Grad, div, rot, and $\Delta$ in Cylindric and Spherical Coordinates

Abstract

The purpose of this chapter is to calculate the operators $\,\,\text{ grad }\,$, $\,\,\text{ rot }\,$, $\,\,\text{ div }\,$, and $\,\Delta$ in cylindric and spherical coordinates. The method of calculations that will be described below can be applied to more complicated cases. This may include derivation of other differential operators, acting on tensors; also derivation in other, more complicated (in particular, non-orthogonal) coordinates and in the case of dimension $\, D\ne 3$. In part, our considerations will repeat those we have already performed above, in Chap. 5, but we shall always make calculations in a slightly different manner, expecting that the reader can benefit from the comparison.