Chapter 10 - Solving Partial Differential Equations in Spherical Coordinates Using Separation of Variables

Abstract

This chapter uses separation of variables to solve partial differential equations (PDEs) expressed in spherical coordinates. The chapter encounters a differential equation called Legendre's equation in addition to a Bessel equation while solving PDEs expressed in spherical coordinates. Legendre equations arise when solving a PDE in spherical coordinates that use the Laplacian; the chapter demonstrates this with the wave equation. The chapter presents the solution to Bessel's equation in spherical coordinates, Legendre's equation and its solutions, associated Legendre functions, and Laplace's equation in spherical coordinates.