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M3P2
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4238fbc8
Commit
4238fbc8
authored
Sep 08, 2024
by
Claude Meny
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Update 12.temporary_ins/08.grad-div-rot/70.combinaisons-of-operators/20.overview/cheatsheet.fr.md
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12.temporary_ins/08.grad-div-rot/70.combinaisons-of-operators/20.overview/cheatsheet.fr.md
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4238fbc8
...
@@ -188,7 +188,7 @@ leurs expressions dans les différents systèmes de coordonnées n'utilisent qu
...
@@ -188,7 +188,7 @@ leurs expressions dans les différents systèmes de coordonnées n'utilisent qu
!!!
*Exemples*
: en coordonnées cartésiennes $
`(x,y,z)`
$,
!!!
*Exemples*
: en coordonnées cartésiennes $
`(x,y,z)`
$,
!!!
*
la propagation d'une onde plane progressive monochromatique $
`\Phi`
$ dans un milieu homogène et isotrope se propageant vers les x positifs
!!!
*
la propagation d'une onde plane progressive monochromatique $
`\Phi`
$ dans un milieu homogène et isotrope se propageant vers les x positifs
!!! selon la loi
!!! selon la loi
!!! $
`\dfrac{\partial^2 \Phi(x,t)}{\partial x^2}
-\dfrac{1}{\mathscr{v}^2}\,-\dfrac{1}{\mathscr{v}^2}\,\dfrac{\partial^2 \Phi(x,t)}{\partial t^2}
`
$.
!!! $
`\dfrac{\partial^2 \Phi(x,t)}{\partial x^2}
\,-\dfrac{1}{\mathscr{v}^2}\,\dfrac{\partial^2 \Phi(x,t)}{\partial t^2}=0
`
$.
!!!
*
L'équation de diffusion d'une grandeur physique de densité $
`\Phi(x,y,z,t)`
$ s'écrit
!!!
*
L'équation de diffusion d'une grandeur physique de densité $
`\Phi(x,y,z,t)`
$ s'écrit
!!! $
`\displaystyle\dfrac{\partial \Phi(\vec{r},t)}{\partial t}=\sum_{x_i=1}^3\sum_{x_j=1}^3\dfrac{\partial}{\partial x_i}\Bigg[\mathscr{D}(\Phi,\vec{r})\,\dfrac{\partial \Phi(\vec{r},t)}{\partial x_j}\Bigg]`
$
!!! $
`\displaystyle\dfrac{\partial \Phi(\vec{r},t)}{\partial t}=\sum_{x_i=1}^3\sum_{x_j=1}^3\dfrac{\partial}{\partial x_i}\Bigg[\mathscr{D}(\Phi,\vec{r})\,\dfrac{\partial \Phi(\vec{r},t)}{\partial x_j}\Bigg]`
$
...
...
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