

\documentclass[12pt,a4paper]{book}

\usepackage[french]{varioref}



\usepackage [french] {babel}


\usepackage[ansinew]{inputenc}
\usepackage[T1]{fontenc}

\setlength{\parindent}{0pt}
\usepackage{pst-plot}
\usepackage[dvips]{color}
\usepackage{shapepar}
\usepackage{pst-text}
\setlength{\parindent}{0pt}
\usepackage{maple2e}

\usepackage{makeidx}

\usepackage{graphicx}
\usepackage{amsthm,
        float,
        amsmath,
        amssymb,
        amsbsy,
        ifthen,
        fancyhdr,
        fancybox,
          float,
        amsmath,
        amssymb,
        amsbsy,
        ifthen,
        fancyhdr,
        fancybox,
        theorem,
         graphics,
      mathrsfs,
        amsthm,
        amsmath,
        amssymb,
        multicol,
        amsbsy,
        ifthen,
        calc,
        fancyhdr,
        fancybox,
        upref,
        amsfonts,
        pifont,
        pst-node,
        pst-plot,
        hhline,
        picins,
        parallel,
        ifthen,
        subfigure,
        array,pst-char,pst-text,
          pstcol,
         pst-grad,pst-fill} 

\usepackage{epsfig}
%\usepackage{geometry}
%\usepackage{palatino}
%%\usepackage{amsmath}
%%\usepackage{amssymb}
%\usepackage[matrix,arrow]{xy}
%\geometry{margin=2cm}

%\input{Makros/Makros}
%\graphicspath{{Figures/}}

\textwidth 17,3cm \textheight 23cm \oddsidemargin -0,4cm\headheight 12.38pt \evensidemargin -0,4cm\topmargin -0,5cm \baselineskip 3.5ex
\headsep 1cm
%
%\textwidth 18cm  \headheight -1cm\textheight 27cm\evensidemargin -1cm  \oddsidemargin -1cm \topmargin 0cm \baselineskip 0ex
\marginparwidth 0cm\linewidth 13.5cm \paperheight 297mm\paperwidth 21cm\footskip 1cm


\renewcommand{\bf}[1]{\textcolor{red}{\textbf{#1}}}


\newcommand{\NoLecon}{}
\newcommand{\NomSection}{}
\newcommand{\NomChap}{}
\newcommand{\NomLecon}{}
\newcommand{\NumLecon}{}

\newcommand{\ill}[2]{\begin{minipage}[t]{0.75\textwidth}\vspace{0cm}#1\end{minipage}\hspace{0.5cm}\begin{minipage}[t]{0.2\textwidth}\vspace{-0.5cm}
\hspace{5.5cm} \begin{flushright}\includegraphics[height=5cm]{#2.eps}\end{flushright}\end{minipage}}


\newcommand{\illps}[3]{\begin{minipage}[t]{0.75\textwidth}\vspace{0cm}#1\end{minipage}\hspace{0.5cm}\begin{minipage}[t]{0.2\textwidth}\vspace{-0.5cm}
\hspace{5.5cm} \begin{flushright}\includegraphics[height=#3cm]{#2.ps}\end{flushright}\end{minipage}}



\newcommand{\fonc}[4]{#1\ :\begin{array}{rll} #2 &\to &#3\\ x& \mapsto &#4 \end{array}}

%\newcommand{\limg}[1]{\ds\lim_{\begin{array}{l} x\to #1\\ x<#1 \end{array}}}

\newcommand{\limd}[1]{\ds\lim_{\begin{array}{l} \scriptscriptstyle {x\to #1}\\ \scriptscriptstyle{x>#1} \end{array}\textstyle}}

