Laplace Transform of Heaviside Step Function

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


 * $\map {u_c} t = \begin{cases}

1 & : t > c \\ 0 & : t < c \end{cases}$

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


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

for $\map \Re s > c$.