Heaviside operational calculus

Summary

The Heaviside operational calculus is the formal method of Oliver Heaviside for linear differential equations, developed for electrical circuits. The derivative $d/dt$ is written as a symbol $p$. The response of a system to a unit step input is written as a function of $p$ applied to the step. This expression is then expanded and interpreted by fixed rules. The method gave correct answers long before it was justified; the Laplace transform and the Bromwich integral later explained why.