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Module MA22S3: Fourier Analysis for Science

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2016-17
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.
Lecturer
Prof Ruth Britto webpage- http://www.maths.tcd.ie/~britto/ma22s3.html
Learning Outcomes
  • Calculate the real and complex Fourier series of a given periodic function;
  • Obtain 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
MA1S11 & MA1S12, co-requisite MA22S1

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 Trinity term. Continuous Assessment will contribute 20% to the final annual grade, with the examination counting for the remaining 80%. Supplemental exam if required will consist of 100% exam.