Definition:Heaviside Step Function/On

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Let $c \ge 0$ be a constant real number.

Let $u_c: \R \to \R$ be the Heaviside step function on $c$:

$\map {u_c} t := \begin{cases} 1 & : t > c \\ 0 & : t < c \end{cases}$

Let $t$ be understood as time.

Let be $f$ a function of $t$ used to model some physical process.


$\map {u_c} t \map f t$

can be understood as:

$f$ is on after time $c$.

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