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Make coin par coeur fit into two pages

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flyingscorpio@arch-desktop 2021-10-10 19:29:57 +02:00
parent 2a5df099ba
commit b1df23d81e
2 changed files with 57 additions and 45 deletions
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28
analyse/main.tex
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@ -40,7 +40,7 @@
\paragraph{Dérivées et Primitives}
Usuelles~:
\begin{multicols}{2}
\begin{tabularx}{\linewidth}{YY}
\toprule
@ -82,9 +82,7 @@
\bottomrule
\end{tabularx}
Composées~:
\begin{multicols}{2}
\columnbreak
\begin{tabularx}{\linewidth}{lY}
\toprule
@ -136,7 +134,6 @@
\bottomrule
\end{tabularx}
\paragraph{Équations différentielles}
\begin{tabularx}{\linewidth}{lllc}
@ -147,11 +144,26 @@
\midrule
\multicolumn{2}{l}{$ay' + by = f(x)$} & $y_0 + \lambda e^{rx} \quad \text{ avec } r = \frac{-b}{a}$ & \makecell{$y_0$ solution particulière de \\ $ay' + by = f(x)$ \\ $f$ une fonction et $a, b, \lambda\in\mathbb{R}$} \\
\midrule
\multirow{3}{*}{$ay'' + by' + cy = 0$} & $\Delta > 0$ & $\lambda e^{r_1 x} + \mu e^{r_2 x} + y_1$ & \multirowcell{3}[0pt][c]{$\lambda, \mu \in \mathbb{R}$, $y_1$ solution particulière \\ $\alpha = \frac{-b}{2a} \quad \beta = \frac{\sqrt{|\Delta|}}{2a}$} \\
\multirow{3}{*}{$ay'' + by' + cy = 0$} & $\Delta > 0$ & $\lambda e^{r_1 x} + \mu e^{r_2 x}$ & \multirowcell{3}[0pt][c]{$\lambda, \mu \in \mathbb{R}$ \\ $\alpha = \frac{-b}{2a} \quad \beta = \frac{\sqrt{|\Delta|}}{2a}$} \\
\cline{2-3}
& $\Delta = 0$ & $(\lambda x + \mu) e^{r_0 x} + y_1$ & \\
& $\Delta = 0$ & $(\lambda x + \mu) e^{r_0 x}$ & \\
\cline{2-3}
& $\Delta < 0$ & $e^{\alpha x}(\lambda\cos{(\beta x)} + \mu\sin{(\beta x)}) + y_1$ & \\
& $\Delta < 0$ & $e^{\alpha x}(\lambda\cos{(\beta x)} + \mu\sin{(\beta x)})$ & \\
\bottomrule
\end{tabularx}
\paragraph{Solutions particulières des équations différentielles de 2\up{nd} ordre}
\begin{tabularx}{\linewidth}{XX}
\toprule
\multicolumn{2}{l}{Second membre du type $e^{\alpha x}P(x)$} \\
$\alpha$ non racine & $y_1 = e^{\alpha x} Q(x)$ \\
$\alpha$ racine simple & $y_1 = x e^{\alpha x} Q(x)$ \\
$\alpha$ racine double & $y_1 = x^2 e^{\alpha x} Q(x)$ \\
\midrule
\multicolumn{2}{l}{Second membre du type $e^{\alpha x}(P_1(x)\cos(\beta x) + P_2(x)\sin(\beta x))$} \\
$\alpha + i\beta$ non racine & $y_1 = e^{\alpha x}(Q_1(x)\cos(\beta x) + Q_2(x)\sin(\beta x))$ \\
$\alpha + i\beta$ racine & $y_1 = x e^{\alpha x}(Q_1(x)\cos(\beta x) + Q_2(x)\sin(\beta x))$ \\
\bottomrule
\end{tabularx}

2
cours.sty
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@ -2,7 +2,7 @@
\usepackage[
%showframe,
a4paper,includeheadfoot,margin=2cm
a4paper,includeheadfoot,margin=2cm,top=1cm,bottom=1cm
]{geometry}
\setcounter{tocdepth}{2}