ABSTRACT
The Fourier transformations—developed, in fact, from the Fourier series representations of functions—are particularly useful tools when dealing with infinite or semi-infinite spatial regions because they are designed for exactly this type of setup and have the added advantage that they reduce the number of ‘active’ variables in the given partial differential equation (PDE) problem. This chapter describes the full Fourier, Fourier sine, and Fourier cosine transformations of PDEs. The Fourier transformation method may also be applied to other suitable problems, including some with non-homogeneous PDEs.
