# Module MAU22S03: Fourier Analysis for Science

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2019-20
Contact Hours
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.
Lecturer
Prof. Anthony Brown
Learning Outcomes
• 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.