ajout exos

exercices/Makefile

+FILTERS = --filter=pandoc-numbering --filter=pandoc-crossref
+TEMPLATE = --template=./default.latex
+PDFENGINE = --pdf-engine pdflatex
+
+all: fourier.pdf
+
+fourier.pdf: fourier.md
+	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+
+# determinants.pdf: determinants.md
+# 	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+
+# matrix_inverse.pdf: matrix_inverse.md
+# 	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+
+# matrice_rot.pdf: matrice_rot.md
+# 	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+
+# matrices.pdf: matrices.md
+# 	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+
+# fun_lin.pdf: fun_lin.md
+# 	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+
+# vecteurs.pdf: vecteurs.md
+# 	pandoc -s -o $@ $< $(FILTERS) $(TEMPLATE) $(PDFENGINE)
+

exercices/default.latex

+\documentclass[$if(fontsize)$$fontsize$,$endif$$if(lang)$$babel-lang$,$endif$$if(papersize)$$papersize$paper,$endif$$for(classoption)$$classoption$$sep$,$endfor$]{$documentclass$}
+$if(beamerarticle)$
+\usepackage{beamerarticle} % needs to be loaded first
+$endif$
+$if(fontfamily)$
+\usepackage[$for(fontfamilyoptions)$$fontfamilyoptions$$sep$,$endfor$]{$fontfamily$}
+$else$
+\usepackage{lmodern}
+$endif$
+$if(linestretch)$
+\usepackage{setspace}
+\setstretch{$linestretch$}
+$endif$
+\usepackage{amssymb,amsmath,bm,array}
+\usepackage{ifxetex,ifluatex}
+\usepackage{fixltx2e} % provides \textsubscript
+\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
+  \usepackage[$if(fontenc)$$fontenc$$else$T1$endif$]{fontenc}
+  \usepackage[utf8]{inputenc}
+$if(euro)$
+  \usepackage{eurosym}
+$endif$
+\else % if luatex or xelatex
+$if(mathspec)$
+  \ifxetex
+    \usepackage{mathspec}
+  \else
+    \usepackage{unicode-math}
+  \fi
+$else$
+  \usepackage{unicode-math}
+$endif$
+  \defaultfontfeatures{Ligatures=TeX,Scale=MatchLowercase}
+$for(fontfamilies)$
+  \newfontfamily{$fontfamilies.name$}[$fontfamilies.options$]{$fontfamilies.font$}
+$endfor$
+$if(euro)$
+  \newcommand{\euro}{€}
+$endif$
+$if(mainfont)$
+    \setmainfont[$for(mainfontoptions)$$mainfontoptions$$sep$,$endfor$]{$mainfont$}
+$endif$
+$if(sansfont)$
+    \setsansfont[$for(sansfontoptions)$$sansfontoptions$$sep$,$endfor$]{$sansfont$}
+$endif$
+$if(monofont)$
+    \setmonofont[Mapping=tex-ansi$if(monofontoptions)$,$for(monofontoptions)$$monofontoptions$$sep$,$endfor$$endif$]{$monofont$}
+$endif$
+$if(mathfont)$
+$if(mathspec)$
+  \ifxetex
+    \setmathfont(Digits,Latin,Greek)[$for(mathfontoptions)$$mathfontoptions$$sep$,$endfor$]{$mathfont$}
+  \else
+    \setmathfont[$for(mathfontoptions)$$mathfontoptions$$sep$,$endfor$]{$mathfont$}
+  \fi
+$else$
+  \setmathfont[$for(mathfontoptions)$$mathfontoptions$$sep$,$endfor$]{$mathfont$}
+$endif$
+$endif$
+$if(CJKmainfont)$
+    \usepackage{xeCJK}
+    \setCJKmainfont[$for(CJKoptions)$$CJKoptions$$sep$,$endfor$]{$CJKmainfont$}
+$endif$
+\fi
+% use upquote if available, for straight quotes in verbatim environments
+\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
+% use microtype if available
+\IfFileExists{microtype.sty}{%
+\usepackage[$for(microtypeoptions)$$microtypeoptions$$sep$,$endfor$]{microtype}
+\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
+}{}
+\PassOptionsToPackage{hyphens}{url} % url is loaded by hyperref
+$if(verbatim-in-note)$
+\usepackage{fancyvrb}
+$endif$
+\usepackage[unicode=true]{hyperref}
+$if(colorlinks)$
+\PassOptionsToPackage{usenames,dvipsnames}{color} % color is loaded by hyperref
+$endif$
+\hypersetup{
+$if(title-meta)$
+            pdftitle={$title-meta$},
+$endif$
+$if(author-meta)$
+            pdfauthor={$author-meta$},
+$endif$
+$if(keywords)$
+            pdfkeywords={$for(keywords)$$keywords$$sep$, $endfor$},
+$endif$
+$if(colorlinks)$
+            colorlinks=true,
+            linkcolor=$if(linkcolor)$$linkcolor$$else$Maroon$endif$,
+            citecolor=$if(citecolor)$$citecolor$$else$Blue$endif$,
+            urlcolor=$if(urlcolor)$$urlcolor$$else$Blue$endif$,
+$else$
+            pdfborder={0 0 0},
+$endif$
+            breaklinks=true}
+\urlstyle{same}  % don't use monospace font for urls
+$if(verbatim-in-note)$
+\VerbatimFootnotes % allows verbatim text in footnotes
+$endif$
+$if(geometry)$
+\usepackage[$for(geometry)$$geometry$$sep$,$endfor$]{geometry}
+$endif$
+$if(lang)$
+\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
+  \usepackage[shorthands=off,$for(babel-otherlangs)$$babel-otherlangs$,$endfor$main=$babel-lang$]{babel}
+$if(babel-newcommands)$
