MTH4311 - Methods of applied mathematics - 2019

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.

On completion of this unit students will be able to:

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.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1h of tutorial per week.

8 hours independent study per week.

See also Unit timetable information

Master of Mathematics