ABSTRACT
Consider a problem in which it is desired to determine the variation of a dependent variable, say φ, in a region of space R which is bounded by a surface S. Let r be a position vector from the origin of the coordinate system to a particle or point in R. Most generally, r is a function of three independent spatial coordinates. The dependent variable may also be a function of time and designated as φ(r,t). The surface S is described by g(r,t) = 0. The problem is an interior problem if g is bounded and the solution is to be obtained for position vectors defi ned within the interior of g, as illustrated in Figure 6.1a. The problem is an exterior problem if the solution is to be obtained for position vectors defi ned outside of g, as illustrated in Figure 6.1b.
