Commit 85551652 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent aec41aa5
Pipeline #13558 canceled with stage
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$`div\,\overrightarrow{U}=\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}`$
* La combinaison des deux expressions permet d'exprimer la
*divergence du gradient de $`f`$ en coordonnées cartésiennes* :
**$`div\,\overrightarrow{grad}\,f`$**$`\;= \dfrac{\partial}{\partial x}\big(\dfrac{\partial f}{\partial x}\big)+\dfrac{\partial}{\partial y}\big(\dfrac{\partial f}{\partial y}\big)+\dfrac{\partial}{\partial z}\big(\dfrac{\partial f}{\partial z}\big)`$
<br>
*$`div\,\overrightarrow{grad}\,f`$*$`\;= \dfrac{\partial}{\partial x}\left(\dfrac{\partial f}{\partial x}\right)+\dfrac{\partial}{\partial y}\left(\dfrac{\partial f}{\partial y}\right)+\dfrac{\partial}{\partial z}\left(\dfrac{\partial f}{\partial z}\right)`$
*$`\quad = \dfrac{\partial^2 f}{\partial x^2}+\dfrac{\partial^2 f}{\partial y^2}+\dfrac{\partial^2 f}{\partial z^2}`$*
<br>
et l'**opérateur $`div\,\overrightarrow{grad}`$ en coordonnées cartésiennes** :
<br>
**$`div\,\overrightarrow{grad}= \dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}+\dfrac{\partial^2}{\partial z^2}`$*
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