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Partial Differential Equations (MAST90133)
Graduate courseworkPoints: 12.5Not available in 2022
From 2023 most subjects will be taught on campus only with flexible options limited to a select number of postgraduate programs and individual subjects.
To learn more, visit COVID-19 course and subject delivery.
Overview
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This subject offers a wide ranging introduction to the modern theory of partial differential equations (PDEs) in pure mathematics. Thus we will study questions of existence, uniqueness, regularity, and long time behaviour (e.g.\ energy dispersion) for solutions to PDEs. We will discuss these questions first for the classical equations (Laplace's equation, the heat equation, and the wave equation) which will lead us to the broader theory of elliptic, parabolic, and hyperbolic equations. The course covers mostly linear equations, but exposes the student also to some of the most interesting non-linear equations arising in physics and geometry.
Further topics may include: Calculus of variations, Hamilton-Jacobi equations, Systems of Conservation laws; Non-linear elliptic equations, Schauder theory; Quasi-linear hyperbolic equations, propagation of singularities, blow up phenomena.
Intended learning outcomes
After completing this subject, students will gain an understanding of:
- Elements of the general theory of PDE's: Principal symbol, solvability.
- The basic theory of elliptic equations: Regularity, Dirichlet's problem, maximum principle.
- The basic theory of hyperbolic equations: Cauchy problem, energy estimates.
- Existence theory for weak solutions, Sobolev spaces.
- Examples of non-linear equations
Generic skills
- 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: 12 November 2022
Eligibility and requirements
Prerequisites
All of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20030 | Differential Equations | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
MAST30021 | Complex Analysis |
Semester 1 (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
|
12.5 |
Corequisites
None
Non-allowed subjects
None
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: 12 November 2022
Assessment
Description | Timing | Percentage |
---|---|---|
Up to 40 pages of assignments (4 assignments worth 10% each spread evenly)
| Throughout the teaching period | 40% |
A written examination
| During the examination period | 60% |
Last updated: 12 November 2022
Dates & times
Not available in 2022
Last updated: 12 November 2022
Further information
- Texts
Prescribed texts
Recommended texts and other resources
L. C. Evans, Partial Differential Equations. Graduate Studies in Mathematics, vol. 19, AMS (2010)
- 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: 12 November 2022