Commit 45180aa2 authored by Claude Meny's avatar Claude Meny

Update cheatshhet.fr.md

parent dd5f2a30
Pipeline #13042 canceled with stage
...@@ -50,15 +50,17 @@ GRADIENT D'UN CHAMP SCALAIRE ...@@ -50,15 +50,17 @@ GRADIENT D'UN CHAMP SCALAIRE
*Expressions du gradient* *Expressions du gradient*
Coordonnées cartésiennes : Coordonnées cartésiennes :
$`\begin{align} $`\begin{align}
\overrightarrow{grad}\,V &=\dfrac{\partial V}{\partial x}\,\overrightarrow{e_x}+\dfrac{\partial V}{\partial y}\,\overrightarrow{e_y}+\dfrac{\partial V}{\partial z}\,\overrightarrow{e_z} \\ \overrightarrow{grad}\,V &=\dfrac{\partial V}{\partial x}\,\overrightarrow{e_x}+\dfrac{\partial V}{\partial y}\,\overrightarrow{e_y}+\dfrac{\partial V}{\partial z}\,\overrightarrow{e_z} \\
&=\nabla\,V\\ &=\nabla\,V
end{align}`$ \end{align}`$
  avec opérateur nabla $`\nabla=\dfrac{\partial}{\partial x}\,\overrightarrow{e_x}+\dfrac{\partial}{\partial y}\,\overrightarrow{e_y}+\dfrac{\partial}{\partial z}\,\overrightarrow{e_z}`$   avec opérateur nabla $`\nabla=\dfrac{\partial}{\partial x}\,\overrightarrow{e_x}+\dfrac{\partial}{\partial y}\,\overrightarrow{e_y}+\dfrac{\partial}{\partial z}\,\overrightarrow{e_z}`$
Coordonnées cylindriques :
Coordonnées cylindriques :
$`\overrightarrow{grad}\,V=\dfrac{\partial V}{\partial \rho}\,\overrightarrow{e_{\rho}}+\dfrac{1}{\rho}\,\dfrac{\partial V}{\partial \varphi}\,\overrightarrow{e_{\varphi}}+\dfrac{\partial V}{\partial z}\,\overrightarrow{e_z}`$ $`\overrightarrow{grad}\,V=\dfrac{\partial V}{\partial \rho}\,\overrightarrow{e_{\rho}}+\dfrac{1}{\rho}\,\dfrac{\partial V}{\partial \varphi}\,\overrightarrow{e_{\varphi}}+\dfrac{\partial V}{\partial z}\,\overrightarrow{e_z}`$
Coordonnées sphériques :
Coordonnées sphériques :
$`\overrightarrow{grad}\,V=\dfrac{\partial V}{\partial \rho}\,\overrightarrow{e_{\rho}}+\dfrac{1}{\rho}\,\dfrac{\partial V}{\partial \theta}\,\overrightarrow{e_{\theta}}+\dfrac{1}{\rho\,sin\,\theta}\,\dfrac{\partial V}{\partial \varphi}\,\overrightarrow{e_5\varphi}`$ $`\overrightarrow{grad}\,V=\dfrac{\partial V}{\partial \rho}\,\overrightarrow{e_{\rho}}+\dfrac{1}{\rho}\,\dfrac{\partial V}{\partial \theta}\,\overrightarrow{e_{\theta}}+\dfrac{1}{\rho\,sin\,\theta}\,\dfrac{\partial V}{\partial \varphi}\,\overrightarrow{e_5\varphi}`$
......
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