# Laplace transform list of properties

Submitted by Structure on Sat, 12/08/2007 - 14:21.

Consider the Laplace transform of a original function f.

We give some useful property if this transform.

Change of scale.

Let then g(t)=f(at) is function which admits Laplace transform and

Multiply by exponential

Let then

has Laplace transform

Product with t variable.

If f is an original function, then for and

Laplace transform for derivative

If f and f' are original function then

Where

If higher order derivatives exists and are originals,

Convolution of originals.

Let f,g be original function.

Then

is an original and

Let f be a periodic function of period T >0, which take value zero on the negative real axis.

Suppose that

is integrable.

Then Laplace transform of f