Tensors of Geophysics Volume Two: Generalized Functions and Curvilinear Coordinates
This volume introduces the idea of distributions or, as they are sometimes called, generalized functions. These let us simplify some of our applied logic by giving us the ability to treat singular functions beyond the intuitive level. The combination of distribution theory and tensor theory affords us the opportunity to develop cylinder functions, e.g., Bessel functions, at some length. Included in this book is the Hankel transform, which is appropriate and convenient when the independent variable is offset. The classical rules of spherical trigonometry and a peek at some of the mathematics of relativity is afforded.