\newcommand{\limg}[1]{\ds\lim_{\begin{array}{l} \scriptscriptstyle {x\to #1}\\ \scriptscriptstyle{x<#1} \end{array}\textstyle}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    DESSIN
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\newcommand{\des}[2]{
\begin{center}
\includegraphics[height=#2cm]{/home/moi/Lycee/TS/figures/#1}
\end{center}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\definecolor{orange}{rgb}{0.589999,0.269997,0.080004}
\definecolor{or}{rgb}{1,0.843104,0}
\definecolor{bleu_ciel}{rgb}{0.635286,0.9693528,1}
\definecolor{bleu_m}{rgb}{0.423524,0.6462352,0.7372784}
\definecolor{vert_e}{rgb}{0,0.790002,0.340007}
\definecolor{bleu_f}{rgb}{0.211762,0.3231176,0.3686392}
\definecolor{0.6white}{rgb}{0.6,0.6,0.6}
\definecolor{bleu}{rgb}{0.629405,0.807794,1}
%%%%%%%%%%% LES MACROS DU BOUQUIN %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\LECOND}[6]{\setcounter{NumPart}{0}
\setcounter{NumDessin}{0}\setcounter{pb}{0}\setcounter{sec}{0}\setcounter{num}{0}\setcounter{solnum}{0}\setcounter{chap}{0}
\setcounter{Def}{0}\setcounter{Prop}{0}\setcounter{Th}{0}\renewcommand{\NomLecon}{#5}
\renewcommand{\NumLecon}{#1}\renewcommand{\NoLecon}{#2}
\thispagestyle{empty}
\begin{minipage}[t]{0.75\textwidth}\vspace{0cm}
\begin{center}
%\pscharpath[linestyle=none,fillstyle=gradient,gradbegin=black,gradend=bleu,gradmidpoint=0.5]
{\LARGE\textsc{#2 Aventure}}\\
\bigskip\bigskip
\pscharpath[linestyle=none,fillstyle=gradient,gradbegin=black,gradend=bleu,gradmidpoint=0.5]
{ \Huge{ #3}} \\ \bigskip\bigskip
\pscharpath[linestyle=none,fillstyle=gradient,gradbegin=black,gradend=bleu,gradmidpoint=0.5]
{\Huge{ #4}}   
\addcontentsline{toc}{chapter}{\protect\numberline{}{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \textcolor{bleu}{\textsc{#2\ \ Aventure} : \ #5}} \ \sm}
\end{center}
\end{minipage}
\begin{minipage}[t]{0.3\textwidth}\vspace{0cm}
\hspace{-1.5cm}
\includegraphics[width=\textwidth]{#6}
\end{minipage}}





\newcommand{\LECON}[5]{\setcounter{NumPart}{0}
\setcounter{NumDessin}{0}\setcounter{pb}{0}\setcounter{sec}{0}\setcounter{num}{0}\setcounter{solnum}{0}
\setcounter{Def}{0}\setcounter{Prop}{0}\setcounter{Th}{0}\renewcommand{\NomLecon}{#5}
\renewcommand{\NumLecon}{#1}
\thispagestyle{empty}
%\begin{minipage}[t]{0.75\textwidth}\vspace{0cm}
\begin{center}
{\LARGE\textsc{#2 Aventure}}\\
 \textbf{{\Huge #3 \\ #4}}
%\addcontentsline{toc}{chapter}{\protect\numberline{}{\!\!\!\!\! #1.\ \textsc{#5}} \ \sm}
\end{center}\bigskip\bigskip\bigskip\bigskip}
%\end{minipage}
%\begin{minipage}[t]{0.3\textwidth}\vspace{0cm}
%\hspace{-1.}5cm}
%\includegraphics[width=\textwidth]{#6.eps}
%\end{minipage}

\newcommand{\bs}{\bigskip}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%           macros deug
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\newcounter{thm}
\renewcommand{\thethm}{\arabic{thm}}

\newlength{\espaceavantenonce}
\newlength{\espaceapresenonce}
\setlength{\espaceavantenonce}{\topsep} \setlength{\espaceapresenonce}{\topsep}

\newenvironment{enonce1}[2]{\refstepcounter{thm} %ref=> ca labelise bien!
\vskip \espaceavantenonce \noindent \textsc{#1 \thethm ~#2} \itshape}%
{\normalfont \vskip \espaceapresenonce}

\newenvironment{enonce1*}[1]{
\vskip\espaceavantenonce \noindent \textsc{#1} \itshape}%
{\normalfont \vskip \espaceapresenonce}

\newenvironment{enonce2}[2]{\refstepcounter{thm} %ref=> ca labelise bien!
\vskip \espaceavantenonce \noindent \textsc{#1 \thethm ~#2} }%
{\vskip \espaceapresenonce}

\newenvironment{enonce2*}[1]{
\vskip\espaceavantenonce \noindent \textsc{#1} }%
{\vskip \espaceapresenonce}



