Sometimes it may only be necessary to find the behaviour of a function at small and/or large times without finding an explicit expression for the inverse of the Laplace Transform. This is particularly so when the Laplace Transform may be an involved expression. To find the behaviour of f(t) for small times the INITIAL VALUE THEOREM shown below may be used. This implies that the small time behaviour is dominated by high frequencies or poles far from the real s axis.

Copyright 1996 © Cuthbert A. Nyack.