Definition:Heaviside Step Function/Off

Definition
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.

Then:
 * $\map {u_c} t \map f t$

can be understood as:


 * ''$f$ is off until time $c$.

or:


 * $f$ does not start until time $c$.

Also see

 * Definition:Heaviside Step Function/On