\newcommand{\espaceexo}{\vspace{0.5cm}}
\newcommand{\espaceseparation}{\vspace{0.8cm}}



\newcommand{\titreglobal}{%
\begin{center}
\textsc{\Large Exercices Alternatifs}\\
\vspace{0.2cm}
Exercices r\'ecents, class\'es par date.\\
{\small \today}
\end{center}
}
%

\newcommand{\titre}[2]{%
\begin{center}
{\LARGE \textsc{#1}\\
\vspace{0.2cm}
#2}

\end{center}
}




\newcommand{\texteseparation}{\thesection. \ecritdate}
\newcommand{\bookmarkseparation}{\ecritdate}

\newcommand{\informations}{\emph{\ecrittheme}. \emph{\ecritniveau}. Angle p\'edagogique~: \emph{\ecritangle}.}


\sloppy

%%%%%%%%% Chiffres romains et arabes pour les numerotations

\renewcommand{\thesection}{\Roman{section}}
\renewcommand{\thesubsection}{\thesection.\arabic{subsection}}

%%%%%%%%%% Macros \partie \qst \sq et \ssq pour les questions des exos %%%%%%%%%%%%%%

\newcounter{partie}
\newcounter{qst}
\newcounter{sq}
\newcounter{ssq}
\renewcommand{\thepartie}{\Roman{partie}}
\renewcommand{\theqst}{\arabic{qst}}
\renewcommand{\thesq}{\alph{sq}}
\renewcommand{\thessq}{\roman{ssq}}

%%%%%
 %   Attention, j'ai eu des problemes de liens (en pdf) vers \sq
 %   si je n'utilise pas une commande \paragraph* pour mettre en forme.
%%%%
\newcommand{\partie}[1]{\refstepcounter{partie}\setcounter{qst}{0}\setcounter{sq}{0}\setcounter{ssq}{0}
\subsection*{\thepartie. #1}}


\newcommand{\qst}[1]{\setcounter{sq}{0}\setcounter{ssq}{0}%
\refstepcounter{qst}\subsubsection*{Question \theqst. #1}}

\newcommand{\sq}[1][]{\setcounter{ssq}{0}\refstepcounter{sq}
\paragraph*{\thesq. #1}}

\newcommand{\ssq}[1][]{\refstepcounter{ssq}

 \subparagraph*{\textnormal{\textit{(\thessq)}. \textsc{#1} ---}}}



\newcounter{ppb}
\newcommand{\SUBSUBSECTION}[1]{\refstepcounter{ppb}\subsubsection*{\textcolor{bleu_f}{\Alph{sec}\,-\,\thepb\,-\,\alph{ppb}~:\ #1}} 
\addcontentsline{toc}{subsubsection}{\protect\numberline{\footnotesize{#1}}} }
%\addtocounter{ppb}{1}
%\medskip\bigskip{\large{{\textit{\Alph{sec}\,-\,\thepb\,-\,\alph{ppb}~:\ #1}}}}
%\bigskip}



\newcounter{pb}
\newcommand{\SUBSECTION}[1]{\refstepcounter{pb}\setcounter{ppb}{0}\textcolor{bleu}{\subsection*{\Alph{sec}\,-\,\thepb~:\ #1}}
%\newcommand{\NomSub}{#1}
\addcontentsline{toc}{subsection}{\protect\numberline{\small{#1}}} }

%\addtocounter{pb}{1}
%\medskip\bigskip{\Large\textbf{\mg{\textit{\Alph{sec}\,-\,\thepb~:\ #1}}}}
%\bigskip}


\newcounter{sec}

%\medskip\bigskip {\LARGE\textbf{\Alph{sec}}\Large\textbf{\textsc{\ -\ #1}}}
%\bigskip
\newcommand{\SECTION}[2]{\refstepcounter{sec}\setcounter{pb}{0}\setcounter{partie}{0}\setcounter{ppb}{0}
\renewcommand{\NomSection}{#2}
\setcounter{qst}{0}
\vspace{1cm}
\psframebox[fillstyle=gradient,gradbegin=bleu_ciel,gradend=bleu]{     {   \LARGE\textbf{\Alph{sec}}\Large\textbf{\textsc{\ -\ #1}}   }           }                                                    
\addcontentsline{toc}{section}{\protect\numberline{\Alph{sec}.#2}}
}


