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M3P2
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6abe4a92
Commit
6abe4a92
authored
Sep 06, 2022
by
Claude Meny
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Update cheatsheet.fr.md
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12.temporary_ins/08.conservative-vector-fields/20.conservative-vector-fields-properties/20.overview/cheatsheet.fr.md
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6abe4a92
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...
@@ -449,11 +449,12 @@ $`\color{brown}{\mathbf{
##### Expression du gradient en coordonnées cartésiennes
$`
\l
eft.
\b
egin{align}
dl_x=dx
\L
ongrightarrow
$
`\dfrac{\partial x}{\partial dl_{x}
}=1\\
dl_y=dy \Longrightarrow
$`
\d
frac{
\p
artial y}{
\p
artial dl_{y}
}=1
\\
dl_z=dz
\L
ongrightarrow
$
`\dfrac{\partial z}{\partial dl_{z}
}=1\\
dl_x=dx
\L
ongrightarrow
\d
frac{
\p
artial x}{
\p
artial dl_x
}=1
\\
dl_y=dy
\L
ongrightarrow
\d
frac{
\p
artial y}{
\p
artial dl_y
}=1
\\
dl_z=dz
\L
ongrightarrow
\d
frac{
\p
artial z}{
\p
artial dl_z
}=1
\\
\e
nd{align}
\r
ight
\}
`$
$
`\Longrightarrow\color{brown}{\mathbf{\overrightarrow{grad}\,\phi=
$`
\L
ongrightarrow
\c
olor{brown}{
\m
athbf{
\o
verrightarrow{grad}
\,\p
hi=
\d
frac{
\p
artial
\p
hi}{
\p
artial x}
\,\o
verrightarrow{e_x}
+
\d
frac{
\p
artial
\p
hi}{
\p
artial y}
\,\o
verrightarrow{e_y}
+
\d
frac{
\p
artial
\p
hi}{
\p
artial z}
\,\o
verrightarrow{e_z}
...
...
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