This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

Documentation / Mathematica / The Mathematica Book / A Practical Introduction to Mathematica / Symbolic Mathematics /

1.5.12 Integral Transforms

Laplace transforms.

This computes a Laplace transform.

In[1]:= LaplaceTransform[t^3 Exp[a t], t, s]

Out[1]=

Here is the inverse transform.

In[2]:= InverseLaplaceTransform[%, s, t]

Out[2]=

Fourier transforms.

This computes a Fourier transform.

In[3]:= FourierTransform[t^4 Exp[-t^2], t, w]

Out[3]=

Here is the inverse transform.

In[4]:= InverseFourierTransform[%, w, t]

Out[4]=

Note that in the scientific and technical literature many different conventions are used for defining Fourier transforms. Section 3.8.4 describes the setup in Mathematica.