Further Properties of the Laplace Transform

Abstract

Sometimes, a function \(F(t)\) represents a natural or engineering process that has no obvious starting value. Statisticians call this a time series. Although we shall not be considering \(F(t)\) as stochastic, it is nevertheless worth introducing a way of “switching on" a function. Let us start by finding the Laplace transform of a step function the name of which pays homage to the pioneering electrical engineer Oliver Heaviside (1850–1925). The formal definition runs as follows.