ABSTRACT
Unlike ordinary differential equations, the general solution of a partial differential equation consists of one or more arbitrary functions. It is not easy to determine the particular form of these functions from the prescribed boundary and initial conditions even if the general solution is known. However, it is often possible to solve a specific boundary value or initial value problem in the form of an infinite series of functions known as eigenfunctions or characteristic functions. This chapter is devoted to developing orthogonal series, trigonometric Fourier series, eigenfunction expansions, and the Bessel functions. Orthogonal expansions are important for the method of separation of variables, which is discussed in the next chapter.
