Operational calculus

Summary

Operational calculus is a method that turns problems of analysis, above all linear differential and integral equations, into algebraic problems. The differentiation operator is treated as an algebraic quantity, so an equation for the unknown function becomes an equation in a ring or field. It is solved there by algebra, and the solution is translated back into a function. The classical forms are the Heaviside operational calculus, its justification by the Laplace transform, and the Mikusiński operational calculus, which avoids integral transforms.