### Possible Answer

We have obtained the Laplacian in polar coordinates as . Example: Let . We know from lecture that is harmonic. Writing in polar coordinates, we obtain . ... [...] proof that the method of partial fractions decomposition works. - read more

In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. ... In polar coordinates, Three dimensions . See also: Del in cylindrical and spherical coordinates. - read more

Please vote if the answer you were given helped you or not, thats the best way to improve our algorithm. You can also submit an answer or search documents about laplacian in polar coordinates proof.