Commit 1c7e63f2 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 8ff7a125
Pipeline #13551 canceled with stage
......@@ -186,14 +186,20 @@ $`\require{cancel}\quad = \left(\begin{array}{l}
* Au total nous obtenons l'expression simple :
**$`\large{\overrightarrow{grad}\big(div\;\overrightarrow{E}\big)
-\overrightarrow{rot}\big(\overrightarrow{rot}\,\overrightarrow{E}\big)}`$**
**$`\quad \large{=
**$`\overrightarrow{grad}\big(div\;\overrightarrow{E}\big)
-\overrightarrow{rot}\big(\overrightarrow{rot}\,\overrightarrow{E}\big)`$**
**$`\quad =
\left(\begin{array}{l}
\dfrac{\partial^2 U_x}{\partial x^2}\\
\dfrac{\partial^2 U_y}{\partial y^2}\\
\dfrac{\partial^2 U_z}{\partial z^2}\\
\end{array}\right)}`$**
\end{array}\right)`$**
Cette combinaison particulière d'opérateurs $`\overrightarrow{grad}`$, $`\overrightarrow{rot}`$ et $`div`$
constitue la **définition de l'opérateur Laplacien vectoriel** :
**$`\large{\overrightarrow{\Delta}=\overrightarrow{grad}\big(div\;\overrightarrow{E}\big)
-\overrightarrow{rot}\big(\overrightarrow{rot}\,\overrightarrow{E}\big)}`$**
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