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1.5.12 Integral Transforms

Laplace transforms.

This computes a Laplace transform.

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


Here is the inverse transform.

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


Fourier transforms.

This computes a Fourier transform.

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


Here is the inverse transform.

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


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.