Fourier analysis involves rewriting functions of position as functions of frequency. In many situations, the behaviour of a system is much simpler when it is viewed as dependent on frequency rather than position. It is therefore a Good Thing to have the output of the system written in terms of frequency. However, it is often much easier to find the values of that system in terms of position. The techniques of Fourier theory allow us to make the best of both: we can read off the values in terms of position and then use Fourier analysis to rewrite these in terms of frequency.

In this course we shall be studying the mathematical tools and ideas behind Fourier theory.