Feat(1ST): ajoute le cours sur les suites
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Bertrand Benjamin 2023-02-20 09:12:37 +01:00
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\documentclass[a4paper,10pt]{article}
\usepackage{myXsim}
\author{Benjamin Bertrand}
\title{Généralité suite - Cours}
\date{Février 2023}
\pagestyle{empty}
\begin{document}
\maketitle
\section{Modélisation avec des suites}
En se basant sur les premières données de malade du covid19, nous avons cherché à prédire le nombre de contaminés les jours suivants.
\begin{center}
\begin{tabular}{|l|c|}\hline%
\bfseries Jour & \bfseries Nombre de cas
\csvreader[head to column names]{./covid_0226_0301.csv}{}%
{\\\jours & \cas}%
\\\hline
\end{tabular}
\smallskip
\textbf{Document:} Nombre de cas cumulé de covid
\end{center}
Pour cela, nous avons étudié deux modèles
\bigskip
\begin{minipage}{0.5\textwidth}
\begin{center}
Modèle 1: Linéaire
\end{center}
\begin{tikzpicture}[
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
]
%Nodes
\node[roundnode] (leftterme) {\makebox[0.5cm]{}};
\node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{}};
%Lines
\path[->] (leftterme.east) edge [bend left] node [above] {$+$....} (centerterm.west);
\end{tikzpicture}
\hspace{1cm}
$ u_{n+1} = u_n + .... $
\medskip
C'est une suite \textbf{arithmétique}.
\medskip
\begin{center}
\includegraphics[scale=0.3]{./fig/covid_arith}
\medskip
\begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=1]
\tkzInit[xmin=0,xmax=5,xstep=1,
ymin=0,ymax=5,ystep=1]
\tkzDrawX[noticks]
\tkzDrawY[noticks]
\end{tikzpicture}
\end{center}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\begin{center}
Modèle 2: Exponentiel
\end{center}
\begin{tikzpicture}[
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
]
%Nodes
\node[roundnode] (leftterme) {\makebox[0.5cm]{}};
\node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{}};
%Lines
\path[->] (leftterme.east) edge [bend left] node [above] {$\times$....} (centerterm.west);
\end{tikzpicture}
\hspace{1cm}
$ u_{n+1} = u_n \times .... $
\medskip
C'est une suite \textbf{géométrique}.
\medskip
\begin{center}
\includegraphics[scale=0.2]{./fig/corid_geo}
\medskip
\begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=1]
\tkzInit[xmin=0,xmax=5,xstep=1,
ymin=0,ymax=5,ystep=1]
\tkzDrawX[noticks]
\tkzDrawY[noticks]
\end{tikzpicture}
\end{center}
\end{minipage}
\afaire{Tracer l'allure du graphique et compléter les pointillés.}
\end{document}

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