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Import work from year 2014-2015

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Benjamin Bertrand
2017-06-16 09:48:07 +03:00
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\documentclass{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classConn}
\renewcommand{\arraystretch}{4}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom - Classe:
\section{Connaissance}
\begin{enumerate}
\item L'ensemble des entiers naturels est noté \parbox{2cm}{\dotfill}.\\
Donner 4 éléments différents de cet ensemble:
\\[0.5cm] . \dotfill
\item Compléter le tableau suivant
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Intervalle & Inéquation & Représentation graphique \\
\hline
$x \in \intOF{a}{b}$ &\hspace{3cm} & \hspace{5cm} \\
\hline
\end{tabular}
\end{center}
\item Faire le calcul suivant
\begin{eqnarray*}
A & = & (2 - 4)\times 3 + 2 (3 - 1)
\end{eqnarray*}
~\\[2cm]
\item Faire le calcul suivant
\begin{eqnarray*}
B & = & \frac{1}{2} + \frac{3}{7}
\end{eqnarray*}
\end{enumerate}
\columnbreak
Nom - Prénom - Classe
\section{Connaissance}
\begin{enumerate}
\item L'ensemble des rationnels est noté \parbox{2cm}{\dotfill}.\\
Donner 4 éléments différents de cet ensemble:
\\[0.5cm] . \dotfill
\item Compléter le tableau suivant
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Intervalle & Inéquation & Représentation graphique \\
\hline
$x \in \intFF{a}{b}$ &\hspace{3cm} & \hspace{5cm} \\
\hline
\end{tabular}
\end{center}
\item Faire le calcul suivant
\begin{eqnarray*}
A & = & (5 - 3)\times 2 + 2 (3 - 6)
\end{eqnarray*}
~\\[2cm]
\item Faire le calcul suivant
\begin{eqnarray*}
B & = & \frac{1}{3} + \frac{2}{4}
\end{eqnarray*}
\end{enumerate}
\end{multicols}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classConn}
\renewcommand{\arraystretch}{4}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom - Classe:
\section{Connaissance}
\begin{enumerate}
\item Expliquer comment résoudre une équation du type $f(x) = k$ \\
(vous devez ajouter les éléments nécéssaire pour répondre)
\hspace{-1cm}\includegraphics[scale=0.3]{./fig/courbe}
\\[2cm]
\item Faire les calculs suivants (simplifier quand c'est possible)
\begin{enumerate}
\item $A = \dfrac{2}{3} + \dfrac{5}{6} = $
\\[1cm]
\item $B = \dfrac{7}{2} \times \dfrac{1}{6} = $
\\[1cm]
\end{enumerate}
\end{enumerate}
\columnbreak
Nom - Prénom - Classe
\section{Connaissance}
\begin{enumerate}
\item Expliquer comment résoudre une équation du type $f(x) = k$ \\
(vous devez ajouter les éléments nécéssaire pour répondre)
\hspace{-1cm}\includegraphics[scale=0.3]{./fig/courbe}
\\[2cm]
\item Faire les calculs suivants (simplifier quand c'est possible)
\begin{enumerate}
\item $A = \dfrac{1}{2} + \dfrac{3}{4} = $
\\[1cm]
\item $B = \dfrac{4}{5} \times \dfrac{1}{4} = $
\\[1cm]
\end{enumerate}
\end{enumerate}
\end{multicols}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classCours}
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
% Title Page
\titre{Images, antécédents et intervalles}
% \seconde \premiereS \PSTMG \TSTMG
\classe{\seconde}
\date{Septembre 2014}
\begin{document}
\maketitle
\section{Intervalles}
\subsection{Les ensembles de nombres}
\begin{Def}
\begin{itemize}
\item L'ensemble des nombres entiers naturels est noté $\N$
\begin{eqnarray*}
