Mikusinski's Operational Calculus

Abstract

Summary Mikusinski's operational calculus provides a simpler approach than the Laplace transform to the solution of the differential equations of science and technology. The mathematical demands of a proper understanding of the Laplace transform can be greatly reduced by adopting Mikusinski's approach, and, in particular, this approach provides a simple algebraic foundation to the generalization of the concept of ‘function’ without the intellectual difficulties of the theory of distributions. This will readily be appreciated by students who have taken ‘modern mathematics’ syllabuses at school since the development of the operational calculus is analogous with the way in which the integers are extended to the set of rational numbers. In addition to the advantage of simplicity, the method has a wider generality than the Laplace transform in that it can be used with certain functions for which there is no Laplace transform image, yet at the same time tables of Laplace transforms can be used where such images...