MTH4311 Methods of applied mathematics
Faculty of Science
MTH4311 Methods of applied mathematics is a level 4, 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 60%
- and 1 other task
This is the 2024 handbook entry. See the 2026 entry.
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Requisites
Before MTH4311
No prerequisites or corequisites besides the enrolment rules below.
After MTH4311
No unit lists MTH4311 as a prerequisite in the 2024 handbook.
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
- Problem Sets40%
- Examination (3 hours and 10 minutes)Exam60%
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
- Applied sessions11 hours
- Seminars36 hours
- Two 1.5 -hour seminars;
- One 1-hour applied class (in weeks 2-12) and
- 8 hours of independent study per week.
Contacts
- Unit Coordinators
- Professor Paul Cally
- Chief Examiners
- Professor Paul Cally
Common questions
What are the prerequisites for MTH4311?
MTH4311 has no prerequisites, but enrolment rules apply.
When is MTH4311 offered?
In 2024, MTH4311 runs in Semester 1 at Clayton.
Does MTH4311 have an exam?
Yes. The exam is worth 60% of the final mark, alongside 1 other task.