\newcounter{chap}
%\fancyhf{}
%\medskip\bigskip {\LARGE\textbf{\Alph{sec}}\Large\textbf{\textsc{\ -\ #1}}}
%\bigskip
\newcommand{\CHAP}[2]{\refstepcounter{chap}\setcounter{sec}{0}\setcounter{pb}{0}\setcounter{partie}{0}\setcounter{ppb}{0}
\renewcommand{\NomChap}{#1}
\setcounter{qst}{0}
\psframebox[fillstyle=solid,fillcolor=bleu]
{     \white{   \LARGE\textbf{\Roman{chap}}\LARGE\textbf{\ -\ #1}   }           }                                                    
\addcontentsline{toc}{chapter}{\protect\numberline{\Roman{chap}.#2}}
}


%%%%%%%%%%%%


\newenvironment{belet}
{\begin{list}{}{\renewcommand{\makelabel}{$\triangleright$}}}{\end{list}}
\newcommand{\bel}{\begin{belet}}
\newcommand{\el}{\end{belet}}



\newenvironment{Abstract}[1]
{\begin{center}
\begin{minipage}{10cm}
\textbf{Résumé} \footnotesize{#1}} {\end{minipage}
\end{center}
\bigskip\bigskip}

%%%%%%%%%





%%%%%%%%%%%%%%

\newcommand{\ENC}[2]{
\bigskip

%\begin{Boxedminipage}{\textwidth}
\psshadowbox*[fillcolor=bleu_ciel]{
\begin{minipage}{\textwidth}
\sm

\textbf{#1}

\sm

#2

\sm
\end{minipage}
}
%\end{Boxedminipage}
\bigskip
}



\newcommand{\enc}[1]{
\begin{center} \psshadowbox*[fillcolor=bleu_ciel]{   #1 } \end{center}  
}




%%%%%%%%%%%%%%%%%%%%
\newcommand{\sm}{\smallskip}

\newcommand{\iii}[1]{
\begin{center}
\includegraphics{Figures.#1}
\end{center}
}

\newcommand{\DESSIN}{\stepcounter{NumDessin}
\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip
\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip


\begin{center}
\textit{Figure \NumLecon. \theNumDessin}
 \end{center}
}


\newcommand{\dessin}[1]{\stepcounter{NumDessin}

\vspace{#1cm}


\begin{center}
\textit{Figure \NumLecon. \theNumDessin}
 \end{center}
}

\newenvironment{Boxedminipage}
{\begin{Sbox}\begin{minipage}} {\end{minipage}\end{Sbox}\fbox{\TheSbox}}

\newcommand{\mg}{\mathversion{bold}}


\newcommand{\mat}{Téhessin}

\newcommand{\fr}{\ds\frac}

\newcommand{\MAT}[1]{
\smallskip

{ \textbf{Téhessin} : #1}

\smallskip
}

\newcommand{\pro}{
\smallskip

 \textbf{Mathémator}~: }


\newcommand{\tsx}{
\smallskip

 \textbf{Téhessin}~: }




%
%\newcommand{\MATA2}[2]{
%\smallskip
%
%{ \textbf{Téhessix (à part)} : #1 \textbf{(tout haut)} : #2} }


\newcommand{\MATA}[1]{
\smallskip

{ \textbf{Téhessin (à part)} : \textit{#1}} }

\newcommand{\REV}{\mat, vous rêvez ! Je vous entends !}

%%%%%%%%%%%%%% MES MACROS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Oij{$\left(\text{O},~\overrightarrow{\imath},~\overrightarrow{\jmath}\right)$}
\def\Oijk{$\left(\text{O},~\overrightarrow{\imath},~\overrightarrow{\jmath},~
\overrightarrow{k}\right)$}
\def\Ouv{$\left(\text{O},~\overrightarrow{u},~\overrightarrow{v}\right)$}

\newcommand{\R}{\bbr}




\newcommand{\lin}{\ds\lim_{n\to +\infty}}
\newcommand{\Lim}[1]{\ds\lim_{x\to #1}}

