Tutorials, packages, documentation for Vector calculus intensive tasks

I work on magnetohydrodynamics theory, and encounter lots vector differentiation, integration, Fourier transforms etc, often in curved co-ordinates. I was hoping where I could get a comprehensive tutorial (as text or video format) that focuses on handling such tasks symbolically in Mathematica, given I know how to use it for single variable calculus and plotting, and am aware of basic programming features at the level of Wolfram’s Introduction Book.

For instance, given an initial electric field configuration in spherical co-ordinates, I would like to obtain analytical expressions for the electric and magnetic fields at a later time in absence of any sources using Maxwell’s equations. Where do I begin?