+  $babel-newcommands$
+$endif$
+\else
+  \usepackage{polyglossia}
+  \setmainlanguage[$polyglossia-lang.options$]{$polyglossia-lang.name$}
+$for(polyglossia-otherlangs)$
+  \setotherlanguage[$polyglossia-otherlangs.options$]{$polyglossia-otherlangs.name$}
+$endfor$
+\fi
+$endif$
+$if(natbib)$
+\usepackage{natbib}
+\bibliographystyle{$if(biblio-style)$$biblio-style$$else$plainnat$endif$}
+$endif$
+$if(biblatex)$
+\usepackage[$if(biblio-style)$style=$biblio-style$,$endif$$for(biblatexoptions)$$biblatexoptions$$sep$,$endfor$]{biblatex}
+$for(bibliography)$
+\addbibresource{$bibliography$}
+$endfor$
+$endif$
+$if(listings)$
+\usepackage{listings}
+$endif$
+$if(lhs)$
+\lstnewenvironment{code}{\lstset{language=Haskell,basicstyle=\small\ttfamily}}{}
+$endif$
+$if(highlighting-macros)$
+$highlighting-macros$
+$endif$
+$if(tables)$
+\usepackage{longtable,booktabs}
+% Fix footnotes in tables (requires footnote package)
+\IfFileExists{footnote.sty}{\usepackage{footnote}\makesavenoteenv{long table}}{}
+$endif$
+$if(graphics)$
+\usepackage{graphicx,grffile}
+\makeatletter
+\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
+\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
+\makeatother
+% Scale images if necessary, so that they will not overflow the page
+% margins by default, and it is still possible to overwrite the defaults
+% using explicit options in \includegraphics[width, height, ...]{}
+\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
+$endif$
+$if(links-as-notes)$
+% Make links footnotes instead of hotlinks:
+\renewcommand{\href}[2]{#2\footnote{\url{#1}}}
+$endif$
+$if(strikeout)$
+\usepackage[normalem]{ulem}
+% avoid problems with \sout in headers with hyperref:
+\pdfstringdefDisableCommands{\renewcommand{\sout}{}}
+$endif$
+$if(indent)$
+$else$
+\IfFileExists{parskip.sty}{%
+\usepackage{parskip}
+}{% else
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{6pt plus 2pt minus 1pt}
+}
+$endif$
+\setlength{\emergencystretch}{3em}  % prevent overfull lines
+\providecommand{\tightlist}{%
+  \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
+$if(numbersections)$
+\setcounter{secnumdepth}{$if(secnumdepth)$$secnumdepth$$else$5$endif$}
+$else$
+\setcounter{secnumdepth}{0}
+$endif$
+$if(subparagraph)$
+$else$
+% Redefines (sub)paragraphs to behave more like sections
+\ifx\paragraph\undefined\else
+\let\oldparagraph\paragraph
+\renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}}
+\fi
+\ifx\subparagraph\undefined\else
+\let\oldsubparagraph\subparagraph
+\renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}}
+\fi
+$endif$
+$if(dir)$
+\ifxetex
+  % load bidi as late as possible as it modifies e.g. graphicx
+  $if(latex-dir-rtl)$
+  \usepackage[RTLdocument]{bidi}
+  $else$
+  \usepackage{bidi}
+  $endif$
+\fi
+\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
+  \TeXXeTstate=1
+  \newcommand{\RL}[1]{\beginR #1\endR}
+  \newcommand{\LR}[1]{\beginL #1\endL}
+  \newenvironment{RTL}{\beginR}{\endR}
+  \newenvironment{LTR}{\beginL}{\endL}
+\fi
+$endif$
+
+% set default figure placement to htbp
+\makeatletter
+\def\fps@figure{htbp}
+\makeatother
+
+$for(header-includes)$
+$header-includes$
+$endfor$
+
+$if(corrige)$
+\newcommand{\comment}[1]{#1}
+$else$
+\newcommand{\comment}[1]{\hphantom{#1}}
+$endif$
+
+$if(title)$
+\title{$title$$if(thanks)$\thanks{$thanks$}$endif$}
+$endif$
+$if(subtitle)$
+\providecommand{\subtitle}[1]{}
+\subtitle{$subtitle$}
+$endif$
+$if(author)$
+\author{$for(author)$$author$$sep$ \and $endfor$}
+$endif$
+$if(institute)$
+\providecommand{\institute}[1]{}
+\institute{$for(institute)$$institute$$sep$ \and $endfor$}
+$endif$
+\date{$date$}
+
+\begin{document}
+$if(title)$
+\maketitle
+$endif$
+$if(abstract)$
+\begin{abstract}
+$abstract$
+\end{abstract}
+$endif$
+
+$for(include-before)$
+$include-before$
+
+$endfor$
+$if(toc)$
+{
+$if(colorlinks)$
+\hypersetup{linkcolor=$if(toccolor)$$toccolor$$else$black$endif$}
+$endif$
+\setcounter{tocdepth}{$toc-depth$}
+\tableofcontents
+}
+$endif$
+$if(lot)$
+\listoftables
+$endif$
+$if(lof)$
+\listoffigures
+$endif$
+$body$
+
+$if(natbib)$
+$if(bibliography)$
+$if(biblio-title)$
+$if(book-class)$
+\renewcommand\bibname{$biblio-title$}
+$else$
+\renewcommand\refname{$biblio-title$}
+$endif$
+$endif$
+\bibliography{$for(bibliography)$$bibliography$$sep$,$endfor$}
+
+$endif$
+$endif$
+$if(biblatex)$
+\printbibliography$if(biblio-title)$[title=$biblio-title$]$endif$
+
+$endif$
+$for(include-after)$
+$include-after$
+
+$endfor$
+\end{document}

