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 … For more content click the Read More button below.

Offerings

S1-01-CLAYTON-ON-CAMPUS
S1-FF-CLAYTON-FLEXIBLE

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Paul Cally

Unit Coordinator(s)

Professor Paul Cally

Learning outcomes

On successful completion of this unit, you should 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.

Assessment summary

Examination (3 hours and 10 minutes): 50% (Hurdle)

Continuous assessment: 50%

Hurdle requirement: If you would otherwise have passed the unit but who do not achieve at least 45% of the marks available for the end-of-semester examination will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Printing, Stationery)- $100.

Availability in areas of study

Master of Mathematics