} \item converges pointwise, \hyperpage{77, 78}, \hyperpage{106, 107} + \item converges strongly, \hyperpage{338} \item converges uniformly, \hyperpage{77, 78}, \hyperpage{106, 107} + \item converges weakly, \hyperpage{338} + \item converges weakly-*, \hyperpage{338} \item convex, \hyperpage{30}, \hyperpage{115} \item convex functional, \hyperpage{308} \item convolution, \hyperpage{79}, \hyperpage{240}, \hyperpage{244} @@ -753,6 +762,7 @@ \item elliptic equation, \hyperpage{277} \item elliptic point, \hyperpage{150} \item elliptic sector, \hyperpage{133} + \item embedded, \hyperpage{340} \item embedded methods, \hyperpage{260} \item empirical distribution, \hyperpage{202} \item empty set, \hyperpage{6} @@ -838,7 +848,8 @@ \item exponential series, \hyperpage{48} \item extended complex plane, \hyperpage{105} \item extended real numbers, \hyperpage{105} - \item extension, \hyperpage{126} + \item extension, \hyperpage{126}, \hyperpage{308}, \hyperpage{340} + \item extension operator, \hyperpage{340} \item exterior, \hyperpage{54} \item exterior angle, \hyperpage{160} \item Exterior angle theorem, \hyperpage{64} @@ -875,7 +886,8 @@ \item field of complex numbers, \hyperpage{104} \item field of fractions, \hyperpage{46}, \hyperpage{163} \item field of rational functions, \hyperpage{163} - \item filtration, \hyperpage{321} + \item filtered probability space, \hyperpage{337} + \item filtration, \hyperpage{321}, \hyperpage{337} \item filtration space, \hyperpage{321} \item finer, \hyperpage{205} \item finer than, \hyperpage{32}, \hyperpage{58} @@ -900,6 +912,7 @@ \item first integral, \hyperpage{134}, \hyperpage{154} \item First isomorphism theorem, \hyperpage{18}, \hyperpage{39}, \hyperpage{44} + \item first order reflection, \hyperpage{341} \item First Sylow theorem, \hyperpage{41} \item Fisher information, \hyperpage{195} \item Fisher's theorem, \hyperpage{197} @@ -966,6 +979,7 @@ \indexspace + \item Gagliardo, Nirengerg and Sobolev's inequality, \hyperpage{340} \item Galerkin approximation, \hyperpage{275} \item Galois, \hyperpage{168} \item Galois extension, \hyperpage{168} @@ -1130,6 +1144,7 @@ \item hypothesis test, \hyperpage{199} \item Hölder condition, \hyperpage{247} \item Hölder conjugates, \hyperpage{302} + \item Hölder continuity, \hyperpage{340} \item Hölder's inequality, \hyperpage{302, 303} \indexspace @@ -1342,6 +1357,7 @@ \item Law of total probability, \hyperpage{174}, \hyperpage{315} \item Lax theorem, \hyperpage{261} \item Lax-Friedrichs scheme, \hyperpage{268} + \item Lax-Milgram theorem, \hyperpage{313} \item Lax-Richtmyer equivalence theorem, \hyperpage{273} \item Lax-Wendroff, \hyperpage{271} \item Lax-Wendroff scheme, \hyperpage{271} @@ -1493,6 +1509,7 @@ \item Markov chain, \hyperpage{318} \item Markov property, \hyperpage{318} \item Markov's inequality, \hyperpage{185} + \item martingale, \hyperpage{337} \item material derivative operator, \hyperpage{277} \item Matrix, \hyperpage{13} \item matrix, \hyperpage{13}, \hyperpage{18} @@ -1574,6 +1591,7 @@ \item more efficient than, \hyperpage{194} \item Morera's theorem, \hyperpage{114} \item morphism of field extensions, \hyperpage{165} + \item Morrey's embedding, \hyperpage{340} \item MSE, \hyperpage{194} \item multi-index notation, \hyperpage{57} \item multicollinearity, \hyperpage{255} @@ -1848,12 +1866,12 @@ \item Poincaré index formula, \hyperpage{139} \item Poincaré inequality, \hyperpage{289} \item Poincaré