 Laplacian in polar coordinates

ID: laplacian-in-polar-coordinates

For a twice differentiable scalar field on the plane,

\nabla^{2} f = \frac{1}{r} \frac{\partial}{\partial r} (r \frac{\partial f}{\partial r}) + \frac{1}{r ^{2}} \frac{\partial ^{2} f}{\partial θ ^{2}} .

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