The Heaviside theory of lumped circuits and differential systems based an causality

Due to an accident of personality and history, the Laplace transform superseded the Heaviside theory of circuits and systems. The main reason was the latter´s lack of rigor-even though it is more general and directly applicable. This paper shows that the Heaviside theory can be made entirely rigorous in an elementary fashion. Furthermore, it exhibits all of the calculational machinery of the Laplace transform. The Laplace transform is shown to fit into the Heaviside theory as a special tool, primarily useful in developing the idea of a spectrum