\renewcommand{\th}{{\rm th}\,}

\newcommand{\im}{{\rm Im}\,}
\newcommand{\ke}{{\rm Ker}\,}

\newcommand{\VF}{ \textsl{VRAI ou FAUX ?} \smallskip }

\newcommand{\ege}[1]{\underset{#1}{=}}
\newcommand{\eqe}[1]{\underset{#1}{\sim}}
\newcommand{\ese}[1]{\underset{#1}{\simeq}}



\newcommand{\ens}[2]{\left\{\left.{#1}\,\right\vert\, {#2}\right\}}
\newcommand{\ensbis}[2]{\left\{\left.{#1}\,\right\mid\, {#2}\right\}}

\newcommand{\AR}{\mathcal{A}}
\newcommand{\BR}{\mathcal{B}}
\newcommand{\CR}{\mathcal{C}}
\newcommand{\DR}{\mathcal{D}}
\newcommand{\ER}{\mathcal{E}}
\newcommand{\FR}{\mathcal{F}}
\newcommand{\GR}{\mathcal{G}}
\newcommand{\HR}{\mathcal{H}}
\newcommand{\IR}{\mathcal{I}}
\newcommand{\JR}{\mathcal{J}}
\newcommand{\KR}{\mathcal{K}}
\newcommand{\LR}{\mathcal{L}}
\newcommand{\MR}{\mathcal{M}}
\newcommand{\NR}{\mathcal{N}}
\newcommand{\OR}{\mathcal{O}}
\newcommand{\PR}{\mathcal{P}}
\newcommand{\QR}{\mathcal{Q}}
\newcommand{\RR}{\mathcal{R}}
\newcommand{\SR}{\mathcal{S}}
\newcommand{\TR}{\mathcal{T}}
\newcommand{\UR}{\mathcal{U}}
\newcommand{\VR}{\mathcal{V}}
\newcommand{\WR}{\mathcal{W}}
\newcommand{\XR}{\mathcal{X}}
\newcommand{\YR}{\mathcal{Y}}
\newcommand{\ZR}{\mathcal{Z}}

\newcommand{\ds}{\displaystyle}

\newcommand{\bet}{\begin{center}\begin{tabular}}
\newcommand{\et}{\end{tabular}\end{center}}

\newcommand{\bmat}{\begin{pmatrix}}
\newcommand{\emat}{\end{pmatrix}}
\newcommand{\ud}{\frac{1}{2}}

\newcommand{\bsys}{\begin{cases}
}%{\left\{\begin{array}}
\newcommand{\esys}{\end{cases}}%{\end{array}\right.}


\newcommand{\bsyf}{\left\{\begin{array}{lcl}}
\newcommand{\esyf}{\end{array}\right.}


\newcommand{\ie}{\leqslant}
\newcommand{\se}{\geqslant}

\newcommand{\bc}{\bbc\,}
\newcommand{\bq}{\bbq\,}





\newcommand{\e}{\varepsilon}
\newcommand{\f}{\varphi}
\newcommand{\g}{\gamma}
\newcommand{\m}{Montrer\ que\ }




\newcommand{\bqa}{\begin{eqnarray}}
\newcommand{\eqa}{\end{eqnarray}}

\newcommand{\bd}{\begin{document}}
\newcommand{\ed}{\end{document}}

\newcommand{\bqas}{\begin{eqnarray*}}
\newcommand{\eqas}{\end{eqnarray*}}

\newcommand{\bex}{\begin{exer}}
\newcommand{\eex}{\end{exer}}

\newcommand{\been}{\begin{enumerate}}
\newcommand{\een}{\end{enumerate}}





%%%%%%%%%%%%%%%% LES MACROS DE DENIS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





\makeatletter
\renewcommand{\@seccntformat}[1]{{\csname the#1\endcsname}.\hspace{0.5em}}
\makeatother



\newcommand{\SSi}{\quad\text{si et seulement si}\quad}
\newcommand{\ssi}{\Longleftrightarrow}
\newcommand{\seulsi}{\Longrightarrow}
\newcommand{\Si}{\Longleftarrow}

