Laplace Transform of Heaviside Step Function

Theorem
Let $\map {u_c} t$ denote the Heaviside step function.

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

The Laplace transform of $\map {u_c} t$ is given by:


 * $\laptrans {\map {u_c} t} = \dfrac {e^{-s c} } s$

for $\map \Re s > c$.

Proof
Hence the result.