A Survey of the Development of Operational Calculus

Summary Although the name of Oliver Heaviside is usually associated with the foundations of operational calculus, he was in fact preceded in introducing operational methods by a number of mathematicians. Heaviside's purely operational approach was often intuitive rather than rigorous and fell into disfavour in mathematical circles, being replaced by methods involving the concept of an integral transformation. In particular, the Laplace transformation came to be adopted by applied mathematicians and engineers despite the need for the Schwartz theory of distributions to account satisfactorily for the Dirac and other impulse functions. Jan Mikusinski,Footnote∗ however, has returned to the earlier operational approach and, by placing operational calculus upon a rigorous algebraic basis, has provided a calculus which is more general than those based upon integral transformations, and one which includes generalized functions without recourse to any specialized external theory. ∗ It is intended that an expository article on Jan Mikusinski's operational calculus by H. G. Flegg will appear in a later issue ‐ Editor.