\N & = & \left\{ 0, 1, 2, \cdots, 42, 43, \cdots, \right\}
\end{eqnarray*}
\item L'ensemble des nombres entiers relatifs est noté $\Z$
\begin{eqnarray*}
\Z & = & \left\{\cdots, -42, \cdots, -2, -1, 0, 1, 2, 3, \cdots, 42, \cdots \right\}
\end{eqnarray*}
\item L'ensemble des nombres rationnels est noté $\Q$
\begin{eqnarray*}
\Q & = & \left\{\mbox{ Les fractions de nombres entiers } \right\}
\end{eqnarray*}
\item L'ensemble des nombres réels est noté $\R$. Ils représentent tous les nombres que l'on connait.
\end{itemize}
\end{Def}
\subsection{Intervalles}
\begin{Def}
Soient $a$ et $b$ deux nombres réels tel que $a < b$ ($a$ plus petit que $b$).
\begin{itemize}
\item Intervalles bornées
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
$x \in \intFF{a}{b} $ & $a \leq x \leq b$ & rep graph \\
\hline
$x \in \intOF{a}{b} $ & $a < x \leq b$ & rep graph \\
\hline
$x \in \intFO{a}{b} $ & $a \leq x < b$ & rep graph \\
\hline
$x \in \intOO{a}{b} $ & $a < x < b$ & rep graph \\
\hline
\end{tabular}
\end{center}
\item Intervalles non bornées
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
$x \in \intFO{a}{+\infty} $ & $a \leq x$ & rep graph \\
\hline
$x \in \intOO{a}{+\infty} $ & $a < x$ & rep graph \\
\hline
$x \in \intOO{-\infty}{a} $ & $a > x$ & rep graph \\
\hline
$x \in \intOF{-\infty}{a} $ & $a \geq x$ & rep graph \\
\hline
\end{tabular}
\end{center}
\end{itemize}
\end{Def}
\begin{Ex}
On fait plusieurs exemples
\end{Ex}
\paragraph{Exo asso:} 1, 2 p 46
\section{Fonctions, images et antécédents}
\begin{Def}
Soit $\mathcal{D}$ un intervalle de $\R$. Définition une fonction $f$ sur $\mathcal{D}$, c'est associer à chaque nombre de $\mathcal{D}$ un unique nombre réel noté $f(x)$.
On note alors
\begin{eqnarray*}
f: & \mathcal{D} \rightarrow & \R \\
& x \mapsto & f(x)
\end{eqnarray*}
\end{Def}
\begin{Rmq}
$x$ est appelé la \textbf{variable}. $\mathcal{D}$ est appelé le \textbf{l'ensemble de définition} de $f$.
\end{Rmq}
\begin{Rmq}
Représentation graphique avec le vocabulaire pour la suite
\end{Rmq}
\begin{Def}
Soit $a$ un réel de l'ensemble de définition de $f$ tel que $f(a) = b$. Alors on dit que
\begin{itemize}
\item $b$ est l'image de $a$ par la fonction $f$.
\item $a$ est l'antécédent de $b$ par la fonction $f$.
\end{itemize}
\end{Def}
\section{Résolution graphique d'équations et d'inéquations}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
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Notes sur le cours autour images et des intervalles
###################################################
:date: 2015-07-01
:modified: 2015-07-01
:tags: Fonctions,Cours, Intervalle
:category: 2nd
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers fonctions_ref.ods <fonctions_ref.ods>`_
`Lien vers Img_ant_inter.pdf <Img_ant_inter.pdf>`_
`Lien vers pres_graph.pdf <pres_graph.pdf>`_
`Lien vers Img_ant_inter.tex <Img_ant_inter.tex>`_
`Lien vers pres_graph.tex <pres_graph.tex>`_
`Lien vers fig/lineaire.jpg <fig/lineaire.jpg>`_
`Lien vers fig/lineaire.png <fig/lineaire.png>`_
`Lien vers fig/affine.png <fig/affine.png>`_
`Lien vers fig/inverse.png <fig/inverse.png>`_
`Lien vers fig/carre.png <fig/carre.png>`_
`Lien vers fig/carre.jpg <fig/carre.jpg>`_
`Lien vers fig/affine.jpg <fig/affine.jpg>`_
`Lien vers fig/inverse.jpg <fig/inverse.jpg>`_

