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Q6Section II (Mathematics)6 of 145

The Laplacian in polar coordinates

Suppose f(x,y)f(x,y) is of class C2C^2, then under the coordinate transformation x=rcos⁡θx=r\cos\theta, y=rsin⁡θy=r\sin\theta, the expression ∂2f∂x2+∂2f∂y2\dfrac{\partial^2f}{\partial x^2}+\dfrac{\partial^2f}{\partial y^2} transforms to:

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