Laplace Transform of Constant Multiple

Theorem
Let $f$ be a function such that $\LL f$ exists.

Let $\laptrans {\map f t} = \map F s$ denote the Laplace transform of $f$.

Let $\map F s$ denote $\laptrans {\map f t}$. Let $a \in \C$ or $\R$ be constant.

Then:


 * $a \laptrans {\map f {a t} } = \map F {\dfrac s a}$

Also presented as
This result can also be given as:
 * $\laptrans {\map f {a t} } = \dfrac 1 a \map F {\dfrac s a}$

Also known as
This property of the Laplace transform operator is sometimes seen referred to as the change of scale property.