ABSTRACT
The method of separation of variables is very convenient because it draws on many well-known mathematical concepts and frequently works well. This chapter introduces this method and illustrates its application by considering various systems that were modeled by partial differential equations. It focuses on the heat, wave, and potential equations that are important in many scientific and engineering applications. The general objective of this method is to reduce the solution of a given partial differential equation into the solution of a number of ordinary differential equations. The whole process follows a logical step-by-step development that terminates in the evaluation of the Fourier coefficients of a Fourier-type series. The chapter examines the method of solution of boundary value problems where there are several initial conditions and two or more are inhomogeneous. In some instances the Laplace transform method provides another technique for the solution of boundary value problems by converting the partial differential equation into an ordinary differential equation.
