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M3P2
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adf57e04
Commit
adf57e04
authored
Nov 11, 2019
by
Claude Meny
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Update textbook.en.md
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10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
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adf57e04
...
@@ -227,7 +227,7 @@ EN : in orthonormal Cartesian coordinate : <br>
...
@@ -227,7 +227,7 @@ EN : in orthonormal Cartesian coordinate : <br>
$
`\Delta = \dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}+\dfrac{\partial^2}{\partial z^2}`
$
$
`\Delta = \dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}+\dfrac{\partial^2}{\partial z^2}`
$
$
`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`
$
<br>
$
`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`
$
<br>
$
`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\
:div\,\overrightarrow{U} - \overrightarrow{rot}\:\overrightarrow{rot}\,
\overrightarrow{U}`
$
<br>
$
`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\
;div\;\overrightarrow{U} - \overrightarrow{rot}\;\overrightarrow{rot}\;
\overrightarrow{U}`
$
<br>
ES : operador laplaciana vectorial, laplaciana vectorial, laplaciana de un campo vectorial
<br>
ES : operador laplaciana vectorial, laplaciana vectorial, laplaciana de un campo vectorial
<br>
FR : opérateur laplacien, laplacien, d'un champ scalaire ou d'un champ vecoriel
<br>
FR : opérateur laplacien, laplacien, d'un champ scalaire ou d'un champ vecoriel
<br>
EN : laplacian operator, vectorial laplacian, laplacian of a vector field
<br>
EN : laplacian operator, vectorial laplacian, laplacian of a vector field
<br>
...
@@ -235,7 +235,7 @@ in orthonormal Cartesian coordinate : <br>
...
@@ -235,7 +235,7 @@ in orthonormal Cartesian coordinate : <br>
$
`\Delta\;\overrightarrow{U} = \overrightarrow{e_x}\left(\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2}\right)
$
`\Delta\;\overrightarrow{U} = \overrightarrow{e_x}\left(\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2}\right)
+\overrightarrow{e_y}\left(\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2}\right)
+\overrightarrow{e_y}\left(\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2}\right)
+\overrightarrow{e_z}\left(\dfrac{\partial^2\;U_z}{\partial x^2}+\dfrac{\partial^2\;U_z}{\partial y^2}+\dfrac{\partial^2\;U_z}{\partial z^2}\right)`
$
<br>
+\overrightarrow{e_z}\left(\dfrac{\partial^2\;U_z}{\partial x^2}+\dfrac{\partial^2\;U_z}{\partial y^2}+\dfrac{\partial^2\;U_z}{\partial z^2}\right)`
$
<br>
$
`\Delta\;\overrightarrow{U} = \left \
{
$
`\Delta\;\overrightarrow{U} = \left \
|
\begin{array}{r c l}
\begin{array}{r c l}
\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2} \\
\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2} \\
\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2} \\
\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2} \\
...
...
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