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Advanced Methods: Differential Equations (MAST90064)
Graduate courseworkPoints: 12.5Not available in 2024
Overview
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|---|
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 be able to:
- Describe how ordinary differential equation models and associated boundary-value problems arise in a variety of areas in applied mathematics and mathematical physics;
- Differentiate the role of series solution methods for differential equations and be able to construct and use such solutions;
- Apply the basic concepts of asymptotic analysis and perturbation methods, implement these techniques and differentiate their value and limitations;
- Recognise the basic properties of special functions of applied mathematics and mathematical physics and their applications; and
- Develop key foundational knowledge to pursue further studies in this discipline 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: 31 January 2024
Eligibility and requirements
Prerequisites
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20030 | Differential Equations | Semester 2 (On Campus - Parkville) |
12.5 |
MAST30029 Partial Differential Equations (pre-2014)
Or equivalent
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 2 (On Campus - Parkville)
Semester 1 (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: 31 January 2024
Assessment
| Description | Timing | Percentage |
|---|---|---|
Continuing assessment up to 40 hours work, worth 40%, throughout the semester
| Throughout the teaching period | 40% |
A written examination
| During the examination period | 60% |
Last updated: 31 January 2024
Dates & times
Not available in 2024
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 31 January 2024
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 Doctor of Philosophy - Engineering Course Ph.D.- Engineering Course Master of Philosophy - Engineering Course Master of Science (Mathematics and Statistics) 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.
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
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 31 January 2024