Advanced Methods: Differential Equations (MAST90064)
Graduate courseworkPoints: 12.5Not available in 2020
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
About this subject
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
| Fees | Look up fees |
|---|
This subject develops the mathematical methods of applied mathematics and mathematical physics with an emphasis on ordinary differential equations. Both analytical and approximate techniques are used to determine solutions of ordinary differential equations. Exact solutions by localised series expansion techniques of second-order linear ordinary differential equations and Sturm-Liouville boundary value problems are explored. Special functions are introduced here. Regular and singular perturbation expansion techniques, asymptotic series solutions, dominant balance, and WKB theory are used to determine approximate solutions of linear and nonlinear differential equations. Throughout, the theory is set in the context of examples from applied mathematics and mathematical physics such as nonlinear oscillators, boundary layers and dispersive phenomena.
Intended learning outcomes
After completing this subject students should:
- have learned how ordinary differential equation models and associated boundary-value problems arise in a variety of areas in applied mathematics and mathematical physics;
- appreciate the role of series solution methods for differential equations and be able to construct and use such solutions;
- understand the basic concepts of asymptotic analysis and perturbation methods, know how to implement these techniques and appreciate their value and limitations;
- be familiar with the basic properties of special functions of applied mathematics and mathematical physics and their applications;
- have the ability to pursue further studies in these and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
One of the following subject, or equivalent:
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20030 | Differential Equations | Semester 2 (On Campus - Parkville) |
12.5 |
MAST30029 Partial Differential Equations (pre-2014)
Corequisites
None
Non-allowed subjects
None
Recommended background knowledge
It is recommended that students have completed, or have concurrent enrolment in:
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30021 | Complex Analysis |
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
| Description | Timing | Percentage |
|---|---|---|
Up to 50 pages of written assignments (two assignments worth 20% each, due mid and late in semester)
| Second half of the teaching period | 40% |
A written examination
| During the examination period | 60% |
Last updated: 3 November 2022
Dates & times
Not available in 2020
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
Bender C. M. and S. A. Orszag. Advanced mathematical methods for scientists and engineers: Asymptotic methods and perturbation theory. Springer. 1999.
Kervorkian J. and J. D. Cole. Multiple scale and singular perturbation. Springer Verlag 1996.
Nayfeh, A. H. Introduction to perturbation techniques. John Wiley and Sons 1981. - Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 3 November 2022