Chapter 1 - Preliminaries

Abstract

This chapter focuses on some of the important equations and techniques of mathematical physics. It is a fortuitous fact that many of the most important such equations are linear. The chapter describes the methods of transforming some important functions to other coordinate systems. The most common coordinate systems, besides Cartesian coordinates, are cylindrical and spherical coordinates. The reason for considering different coordinate systems is that many problems can be simplified if the appropriate coordinate system is used. For example, the most important partial differential equations in physics and mathematics—Laplace's equation, the heat equation, and the wave equation—can often be solved by separation of variables if the problem is analyzed using Cartesian, cylindrical, or spherical coordinates.