## Content

Fourier analysis is one of the most important pieces of machinery in the toolbox of the modern applied mathematician. It is based on the fact that most functions or digital signals can be approximated well by a small number of sine and cosine functions. In the module we study approximations on a finite interval (Fourier series) and an infinite interval (Fourier integrals). We look at the implementation of these on a computer and the idea behind the famous FFT (fast Fourier transform). Applications are taken from classical Applied Mathematics (solving PDEs like the wave and diffusion equations) as well as more modern signal and image/video processing.

## Outcomes

Upon completion of this module the student will be able to use Fourier methods to solve a wide variety of problems in classical as well as modern Applied Mathematics, with the aid of the computer if necessary.

## Assessment

Assessment will consist of tutorial tests, computer assignments, and two formal written tests. The two tests are: A1 which covers the work done in Term 3, and A2 which covers the work done in Term 4. At the end of Term 4, a student's mark for the module is calculated as follows:

 tut-tests and assignments 30% A1 35% A2 35%
A student then has the option to write A3 during the university's exam period, on all the work done in both terms. Those who missed A1 or A2, e.g. due to illness, will have to write A3. The mark obtained for A3 will replace the lowest of the marks obtained for A1 and A2 (even if A3 is lower than the lowest of A1 and A2), and the student's mark will be recalculated with the above weights.

## Test dates and times

Note: A1 and A2 will each be written during the module's tutorial time slot on a Thursday afternoon, and A3 during the exam period (as scheduled by the university).

 A1 Thursday 31 August at 14:00 A2 Thursday 12 October at 14:00 A3 (optional) Thursday 26 October at 14:00