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M3P2
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aa607bc9
Commit
aa607bc9
authored
Sep 27, 2022
by
Claude Meny
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Update cheatsheet.fr.md
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@@ -70,17 +70,17 @@ visible: false
#### Relations entre les propriétés locales d'un champ scalaire et sa propagation
*
Tout champ scalaire $
`f`
$ (continue et au moins deux fois dérivable) possède son champ de gradient $
`\overrightarrow{f}`
$.
*
*Si le gradient $`\overrightarrow{f}`$ vérifie l'*
**équation d'onde**
:
*
*Si le gradient $`\overrightarrow{f}`$ vérifie l'*
**équation d'onde**
:
<br>
*$`div\,\overrightarrow{grad}\,f-\dfrac{1}{\mathscr
‘
v}^2}\dfrac{\partial^2 f}{\partial t^2}`$*
*$`div\,\overrightarrow{grad}\,f-\dfrac{1}{\mathscr
{
v}^2}\dfrac{\partial^2 f}{\partial t^2}`$*
<br>
ou écrit avec le laplacien scalaire :
<br>
**$`\Delta\,f-\dfrac{1}{\mathscr
‘
v}^2}\dfrac{\partial^2 f}{\partial t^2}`$**
**$`\Delta\,f-\dfrac{1}{\mathscr
{
v}^2}\dfrac{\partial^2 f}{\partial t^2}`$**
<br>
**alors le champ scalaire $ f`$ se propage à la célérité $`\mathscr{v}`$**
.
<br><br>
#### L'opérateur laplacien vectoriel, et la propagation d'un champ vectoriel
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