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