Commit 6a1d2481 authored by Claude Meny's avatar Claude Meny

Update textbook.en.md

parent 3800c1ae
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......@@ -758,17 +758,33 @@ Mecánica newtoniana : espacio y el tiempo son desacoplados $`\Longrightarrow`$
$`\displaystyle\iint_S \overrightarrow{rot}\,\overrightarrow{E}\cdot \overrightarrow{dS}
= - \dfrac{\partial}{\partial t} \left( \displaystyle\iint_S \overrightarrow{B}\cdot \overrightarrow{dS}\right)`$
Stokes' theorem =
for all vectorial field $`\vec{X}`$,
$`\displaystyle\iint_{S\,orient.} \;\overrightarrow{rot}\;\overrightarrow{X} \cdot dS
= \displaystyle \oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{X}\cdot\overrightarrow{dl}`$
$`\displaystyle\iint_{S\,orient.} \overrightarrow{rot} \,\overrightarrow{E}\cdot \overrightarrow{dS}
= \displaystyle \oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}
= -\displaystyle\iint_{S \leftrightarrow \tau} \dfrac{\partial \overrightarrow{B}}{\partial t}\cdot \overrightarrow{dS}`$
Ostrogradsky’s theorem = divergence theorem (= Gauss's theorem) :
for all vectorial field $`\vec{X}`$,
$`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle \oiint_{S\leftrightarrow\tau} \overrightarrow{X}\cdot\overrightarrow{dS}`$
$`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle
\oiint_{S\leftrightarrow\tau} \overrightarrow{X}\cdot\overrightarrow{dS}`$
Stokes' theorem =
for all vectorial field $`\vec{X}`$,
$`\displaystyle\iint_{S\,orient.} \;\overrightarrow{rot}\;\overrightarrow{X} \cdot dS = \displaystyle \oint_{\Gamma\,orient.\overrightarrow{S}} \overrightarrow{X}\cdot\overrightarrow{dl}`$
$`\displaystyle\iint_{S\,orient.} \;\overrightarrow{rot}\;\overrightarrow{X} \cdot dS = \displaystyle
\oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{X}\cdot\overrightarrow{dl}`$
......
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