\newcommand{\Loc}{\operatorname{Loc}}
\newcommand{\Arg}{\operatorname{Arg}}
\newcommand{\ch}{\operatorname{ch}}
\newcommand{\sh}{\operatorname{sh}}
\newcommand{\cotan}{\operatorname{cotan}}
\renewcommand{\tanh}{\operatorname{th}}
\newcommand{\Arccos}{\operatorname{Arccos}}
\newcommand{\Arcsin}{\operatorname{Arcsin}}
\newcommand{\Arctan}{\operatorname{Arctan}}
\newcommand{\Argch}{\operatorname{Argch}}
\newcommand{\Argsh}{\operatorname{Argsh}}
\newcommand{\Argth}{\operatorname{Argth}}
\newcommand{\val}{\operatorname{val}}

\newcommand{\pa}[1]{\left({#1}\right)}
\newcommand{\cro}[1]{\left[{#1}\right]}
\newcommand{\ab}[1]{\left|{#1}\right|}
\newcommand{\ac}[1]{\left\{{#1}\right\}}

\newcommand{\al}{\alpha}

\newcommand{\de}{\delta}
\newcommand{\De}{\Delta}

\newcommand{\ga}{\gamma}

\newcommand{\Ga}{\Gamma}

\newcommand{\La}{\Lambda}
\newcommand{\la}{\lambda}
\renewcommand{\o}{\omega}
\newcommand{\si}{\sigma}
\newcommand{\Th}{\Theta}

\newcommand{\bfi}{\begin{figure} }

\newcommand{\efi}{\end{figure}}

\newcommand{\id}{\IR\!d}

\newcommand{\ba}{\begin{array}}
\newcommand{\ea}{\end{array}}

\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}

\newcommand{\bi}{\begin{itemize}}
\newcommand{\ei}{\end{itemize}}

\renewcommand{\theenumi}{\arabic{enumi}}
        \renewcommand{\labelenumi}{\theenumi)}
\renewcommand{\theenumii}{\alph{enumii}}
        \renewcommand{\labelenumii}{\theenumii)}
\renewcommand{\theenumiii}{\roman{enumiii}}
        \renewcommand{\labelenumiii}{\theenumiii)}

\def\labellisti{$\bullet$}
\def\labellistii{$\ast$}
\def\labellistiii{$\cdot$}
\def\labellistiv{\bf --}

\def\labelitemi{$\bullet$}
\def\labelitemii{$\ast$}
\def\labelitemiii{$\cdot$}
\def\labelitemiv{\bf --}


\newdimen\AAdi%
\newbox\AAbo%
\font\AAFf=cmex10%   %ou cmex10
\def\AArm{\fam0 \rm}%
\def\AAk#1#2{\setbox\AAbo=\hbox{#2}\AAdi=\wd\AAbo\kern#1\AAdi{}}%
\def\AAr#1#2#3{\setbox\AAbo=\hbox{#2}\AAdi=\ht\AAbo\raise#1\AAdi\hbox{#3}}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% alphabet blackboard
\def\bba{{\AArm A}}%
\def\bbb{\mathbb{B}}%
\def\bbc{\mathbb{C}}%
\def\bbd{\mathbb{D}}%
\def\bbe{\mathbb{E}}%
\def\bbf{\mathbb{F}}%
\def\bbg{{\AArm G\AAk{-1.02}{G}\AAr{.9}{I}{\AAFf\char"3F}}}%
\def\bbh{\mathbb{H}}%
\def\bbi{\mathbb{I}}%
\def\bbj{{\AArm J}}%
\def\bbk{\mathbb{K}}%
\def\bbl{\mathbb{L}}%
\def\bbm{\mathbb{M}}%
\def\bbn{\mathbb{N}}%
\def\bbo{{\AArm O\AAk{-1.02}{O}\AAr{.9}{I}{\AAFf\char"3F}}}%
\def\bbp{\mathbb{P}}%
\def\bbq{\mathbb{Q}}%
\def\bbr{\mathbb{R}}%
\def\bbs{{\AArm S}}%
\def\bbt{{\AArm T\AAk{-.62}{T}T}}%
\def\bbu{{\AArm U\AAk{-1}{U}\AAr{.95}{I}{\AAFf\char"3F}}}%
\def\bbv{{\AArm V}}%
\def\bbw{{\AArm W}}%
\def\bbx{{\AArm X}}%
\def\bby{{\AArm Y}}%
\def\bbz{\mathbb{Z}}%
%% 1 blackboard
\def\BBone{{\AArm 1\AAk{-.8}{I}I}}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\mc}{\mathcal}

