ABSTRACT
The concept of using generalized functions in the derivation of integral theorems is straightforward. By application of the rules developed in Chapter 4, line integrals, surface integrals and volume integrals can be transformed to integrals over all space with the generalized functions and/or their derivatives appearing in the integrand. Subsequent manipulations involving generalized functions, required to arrive at concise and acceptable formulations of the integral theorems, are extensive in some cases. However, when compared to alternative derivations, they are reasonably simple and easy to follow. Repeated application of the chain rule for differentiation is required to convert integrals of space or time derivatives to derivatives of integrals and to eliminate the generalized functions and their derivatives from the resulting expressions. Fortunately, a number of rules that are generally valid can be applied to reduce the amount of work required in deriving these theorems.
