MTH5311 · Methods of applied mathematics

Overview

This unit covers the key principles to approximate and understand solutions of linear, weakly nonlinear, and strongly nonlinear equations by asymptotic analysis and dynamical systems theory. The main topics are: local analysis of linear ODEs, including irregular singular points and asymptotic series; asymptotic expansion of integrals, including stationary phase and steepest descent; introduction to regular/singular perturbation series; matched asymptotic expansion; multiple scale analysis, WKB theory; dynamical systems theory, including bifurcation, stability, and an introduction to chaos.

Areas of study: Master of Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Appreciate the need for advanced approximate methods in applied mathematics when exact solutions are not available and for when numerical solution requires asymptotic boundary conditions
2. Formally explain the meanings of asymptotic relations and be able to apply them in comparing particular functions
3. Use sophisticated asymptotic methods to obtain local and global approximate solutions to a variety of problems arising in applied mathematics
4. Employ regular and singular perturbation methods to obtain approximate solutions of problems containing small parameters
5. Recognize and apply the mathematical concepts and tools underlying the evolution of nonlinear dynamical systems and the transition to chaos.

Workload

• Two 1.5 -hour seminars; • One 1-hour applied class (in weeks 2-12) and • 8 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.