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名书镇贴 东西慢慢加进来好了，顺便看看公式渲染的情况。
名书镇贴
东西慢慢加进来好了，顺便看看公式渲染的情况。
$$ (\nabla u)_r = \frac{\partial u}{\partial r},\ (\nabla u)_{\theta} = \frac 1 r \frac{\partial u}{\partial \theta},\ (\nabla u)_z = \frac{\partial u}{\partial z} $$
$$ \nabla \cdot \mathbf{A} = \frac 1 r \frac{\partial (r Ar)}{\partial r} + \frac 1 r \frac{\partial A{\theta}}{\partial \theta} + \frac{\partial A_z}{\partial z} $$
$$ \nabla \times \mathbf{A} = \frac 1 r \left[\frac{\partial Az}{\partial \theta} - \frac{\partial (rA{\theta})}{\partial z}\right]\mathbf{e_r} + \left[\frac{\partial A_r}{\partial z} - \frac{\partial Az}{\partial r}\right]\mathbf{e{\theta}} + \frac 1 r \left[\frac{\partial (rA_{\theta})}{\partial r} - \frac{\partial A_r}{\partial \theta}\right]\mathbf{e_z} $$
$$ (\nabla u)_r = \frac{\partial u}{\partial r},\ (\nabla u)_{\theta} = \frac 1 r \frac{\partial u}{\partial \theta},\ (\nabla u)_{\phi} = \frac{1}{r \sin \theta} \frac{\partial u}{\partial \phi} $$
$$ \nabla \cdot \mathbf{A} = \frac{1}{r^2} \frac{\partial (r^2 Ar)}{\partial r} + \frac{1}{r \sin \theta} \frac{\partial (\sin \theta A{\theta})}{\partial \theta} + \frac{1}{r \sin \theta} \frac{\partial A_{\phi}}{\partial \phi} $$
$$ \nabla \times \mathbf{A} = \frac{1}{r \sin \theta} \left[\frac{\partial (\sin \theta A{\phi})}{\partial \theta} - \frac{\partial A{\theta}}{\partial \phi}\right]\mathbf{e_r} + \frac 1 r \left[\frac{1}{\sin \theta}\frac{\partial Ar}{\partial \phi} - \frac{\partial (r A{\phi})}{\partial r}\right]\mathbf{e{\theta}} + \frac 1 r \left[\frac{\partial (rA{\theta})}{\partial r} - \frac{\partial Ar}{\partial \theta}\right]\mathbf{e{\phi}} $$
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柱坐标系下的梯度散度旋度公式
$$ (\nabla u)_r = \frac{\partial u}{\partial r},\ (\nabla u)_{\theta} = \frac 1 r \frac{\partial u}{\partial \theta},\ (\nabla u)_z = \frac{\partial u}{\partial z} $$
$$ \nabla \cdot \mathbf{A} = \frac 1 r \frac{\partial (r Ar)}{\partial r} + \frac 1 r \frac{\partial A{\theta}}{\partial \theta} + \frac{\partial A_z}{\partial z} $$
$$ \nabla \times \mathbf{A} = \frac 1 r \left[\frac{\partial Az}{\partial \theta} - \frac{\partial (rA{\theta})}{\partial z}\right]\mathbf{e_r} + \left[\frac{\partial A_r}{\partial z} - \frac{\partial Az}{\partial r}\right]\mathbf{e{\theta}} + \frac 1 r \left[\frac{\partial (rA_{\theta})}{\partial r} - \frac{\partial A_r}{\partial \theta}\right]\mathbf{e_z} $$
球坐标系下的梯度散度旋度公式
$$ (\nabla u)_r = \frac{\partial u}{\partial r},\ (\nabla u)_{\theta} = \frac 1 r \frac{\partial u}{\partial \theta},\ (\nabla u)_{\phi} = \frac{1}{r \sin \theta} \frac{\partial u}{\partial \phi} $$
$$ \nabla \cdot \mathbf{A} = \frac{1}{r^2} \frac{\partial (r^2 Ar)}{\partial r} + \frac{1}{r \sin \theta} \frac{\partial (\sin \theta A{\theta})}{\partial \theta} + \frac{1}{r \sin \theta} \frac{\partial A_{\phi}}{\partial \phi} $$
$$ \nabla \times \mathbf{A} = \frac{1}{r \sin \theta} \left[\frac{\partial (\sin \theta A{\phi})}{\partial \theta} - \frac{\partial A{\theta}}{\partial \phi}\right]\mathbf{e_r} + \frac 1 r \left[\frac{1}{\sin \theta}\frac{\partial Ar}{\partial \phi} - \frac{\partial (r A{\phi})}{\partial r}\right]\mathbf{e{\theta}} + \frac 1 r \left[\frac{\partial (rA{\theta})}{\partial r} - \frac{\partial Ar}{\partial \theta}\right]\mathbf{e{\phi}} $$