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\documentclass[a4paper,10pt,xcolor=table]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classPres}
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
\author{}
\title{}
\date{}
\begin{document}
\begin{frame}{Fonction affine \\$f :x \mapsto 7x + 3$}
\begin{center}
\includegraphics[scale=0.26]{./fig/affine}
\end{center}
\end{frame}
\begin{frame}{Fonction linéaire \\$g :x \mapsto -3x$}
\begin{center}
\includegraphics[scale=0.26]{./fig/lineaire}
\end{center}
\end{frame}
\begin{frame}{Fonction carré \\$h :x \mapsto x^2$}
\begin{center}
\includegraphics[scale=0.26]{./fig/carre}
\end{center}
\end{frame}
\begin{frame}{Fonction inverse \\$i :x \mapsto \frac{1}{x}$}
\begin{center}
\includegraphics[scale=0.26]{./fig/inverse}
\end{center}
\end{frame}
\end{document}

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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classCours}
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
% Title Page
\titre{Fiches fonctions}
\classe{\seconde}
\date{Septembre 2014}
\begin{document}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.7]{./fig/graph.pdf}
\begin{center}
$f:x \mapsto x$
\end{center}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.7]{./fig/graph2.pdf}
\begin{center}
$g:x \mapsto 2x - 2$
\end{center}
\end{minipage}
\vspace{0.5cm}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.7]{./fig/graph3.pdf}
\begin{center}
$h:x \mapsto (x-1)^2 - 3$
\end{center}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.7]{./fig/graph4.pdf}
\begin{center}
$i:x \mapsto \frac{1}{3}x^3 - x^2 - \frac{1}{3}x + 1$
\end{center}
\end{minipage}
\vspace{0.5cm}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.7]{./fig/graph5.pdf}
\begin{center}
$j:x \mapsto x-1$
\end{center}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.7]{./fig/graph6.pdf}
\begin{center}
$k:x \mapsto (x+1)^2 - 2$
\end{center}
\end{minipage}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\begin{pspicture}(-5,-5)(5.2,5.2)
\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0, gridcolor=black!40]
\psaxes
[
%ytrigLabels=true,
linewidth=\pslinewidth,
%labelFontSize=\scriptscriptstyle,
tickcolor=gray,
ticksize=-1.5pt 1.5pt,
xlabelsep=3pt,
arrowscale=1,
%trigLabelBase=4,
]{->}(0,0)(-5,-5)(5,5)[$x$,90][$f(x)$,0]
\psset{algebraic,linewidth=1.5pt}
\psplot{-5}{5}{x}
\end{pspicture}

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\begin{pspicture}(-5,-5)(5.2,5.2)
\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0, gridcolor=black!40]
\psaxes
[
%ytrigLabels=true,
linewidth=\pslinewidth,
%labelFontSize=\scriptscriptstyle,
tickcolor=gray,
ticksize=-1.5pt 1.5pt,
xlabelsep=3pt,
arrowscale=1,
%trigLabelBase=4,
]{->}(0,0)(-5,-5)(5,5)[$x$,90][$g(x)$,0]
\psset{algebraic,linewidth=1.5pt}
\psplot{-5}{5}{2 * x - 2}
\end{pspicture}

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\begin{pspicture}(-5,-5)(5.2,5.2)
\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0, gridcolor=black!40]
\psaxes
[
%ytrigLabels=true,
linewidth=\pslinewidth,
%labelFontSize=\scriptscriptstyle,
tickcolor=gray,
ticksize=-1.5pt 1.5pt,
xlabelsep=3pt,
arrowscale=1,
%trigLabelBase=4,
]{->}(0,0)(-5,-5)(5,5)[$x$,90][$h(x)$,0]
\psset{algebraic,linewidth=1.5pt}
\psplot{-5}{5}{(x-1)^2 - 3}
\end{pspicture}

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\begin{pspicture}(-5,-5)(5.2,5.2)
\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0, gridcolor=black!40]
\psaxes
[
%ytrigLabels=true,
linewidth=\pslinewidth,
%labelFontSize=\scriptscriptstyle,
tickcolor=gray,
ticksize=-1.5pt 1.5pt,
xlabelsep=3pt,
arrowscale=1,
%trigLabelBase=4,
]{->}(0,0)(-5,-5)(5,5)[$x$,90][$i(x)$,0]
\psset{algebraic,linewidth=1.5pt}
\psplot{-5}{5}{1/3 * x^3 - 1*x^2 - 1/3*x + 1}
\end{pspicture}

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\begin{pspicture}(-5,-5)(5.2,5.2)
%\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0, gridcolor=black!40]
\psaxes
[
%ytrigLabels=true,
linewidth=\pslinewidth,
%labelFontSize=\scriptscriptstyle,
tickcolor=gray,
ticksize=-1.5pt 1.5pt,
xlabelsep=3pt,
arrowscale=1,
%trigLabelBase=4,
]{->}(0,0)(-5,-5)(5,5)[$x$,90][$j(x)$,0]
\psset{algebraic,linewidth=1.5pt}
\psplot{-5}{5}{x - 1}
\end{pspicture}

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\begin{pspicture}(-5,-5)(5.2,5.2)
%\psgrid[griddots=10,gridlabels=0pt, subgriddiv=0, gridcolor=black!40]
\psaxes
[
%ytrigLabels=true,
linewidth=\pslinewidth,
%labelFontSize=\scriptscriptstyle,
tickcolor=gray,
ticksize=-1.5pt 1.5pt,
xlabelsep=3pt,
arrowscale=1,
%trigLabelBase=4,
]{->}(0,0)(-5,-5)(5,5)[$x$,90][$k(x)$,0]
\psset{algebraic,linewidth=1.5pt}
\psplot{-5}{5}{(x+1)^2 - 2}
\end{pspicture}

