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.