## Laplace transform list of properties

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