Update cheatsheet.fr.md

12.temporary_ins/08.grad-div-rot/20.div/20.overview/cheatsheet.fr.md

@@ -14,50 +14,18 @@ visible: false
 
 ##### Expression de la divergence en coordonnées cartésiennes
 
-<br>**$`\mathbf{
-div\,\overrightarrow{X}}`$**$`\mathbf{\;=\dfrac{d\Phi_X}{d\tau}}`$**$`\;\mathbf{=\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z}
-}`$**
-
-<br>**$`\mathbf{
-div\,\overrightarrow{X}}\;\color{black}{=\;\dfrac{d\Phi_X}{d\tau}}\;
-=\;\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z}}`$**
-
-<br>**$`div\,\overrightarrow{X}\;=\;\color{gray}{\dfrac{d\Phi_X}{d\tau}}\;=\;\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z}
-`$**
-
 <br>**$`\mathbf{div\,\overrightarrow{X}\;=\;\color{black}{\dfrac{d\Phi_X}{d\tau}}\;=\;\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z}
 }`$**
 
 ##### Expression de la divergence en coordonnées cylindriques
 
-<br>**$`\mathbf{div\,\overrightarrow{X}}`$**$`\boldsymbol{\mathbf{\;=\dfrac{d\Phi_X}{d\tau}}}`$**$`\boldsymbol{\mathbf{\;=\dfrac{1}{\rho}\;\dfrac{\partial\,(\,\rho\,X_{\rho})}{\partial\,\rho}
-+\dfrac{1}{\rho}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}+\dfrac{\partial\,X_{z}}{\partial\,z}}}`$**
-
-<br>
-
 <br>**$`div\,\overrightarrow{X}\;\color{gray}{=\;\dfrac{d\Phi_X}{d\tau}}\;=\;\dfrac{1}{\rho}\;\dfrac{\partial\,(\,\rho\,X_{\rho})}{\partial\,\rho}
 +\dfrac{1}{\rho}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}+\dfrac{\partial\,X_{z}}{\partial\,z}`$**
 
 
 ##### Expression de la divergence en coordonnées sphériques
 
-**$`\boldsymbol{\mathbf{\begin{align}
-div\,\overrightarrow{X}\color{grey{\;=\;\dfrac{d\Phi_X}{d\tau}}\,=\; &\dfrac{1}{r^2}\;\dfrac{\partial\,(r^2\,X_r}{\partial\,r}\\
-\\
-& \quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}\\
-\\
-& \quad\quad\quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}\end{align}}}`$**
-
-<br>
-
-**$`\mathbf{\boldsymbol{\begin{align}
+*<br>*$`\mathbf{\boldsymbol{\begin{align}
 div\,\overrightarrow{X}\color{gray}{\;=\dfrac{d\Phi_X}{d\tau}}\,= &\dfrac{1}{r^2}\;\dfrac{\partial\,(r^2\,X_r}{\partial\,r}\\
 & \quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}\\
 & \quad\quad\quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}\end{align}}}`$**
-
-<br>
-
-**$`\mathbf{\boldsymbol{\begin{align}
-div\,\overrightarrow{X}\,= &\dfrac{1}{r^2}\;\dfrac{\partial\,(r^2\,X_r}{\partial\,r}\\
-& \quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}\\
-& \quad\quad\quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}\end{align}}}`$**