# MTH5311 - Methods of applied mathematics - 2019

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)

Prerequisites

Enrolment in the Master of Mathematics

Prohibitions

MTH4311

## Synopsis

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.

## Outcomes

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.

## Assessment

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.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5311 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4311. The assignments and exam in this unit will use some common items from the MTH4311 assessment tasks, in combination with several higher level questions and tasks.