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)}

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