This module extends the material covered in MATH 4801 (Partial Differential Equations) and MATH 3802 (Ordinary Differential Equations) by introducing further topics and solution methods for Partial and Ordinary Differential Equations. It also introduces theoretical concepts from Integral Equations and some of their applications.
Introduction to Fourier transforms (exponential, sine, cosine and finite). Applications of Fourier transforms to solving ordinary and partial differential equations.
The heat, wave and Laplace equations in spherical and cylindrical coordinates.
Introduction to linear Volterra and Fredholm integral equations. Equivalence to ordinary differential equations. Solution of separable equations by integral transforms.
The method of successive approximations and resolvent kernel for Volterra equations. The Fredholm Alternative. Applications of integral equations.
Lectures supported by problem-solving tutorials. Modelling examples from physics and engineering applications solved with the aid of mathematical software packages.
Lectures: 2 hours/week
Tutorials: 1 hour/week
|Module Content & Assessment