Partial Differential Equations (MAP 314)

LECTURER: D. Pollney

Description

Partial differential equations (PDEs) are a primary tool for modelling systems in a diverse range of fields from physics to biology to economics. By understanding their structure and the properties of their solution space we develop powerful tools for analyzing a broad class of problems. This course  focusses on building insight into the nature of PDE problems, as well as solution techniques. Along the way we develop a number of new mathematical tools, most notably Fourier techniques, which also have a host of applications in signal processing and statistics.

Topics

First-order partial equations, classification of second-order equations, derivation of the classical equations of mathematical physics (wave equation, Laplace equation, and heat equation), method of characteristics, construction and behaviour of solutions, maximum principles, energy integrals. Fourier series and the Fourier transforms.

Last Modified: Sat, 15 Feb 2014 12:28:29 SAST