Coordinate Conversions for the Laplace Operator
It is most common to use the Laplace Operator $ \Delta $ in three-dimensions, as that is the dimensionality of our physical universe. Thus, the Laplace Operator is often used in 3-D Cartesian coordinates, cylindrical coordinates, and spherical coordinates.
$ \Delta f=\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}+\frac{\partial^{2} f}{\partial z^{2}}\ $
