This module is an introduction to the theory of Partial Differential Equations and their applications in the Physical Sciences. It builds on the knowledge gained in MATH 3802 (Ordinary Differential Equations) and makes extensive use of the methods and techniques introduced in that module.
First order partial differential equations (linear and quasi-linear).
Conservation laws, characteristics and shocks. Traffic flow problems. Second order linear partial differential equations: classification into parabolic, hyperbolic and elliptic equations.
Characteristics. Solving first and second order equations using Laplace transforms.
The method of separation of variables.
The heat, wave and Laplace equation with various boundary conditions and their applications to problems in physical sciences.
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