Nabla in verschillende assenstelsels: verschil tussen versies

! style="background: white" | Vector Laplaciaan <span style="font-weight: normal">{{math|∇²'''A''' ≡ ∆'''A'''}}</span>

| <math>\nabla^2 A_x \hat{\mathbf x} + \nabla^2 A_y \hat{\mathbf y} + \nabla^2 A_z \hat{\mathbf z} </math>

\mathopen{}\left(\nabla^2 A_\rho - \frac{A_\rho}{\rho^2} - \frac{2}{\rho^2} \frac{\partial A_\varphi}{\partial \varphi}\right)\mathclose{} &\hat{\boldsymbol \rho} \\

+ \mathopen{}\left(\nabla^2 A_\varphi - \frac{A_\varphi}{\rho^2} + \frac{2}{\rho^2} \frac{\partial A_\rho}{\partial \varphi}\right)\mathclose{} &\hat{\boldsymbol \varphi} \\

{}+ \nabla^2 A_z &\hat{\mathbf z}

\end{align}</math>

\left(\nabla^2 A_r - \frac{2 A_r}{r^2}

- \frac{2}{r^2\sin\theta} \frac{\partial \left(A_\theta \sin\theta\right)}{\partial\theta}

+ \frac{2 \cos\theta}{r^2\sin^2\theta} \frac{\partial A_\theta}{\partial \varphi}\right) &\hat{\boldsymbol \varphi}

\end{align}</math>

 

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