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

Sources

• For a video presentation of the contents of this page, visit the Khan Academy.