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@ -227,7 +227,7 @@ EN : in orthonormal Cartesian coordinate : <br> |
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$`\Delta = \dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}+\dfrac{\partial^2}{\partial z^2}`$ |
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$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`$ <br> |
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$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\:div\,\overrightarrow{U} - \overrightarrow{rot}\:\overrightarrow{rot}\,\overrightarrow{U}`$ <br> |
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$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\;div\;\overrightarrow{U} - \overrightarrow{rot}\;\overrightarrow{rot}\;\overrightarrow{U}`$ <br> |
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ES : operador laplaciana vectorial, laplaciana vectorial, laplaciana de un campo vectorial <br> |
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FR : opérateur laplacien, laplacien, d'un champ scalaire ou d'un champ vecoriel <br> |
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EN : laplacian operator, vectorial laplacian, laplacian of a vector field <br> |
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@ -235,7 +235,7 @@ in orthonormal Cartesian coordinate : <br> |
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$`\Delta\;\overrightarrow{U} = \overrightarrow{e_x}\left(\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2}\right) |
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+\overrightarrow{e_y}\left(\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2}\right) |
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+\overrightarrow{e_z}\left(\dfrac{\partial^2\;U_z}{\partial x^2}+\dfrac{\partial^2\;U_z}{\partial y^2}+\dfrac{\partial^2\;U_z}{\partial z^2}\right)`$ <br> |
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$`\Delta\;\overrightarrow{U} = \left \{ |
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$`\Delta\;\overrightarrow{U} = \left \| |
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\begin{array}{r c l} |
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\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2} \\ |
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\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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