Module MA22S3: Fourier Analysis for Science

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2015-16
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
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.