11 weeks. There are 3 lectures per week, which do not include tutorials. Tutorials are separate, and tutorial attendance is mandatory for continuous assessment purposes. These tutorials will last 1 hour per week.

Calculate and interpret the real and complex Fourier series of a given periodic function;

Obtain and interpret the Fourier transform of non-periodic functions;

Evaluate integrals containing the Dirac Delta;

Solve ordinary differential equations with constant coefficients of first or second order, both homogenous and inhomogenous;

Obtain series solutions (including Frobenius method) to ordinary differential equations of first or second order;

apply their knowledge to the sciences where relevant.

Module Content

Vector spaces and inner products of functions

Fourier series

Fourier transform

Dirac delta function

Applications of Fourier analysis

Ordinary differential equations (ODE)

Exact solutions of 1st and 2nd order ODE

Series solutions of ODE and the Frobenius method

Module Prerequisite

MAU11S01 & MAU11S02, co-requisite MAU22S01

Suggested Reference

Advanced Engineering Mathematics, E. Kreyszig in collaboration with H. Kreyszig, E. J. Norminton; Wiley (Hamilton 510.24 L21*9)

Assessment Detail

This module will be examined in a 2 hour examination in Michaelmas term. Continuous Assessment will contribute 20% to the final annual grade, with the examination counting for the remaining 80%. Supplementals if required will consist of 100% exam.