exercices/fourier.md

+---
+# author:
+# - Orestis Malaspinas
+title: Exercices sur Fourier
+autoSectionLabels: true
+autoEqnLabels: false
+eqnPrefix: 
+  - "éq."
+  - "éqs."
+chapters: true
+numberSections: true
+chaptersDepth: 1
+sectionsDepth: 3
+lang: fr
+documentclass: article
+papersize: A4
+cref: false
+pandoc-numbering:
+  - category: exercice
+urlcolor: blue
+---
+\newcommand{\real}{\mathbb{R}}
+\newcommand{\vectwo}[2]{\begin{pmatrix}#1 \\ #2 \end{pmatrix}}
+\newcommand{\vecthree}[3]{\begin{pmatrix}#1 \\ #2 \\ #3 \end{pmatrix}}
+\newcommand{\mat}[1]{\underline{\underline{#1}}}
+\newcommand{\mattwo}[4]{\begin{pmatrix}
+								#1 & #2 \\
+								#3 & #4
+						\end{pmatrix}}
+
+Série d'exercices {#fourier .unnumbered}
+=================
+
+Exercices (Séries de Fourier) #
+
+Calculer les séries de Fourier des fonctions suivantes.
+
+1. La fonction $10$-périodique
+\begin{equation}
+f(x)=\left\{
+\begin{matrix}
+0,\ -5 < x < 0 \\
+3,\ 0 < x < 5 \\
+\end{matrix}
+\right.
+\end{equation}
+
+2. La fonction $2\pi$-périodique
+\begin{equation}
+f(x)=x^2.
+\end{equation}
+En déduire que la série 
+$$
+\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}.
+$$
+
+3.  La fonction $6$-périodique
+\begin{equation}
+f(x)=\left\{
+\begin{matrix}
+2,\ -3 < x < 0 \\
+-2,\ 0 < x < 3 \\
+\end{matrix}
+\right.
+\end{equation}
+
+4. La fonction $2\pi$-périodique
+\begin{equation}
+f(x)=\left\{
+\begin{matrix}
+\cos(x),\ 0 < x < \pi \\
+0,\ \pi < x < 2\pi \\
+\end{matrix}
+\right.
+\end{equation}
+
+Exercices (Transformées de Fourier) #
+
+Déterminer la transformée de Fourier de
+
+1. La fonction 
+\begin{equation}
+f(x)=\left\{
+\begin{matrix}
+e^{2x},\ x < 0 \\
+e^{-x},\ x > 0 \\
+\end{matrix}
+\right.
+\end{equation}
+
+2. La fonction 
+\begin{equation}
+f(x)=\left\{
+\begin{matrix}
+x,\ 0 < x < 1, \\
+0,\ \mathrm{sinon} \\
+\end{matrix}
+\right.
+\end{equation}
+
+3. La fonction 
+\begin{equation}
+f(x)=\left\{
+\begin{matrix}
+x^2,\ 0 < x < a, \\
+0,\ \mathrm{sinon} \\
+\end{matrix}
+\right.
+\end{equation}
+
+Exercices (Transformées de Fourier discrètes) #
+
+Déterminer la transformée de Fourier discrète de
+
+1. La suite 
+\begin{equation}
+\vec f=\{1,1,1,1\}.
+\end{equation}
+2. La suite 
+\begin{equation}
+\vec f=\{1,-1,1,-1\}.
+\end{equation}