Often referred to as the

unit step function or just the

step function, the Heaviside function was dreamed up by the English

electrical engineer Oliver Heaviside while he was developing practical

Laplace transformation techniques. It is usually denoted as:

`u(t-a) = { 1 for t > a (a >= 0)
{ 0 for t < a`

Not only is this function useful for defining other

piecewise functions without using the space-consuming piecewise

notation (eg, if a function is equal to sin(t) for t between 1 and 2, but is zero elsewhere, we can write f(t) = (u(t-1)-u(t-2))*sin(x)), it also simplifies certain

Laplace transformations and

inverse transforms as a result of the

second-shifting theorem:

**L{f(t-a)u(t-a)} = exp(-as)*F(s)** (where F(s) = L{f(t)})

**f(t-a)u(t-a) = L**^{-1}{exp(-as)*F(s)}