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victorballester7 · Sep 18, 2023 · bcf043b · bcf043b
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diff --git 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
@@ -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}
diff --git a/...5th/Introduction_to_non_linear_elliptic_PDEs/Introduction_to_non_linear_elliptic_PDEs.tex b/...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}
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
@@ -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}
diff --git a/Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex 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}
diff --git 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
@@ -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.