ABSTRACT
Green's functions provide a method for dealing with source terms in differential equations. The Green's function for the wave equation has a direct physical interpretation. The image method basically a trick. The retarded potential solution is of basic importance in electrodynamics. The surface integral in this expression vanishes because of the boundary conditions. Naturally one prefers the closed expression to the infinite series. However, the method employed is more general and can be used in problems where the image method fails. The series expansion method can also be employed for the Helmholtz equation. The chapter illustrates the Green's function for the Helmholtz equation with a two dimensional example, the round drumhead. Evidently the same techniques could be employed for three dimensional problems, e.g. the interior of a cylinder or the interior of a sphere.