map, \hyperpage{136} - \item Poincaré's inequality, \hyperpage{338} + \item Poincaré's inequality, \hyperpage{339} \item Poincaré's method, \hyperpage{226} \item Poincaré-Bendixson theorem, \hyperpage{136} \item Poincaré-Hopf theorem, \hyperpage{139}, \hyperpage{161} \item Poincaré-Hopf theorem on $S^2$, \hyperpage{139} - \item Poincaré-Wirtinger's inequality, \hyperpage{338} + \item Poincaré-Wirtinger's inequality, \hyperpage{339} \item points, \hyperpage{63}, \hyperpage{205} \item points of the quadric, \hyperpage{73} \item pointwise bounded, \hyperpage{125}, \hyperpage{304} @@ -1948,7 +1966,6 @@ \item projective plane, \hyperpage{66} \item projective subvariety, \hyperpage{66} \item projectivity, \hyperpage{69} - \item prolongation, \hyperpage{308} \item Propagation of absolute errors, \hyperpage{89} \item Propagation of relative errors, \hyperpage{89} \item proper, \hyperpage{37} @@ -2045,7 +2062,7 @@ \item Reducible linear ode of second order, \hyperpage{123} \item reflection, \hyperpage{71}, \hyperpage{120} \item Reflections, \hyperpage{71} - \item reflexive, \hyperpage{308} + \item reflexive, \hyperpage{307, 308} \item refractive index, \hyperpage{278} \item region, \hyperpage{115}, \hyperpage{148}, \hyperpage{204} \item regression axis, \hyperpage{151} @@ -2060,10 +2077,11 @@ \item regular domain, \hyperpage{148} \item regular region, \hyperpage{160} \item regular surface, \hyperpage{147} + \item Reillich-Kondrachov's compactness theorem, \hyperpage{341} \item Related samples with unknown variances, \hyperpage{199} \item relative condition numbers, \hyperpage{90} \item relative error, \hyperpage{89} - \item relatively compact, \hyperpage{121} + \item relatively compact, \hyperpage{121}, \hyperpage{304} \item relatively prime, \hyperpage{10, 11} \item relaxation factor, \hyperpage{100} \item Removable discontinuity, \hyperpage{28} @@ -2247,7 +2265,7 @@ \item Slutsky's theorem, \hyperpage{190} \item small change, \hyperpage{279} \item Sobolev space, \hyperpage{289} - \item Sobolev spaces, \hyperpage{338} + \item Sobolev spaces, \hyperpage{339} \item solution, \hyperpage{90}, \hyperpage{139} \item solution of a system of equations, \hyperpage{13} \item solution of the ode, \hyperpage{122} @@ -2259,7 +2277,7 @@ \item special orthogonal group, \hyperpage{145} \item specific heat capacity, \hyperpage{278} \item spectral radius, \hyperpage{98} - \item Spectral theorem, \hyperpage{24}, \hyperpage{313} + \item Spectral theorem, \hyperpage{24}, \hyperpage{314} \item spectral values, \hyperpage{309} \item spectrum, \hyperpage{97}, \hyperpage{309} \item sphere, \hyperpage{54} @@ -2317,7 +2335,8 @@ \item Stokes' theorem, \hyperpage{62} \item Stolz-Cesàro theorem, \hyperpage{27} \item Stone-Weierstra\ss \ theorem, \hyperpage{304} - \item stopping time, \hyperpage{321} + \item stopped process, \hyperpage{337} + \item stopping time, \hyperpage{321}, \hyperpage{337} \item strict Lyapunov function, \hyperpage{137} \item strictly concave, \hyperpage{30} \item strictly convex, \hyperpage{30} @@ -2329,6 +2348,7 @@ \item Strong law, \hyperpage{191} \item Strong Markov property, \hyperpage{321, 322} \item strongly consistent estimator, \hyperpage{194} + \item strongly lower-semicontinuous, \hyperpage{338} \item Strum's sequence, \hyperpage{92} \item Student's $t$-distribution with $n$ degrees of freedom, \hyperpage{197} @@ -2346,6 +2366,7 @@ \item sublinear, \hyperpage{306} \item submanifold, \hyperpage{146} \item