A Brief Treatment of Generalized Functions for Use in Teaching the Laplace Transform

A simple yet rigorous treatment of generalized functions is presented, which avoids the complications of a full-fledged theory while covering the situations that occur in engineering applications. This treatment of functions with singularities is both sufficiently concrete to be quickly understood and sufficiently general to be widely useful. Using this treatment as a foundation, an approach to the unilateral Laplace transform that accepts the presence of impulses and arbitrary initial conditions is easily presented and explained