Justification of Heaviside methods

THE METHODS of Heaviside for solving differential equations commonly arising in problems of engineering and physics, are of great value and are very widely used. However, Heaviside did not fully justify his methods, saying that “reservations should be learned by experience.” Mathematicians, therefore, have generally preferred to approach the same goals by use of the Laplace transformation. However, the recent work of the French mathematician, Laurent Schwartz, provides justification of Heaviside's methods, and opens the way to their wider use.