Divergence
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Divergence
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관련코스
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다변수 미적분학
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소분류
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수학, 물리
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선행 키워드
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연관 키워드
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Definition
- [math]\nabla\cdot\mathbf{A} = \cfrac{1}{\prod_j h_j} \frac{\partial }{\partial q^i}(A^i\prod_{j\ne i} h_j) [/math]
- Or, more explicitly in 3-dim,
- [math]\nabla\cdot\mathbf{A} = \cfrac{1}{h_1h_2h_3} \left[ {\partial\over\partial q_1}(A_1h_2h_3) + {\partial\over\partial q_2}(A_2h_3h_1) + {\partial\over\partial q_3}(A_3h_1h_2) \right][/math]
Cartesian coordinates
- [math]\nabla\cdot\mathbf{A} = {\partial A_x \over \partial x} + {\partial A_y \over \partial y} + {\partial A_z \over \partial z}[/math]
Cylindrical coordinates
- [math]\nabla\cdot\mathbf{A} = {1 \over \rho}{\partial \left( \rho A_\rho \right) \over \partial \rho}
+ {1 \over \rho}{\partial A_\varphi \over \partial \varphi}
+ {\partial A_z \over \partial z}[/math]
Spherical coordinates
- [math]\nabla\cdot\mathbf{A} = {1 \over r^2}{\partial \left( r^2 A_r \right) \over \partial r}
+ {1 \over r\sin\theta}{\partial \over \partial \theta} \left( A_\theta\sin\theta \right)
+ {1 \over r\sin\theta}{\partial A_\varphi \over \partial \varphi}[/math]