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 2020 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2020
- Semester 1
- Clayton
This is the 2020 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 2020 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 2020
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
| First semester (Fully flex) | Clayton | Flexible |
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
- 3 hours of lectures
- 1 hour applied class and
- 10 hours of independent study per week
Contacts
- Chief Examiners
- Professor Paul Cally
- Unit Coordinators
- Professor Paul Cally
Common questions
What are the prerequisites for MTH5311?
MTH5311 has no prerequisites, but enrolment rules apply.
When is MTH5311 offered?
In 2020, MTH5311 runs in Semester 1 at Clayton.