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Module MA22S3: Fourier Analysis for Science

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2017-18
Contact Hours
11 weeks, 3 lectures plus tutorials per week
Lecturer
Prof Ruth Britto For further module information 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
MA1S12
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.