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#!/bin/sh
# on enlève l’extension du 1er argument
FILE=${1%.*}
TMPFILE=pstemp
# création d’un fichier temporaire psttemp.tex
cat > $TMPFILE.tex <<EOF
\documentclass{article}
\usepackage{pstricks}
\usepackage{pstricks-add}
\usepackage{pst-eps}
\usepackage{pst-eucl}
\usepackage{pst-plot}
\usepackage{pst-math}
\thispagestyle{empty}
\begin{document}
\begin{TeXtoEPS}
\input{$FILE}
\end{TeXtoEPS}
\end{document}
EOF
# Création du fichier dvi
latex $TMPFILE
# Création du fichier eps
dvips -E $TMPFILE.dvi -o $TMPFILE.eps
# Création du fichier pdf
epstopdf $TMPFILE.eps --debug --outfile=$FILE.pdf
# effacement des fichiers temporaires
rm -f $TMPFILE.*

39
2nd/Fonctions/Img_and_inter/fiche_fct/index.rst Normal file
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Notes sur une fiche avec des graphiques pour la réslution d'équation et d'inéquations.
######################################################################################
:date: 2015-07-01
:modified: 2015-07-01
:tags: Fonctions
:category: 2nd
:authors: Benjamin Bertrand
:summary: Feuille avec des graphiques pour résoudre graphiquement des équations et des inéquations.
`Lien vers fiche_fct.pdf <fiche_fct.pdf>`_
`Lien vers fiche_fct.tex <fiche_fct.tex>`_
`Lien vers fig/graph2.pdf <fig/graph2.pdf>`_
`Lien vers fig/graph6.tex <fig/graph6.tex>`_
`Lien vers fig/graph3.pdf <fig/graph3.pdf>`_
`Lien vers fig/graph6.pdf <fig/graph6.pdf>`_
`Lien vers fig/graph.pdf <fig/graph.pdf>`_
`Lien vers fig/graph.tex <fig/graph.tex>`_
`Lien vers fig/graph2.tex <fig/graph2.tex>`_
`Lien vers fig/graph4.tex <fig/graph4.tex>`_
`Lien vers fig/graph4.pdf <fig/graph4.pdf>`_
`Lien vers fig/graph3.tex <fig/graph3.tex>`_
`Lien vers fig/graph5.pdf <fig/graph5.pdf>`_
`Lien vers fig/graph5.tex <fig/graph5.tex>`_

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2nd/Fonctions/Img_and_inter/fiche_fct2/fiche_fct2.tex Normal file
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classCours}
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
% Title Page
\titre{Fiches fonctions}
\classe{\seconde}
\date{octobre 2014}
\begin{document}
\hspace{-2cm}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.35]{./fig/graph1}
\end{minipage}
\hspace{1cm}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.32]{./fig/graph2}
\end{minipage}
\vspace{0.5cm}
\begin{minipage}{0.5\textwidth}
$f:x \mapsto x^2 + x - 2$
\begin{tikzpicture}
\draw[very thin, gray] (-3,-3) grid (3,5);
\draw[->, thick] (-3,0) -- (3,0) node[below right] {$x$};
\draw[->, very thick] (0,-3) -- (0,5) node[above] {$y$};
\draw (0,0) node[below right, scale=0.7 ] {$O$};
\draw (0,1) node {-} node[left] {$J$};
\draw (1,0) node[rotate=90] {-} node[below] {$I$};
\clip (-3,-3) rectangle (3,5);
\draw[very thick] plot [domain=-3:3] (\x, {(\x+2)*(\x - 1)});
\end{tikzpicture}
\end{minipage}
\begin{minipage}{0.5\textwidth}
$g:x \mapsto 2x + 1$
\begin{tikzpicture}
\draw[very thin, gray] (-3,-3) grid (3,5);
\draw[->, thick] (-3,0) -- (3,0) node[below right] {$x$};
\draw[->, very thick] (0,-3) -- (0,5) node[above] {$y$};
\draw (0,0) node[below right, scale=0.7 ] {$O$};
\draw (0,1) node {-} node[left] {$J$};
\draw (1,0) node[rotate=90] {-} node[below] {$I$};
\clip (-3,-3) rectangle (3,5);
\draw[very thick] plot [domain=-3:3] (\x, {2*\x + 1});
\end{tikzpicture}
\end{minipage}
\vspace{0.5cm}
\begin{center}
\includegraphics[scale=0.6]{./fig/2graph}
\end{center}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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2nd/Fonctions/Img_and_inter/fiche_fct2/index.rst Normal file
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Notes sur une autre fiche avec des graphiques pour la réslution d'équation et d'inéquations.
############################################################################################
:date: 2015-07-01
:modified: 2015-07-01
:tags: Fonctions
:category: 2nd
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers fiche_fct2.tex <fiche_fct2.tex>`_
`Lien vers fiche_fct2.pdf <fiche_fct2.pdf>`_
`Lien vers fig/graph2.pdf <fig/graph2.pdf>`_
`Lien vers fig/graph1.pdf <fig/graph1.pdf>`_
`Lien vers fig/2graph.png <fig/2graph.png>`_