submanifold with boundary, \hyperpage{157} + \item submartingale, \hyperpage{337} \item Submersion, \hyperpage{146} \item submersion, \hyperpage{146} \item subordinated matrix norm, \hyperpage{97} @@ -2368,8 +2389,10 @@ \hyperpage{107} \item sum of the series in an uniform sense, \hyperpage{78}, \hyperpage{107} + \item supermartingale, \hyperpage{337} \item support, \hyperpage{8}, \hyperpage{79}, \hyperpage{146}, \hyperpage{176}, \hyperpage{180}, \hyperpage{242} + \item support plane, \hyperpage{338} \item support points, \hyperpage{93} \item supremum, \hyperpage{25} \item Supremum axiom, \hyperpage{25} @@ -2384,7 +2407,7 @@ \item Sylow $p$-subgroup, \hyperpage{41} \item Sylvester's criterion, \hyperpage{58} \item Sylvester's law of inertia, \hyperpage{23} - \item symmetric, \hyperpage{22}, \hyperpage{62} + \item symmetric, \hyperpage{22}, \hyperpage{62}, \hyperpage{313} \item Symmetric difference formula of order 1, \hyperpage{95} \item Symmetric difference formula of order 2, \hyperpage{95} \item symmetric group, \hyperpage{8}, \hyperpage{38} @@ -2467,6 +2490,7 @@ \item tower of fields, \hyperpage{165} \item Tower property, \hyperpage{337} \item trace, \hyperpage{141}, \hyperpage{289} + \item trace operator, \hyperpage{341} \item Trace theorem, \hyperpage{289} \item Traffic flow equation, \hyperpage{280} \item trail, \hyperpage{49} @@ -2527,6 +2551,7 @@ \item uniformly continuous, \hyperpage{33}, \hyperpage{55} \item uniformly convergent, \hyperpage{117} \item uniformly equicontinuous, \hyperpage{125}, \hyperpage{304} + \item uniformly integrable, \hyperpage{337} \item uniformly most powerful, \hyperpage{200} \item union, \hyperpage{6} \item unique factorization domain, \hyperpage{45} @@ -2600,7 +2625,9 @@ \item Weak duality theorem, \hyperpage{51} \item weak formulation, \hyperpage{275} \item Weak law, \hyperpage{190} + \item weak-* lower-semicontinuity, \hyperpage{338} \item weakly consistent estimator, \hyperpage{194} + \item weakly lower-semicontinuity, \hyperpage{338} \item Weierstra\ss ' theorem, \hyperpage{55}, \hyperpage{114}, \hyperpage{214} \item Weierstra\ss \ approximation theorem, \hyperpage{79} diff --git a/main_math.tex b/main_math.tex index 8c22fdf..c435b75 100644 --- a/main_math.tex +++ b/main_math.tex @@ -107,6 +107,19 @@ \chapter{Fifth year} \subfile{Mathematics/5th/Advanced_topics_in_functional_analysis_and_PDEs/Advanced_topics_in_functional_analysis_and_PDEs.tex} \cleardoublepage +\subfile{Mathematics/5th/Introduction_to_evolution_PDEs/Introduction_to_evolution_PDEs.tex} +\cleardoublepage + +\subfile{Mathematics/5th/Introduction_to_non_linear_elliptic_PDEs/Introduction_to_non_linear_elliptic_PDEs.tex} +\cleardoublepage + +\subfile{Mathematics/5th/Limit_theorems_and_large_deviations/Limit_theorems_and_large_deviations.tex} +\cleardoublepage + +\subfile{Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex} +\cleardoublepage + + \printindex \end{document} diff --git a/preamble_formulas.sty b/preamble_formulas.sty index 0dedb32..2c4bed5 100644 --- a/preamble_formulas.sty +++ b/preamble_formulas.sty @@ -91,6 +91,10 @@ {SP}{\sta} % stochastic processes {ATFAPDE}{\ana} % advanced topics in functional analysis and pdes {AP}{\sta} % advanced probability + {INLEPDE}{\ana} % introduction to non linear elliptic pdes + {IEPDE}{\ana} % introduction to evolution pdes + {LTLD}{\sta} % limit theorems and large deviations + {SC}{\sta} % stochastic calculus }{\col}% } \ExplSyntaxOff