Mathematica Tutorial

Integral Transforms

LaplaceTransform[expr,t,s]	find the Laplace transform of expr
InverseLaplaceTransform[expr,s,t]
	find the inverse Laplace transform of expr

Laplace transforms.

This computes a Laplace transform.

In[1]:=

Out[1]=

Here is the inverse transform.

In[2]:=

Out[2]=

FourierTransform[expr,t,w]	find the symbolic Fourier transform of expr
InverseFourierTransform[expr,w,t]
	find the inverse Fourier transform of expr

Fourier transforms.

This computes a Fourier transform.

In[3]:=

Out[3]=

Here is the inverse transform.

In[4]:=

Out[4]=

Note that in the scientific and technical literature many different conventions are used for defining Fourier transforms. The setup for specifying different conventions is described in FourierTransform.