\newcommand{\er}{\textsuperscript{er}\ }
\newcommand{\eme}{\textsuperscript{ème}\ }
\newcommand{\ere}{\textsuperscript{ère}\ }

%\newcommand{\ei}[2]{e^{i#1\pi/#2}}
\newcommand{\emi}[2]{e^{-i#1\pi/#2}}
\newcommand{\intt}{\ds\int\!\!\!\int}
\newcommand{\ve}{\overrightarrow}
\newcommand{\eq}{\mathrel{\sim}}
\newcommand{\widefrown}{\resizebox{0.6cm}{0.13cm}{$\frown$}}
\newcommand{\rg}{{\rm rg}\,}
\newcommand{\vect}[1]{{\rm Vect}\{#1\}}
\renewcommand{\dim}{\dim\,}
\newcommand{\un}{$(u_n)_{n\in\bbn}\ $}
\newcommand{\vn}{$(v_n)_{n\in\bbn}\ $}
\newcommand{\co}{\choose}

\newcommand{\bsyc}{\left\{\begin{array}{rcl}}
\newcommand{\esyc}{\end{array}\right.}
\newcommand{\jok}[1]{\begin{flushright}\rotatebox{180}{\textit{#1}}\end{flushright}}

\newcommand{\ut}{\fr{1}{3}}
\newcommand{\dt}{\fr{2}{3}}


\newcommand{\ao}[2]{\pa{\ve{#1},\ve{#2}}}
\newcommand{\ps}[2]{\ve{#1}\cdot\ve{#2}}
\newcommand{\C}{\bbc}
\renewcommand{\bar}{\overline}
\def\Oijk{$\left(\text{O},~\ve{i},~ \ve{j},~ \ve{k}\right)$}
\def\Oij{$\left(\text{O},~\ve{i},~ \ve{j}\right)$}
\newcommand{\coo}[3]{#1\pa{#2\, ;\, #3}}

\newcommand{\qcm}{\bigcirc\  }

\newcommand{\maj}{\mathscr}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Tableau de variation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\croi}{% croissante
\unitlength=1cm
\begin{minipage} {1cm}%pour centrer verticalement f(x)
\begin{picture}(1,1) % dessin de 2 X 2
\put(0,0){\vector(1,1){1}} % 1 à partir (0,0) direction (1,1)
\end{picture}
\end{minipage}}


\newcommand{\dec}{%décroissante
\setlength{\unitlength}{1cm}
\begin{minipage} {1cm}%pour centrer verticalement f(x)
\begin{picture}(1,1) % dessin de 2 X 2
\put(0,1){\vector(1,-1){1}}
\end{picture}
\end{minipage}
}














\newcommand{\map}[1]{

 \smallskip

 \texttt{> #1}

  \smallskip

  }



\newcommand{\mup}[1]{

 \smallskip

 \texttt{$>>$ #1}

  \smallskip

  }

  \newcommand{\p}{\textasciicircum}


\newcommand{\cas}[1]{

 \smallskip 


\textcolor{blue}{\texttt{#1}}


  \smallskip

}







%%%%%%%%%%%%%%%%%%%% Macros matrices systemes et vecteurs %%%%%%%%%

%\newcommand{\Det}[1]{\left|\begin{matrix} #1 \end{matrix}\right|}
\newcommand{\Mx}[1]{\left(\begin{matrix} #1 \end{matrix}\right)}
\renewcommand{\vect}[1]{\left(\begin{matrix} #1
\end{matrix}\right)}
\newcommand{\sys}[1]{\left\{\begin{matrix} #1 \end{matrix}\right.}
\def \vi {\vec \imath}
\def \vj {\vec \jmath}


\newcommand{\env}[1]{\begin{flushright}\rotatebox{180}{\textit{#1}}\end{flushright}}

\usepackage{fancyhdr}
%
%\textwidth 18cm \headsep 0cm \headheight -1cm\textheight 27cm\evensidemargin -1cm  \oddsidemargin -1cm \topmargin 0cm \baselineskip 0ex
%\marginparwidth 0cm\linewidth 13.5cm \paperheight 29.7cm\paperwidth 21cm\footskip 0cm
%
\newcommand{\entete}[3]{
\fancyfoot[C]{{\scriptsize\textsl{ Guillaume Connan, #3, 2005-2006}}}
 \fancyhead[RO,LE]{\thepage}
 \fancyhead[CO]{  #1 } \fancyhead[CE]{#2  }
\renewcommand{\headrulewidth}{0.4pt}
 \pagestyle{fancy}
}


