MTH5311 Methods of applied mathematics
Faculty of Science
MTH5311 Methods of applied mathematics is a level 5, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2024 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2024
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 2 other tasks
This is the 2024 handbook entry. See the 2027 entry.
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Requisites
Before MTH5311
No prerequisites or corequisites besides the enrolment rules below.
After MTH5311
No unit lists MTH5311 as a prerequisite in the 2024 handbook.
Enrolment rules
COREQUISITE: Enrolment in the Master of Mathematics
Equivalent units
The same content under another code. Only one of them counts.
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.
Offerings in 2024
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Selected problems from problem sheets 1-3Other17%
- Selected problems from problem sheets 4-8Other33%
- Examination (3 hours and 10 minutes)Exam50%
Learning outcomes
When you finish 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.
Workload and teaching
- Seminars36 hours
- Applied sessions11 hours
- Two 1.5 -hour seminars;
- One 1-hour applied class (in weeks 2-12) and
- 8 hours of independent study per week.
Learning resources
Required resources
Glendinning, P., Stability, Instability and Chaos , Cambridge University Press 1994 [G94].
Contacts
- Unit Coordinators
- Professor Paul Cally
- Chief Examiners
- Professor Paul Cally
Common questions
What are the prerequisites for MTH5311?
MTH5311 has no prerequisites, but enrolment rules apply.
When is MTH5311 offered?
In 2024, MTH5311 runs in Semester 1 at Clayton.
Does MTH5311 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 2 other tasks.