By definition, the Laplace Transform of a function of time 
is
where 
indicates the Laplace Transform.
The inverse Laplace Transform is given by
where 
indicates the inverse Laplace Transform and 
.
The two above equations form the Laplace transform pair. Given a
function , we integrate the first one to find its Laplace
transform 
. Then if this function is used to evaluate
the second equation, the result will be the original value of
. The value of 
in equation [2] is determined by the
region of convergence of equation [1].