\newcommand{\entetalice}[2]{
\fancyfoot[C]{ }
 \fancyhead[RO,LE]{\thepage} \fancyhead[LO,RE]{ }
 \fancyhead[CO]{ \textbf{ #1} } \fancyhead[CE]{#2  }
\renewcommand{\headrulewidth}{0.4pt}
 \pagestyle{fancy}
}


%\fancyfoot{}
% \fancyhead[RO,LE]{\thepage}
 %\fancyhead[CO]{ \textsc{ }} \fancyhead[CE]{\textsc{ } }
%\renewcommand{\headrulewidth}{0.4pt}
% \pagestyle{fancy}


\newcounter{NumPart}
\newcounter{NumDessin}
\setcounter{tocdepth}{4} %\setcounter{page}{0}


\pagenumbering{arabic} \setlength{\unitlength}{1cm} \setlength{\parindent}{0mm} \floatplacement{figure}{H}
 %\setcounter{page}{0}
%\newcommand{\NomLecon}{}
%\newcommand{\NumLecon}{}
\setlength{\parindent}{0mm}
%############################# Début du bouquin ##############
%###################################################################

\setlength{\parindent}{0mm}

% \setcounter{page}{0}

\makeatletter
\def\addcontentsline@toc#1#2#3{\addtocontents{#1}{\protect\thispagestyle{empty}}%
\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}}}

\def\addcontentsline#1#2#3{\expandafter\@ifundefined{addcontentsline@#1}%
{\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}}} {\csname addcontentsline@#1\endcsname{#1}{#2}{#3}}}




 %\setcounter{page}{0}


\setlength{\parindent}{0pt}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\newcounter{num}

\newcommand{\exo}[1]{\addtocounter{num}{1}

\medskip{\textbf{\textsf{Exercice~\thenum}}}\\
\ #1}

\newcommand{\exot}[2]{\addtocounter{num}{1}

\medskip{\textbf{\textsf{Exercice~\thenum\ \ #1}}}\\
\ #2}


\newcounter{solnum}
\newcommand{\sol}[2]{\addtocounter{solnum}{1}
\medskip   \textbf{\textsf{Solution~\thesolnum\ \ #1}}\\
\ \textsf{#2}}





\newcounter{Def}
\newcommand{\Def}[1]{\addtocounter{Def}{1}  \textbf{Définition \NumLecon-\theDef}}


\newcounter{Prop}
\newcommand{\Prop}[1]{\addtocounter{Prop}{1}  \textbf{Propriété \NumLecon-\theProp}}
\newcommand{\Props}[1]{\addtocounter{Prop}{1}  \textbf{Propriétés \NumLecon-\theProp}}


\newcounter{Th}
\newcommand{\Thm}[1]{\addtocounter{Th}{1}  \textbf{Théorème \NumLecon-\theTh\ \ }}




\renewcommand{\theenumi}{\arabic{enumi}}
        \renewcommand{\labelenumii}{\theenumii)}
\renewcommand{\theenumii}{\alph{enumii}}
        \renewcommand{\labelenumiii}{\theenumii)}
\renewcommand{\theenumiii}{\roman{enumii}}
\renewcommand{\un}{(u_n)_{n\in\bbn}\ }
\newcommand{\ouv}{(O,\,\ve{u},\,\ve{v}\,)}
\renewcommand{\contentsname}{\pscharpath[linestyle=none,fillstyle=gradient,gradbegin=black,gradend=bleu,gradmidpoint=0.5]{SOMMAIRE}}



\renewcommand{\d}{\text{d}}




\newcommand{\figpara}[2]{\begin{minipage}[t]{0.45\textwidth}\vspace{0cm}\begin{flushleft}\includegraphics[height=5cm]{#1.eps}\end{flushleft}\end{minipage}\hspace{0.5cm}\begin{minipage}[t]{0.45\textwidth}\vspace{-0.5cm}
\hspace{5.5cm}
\begin{flushright}\includegraphics[height=5cm]{#2.eps}\end{flushright}\end{minipage}}


\makeindex