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Unit of study_
MATH4078: PDEs and Applications
2025 unit information
The aim of this unit is to introduce some fundamental concepts of the theory of partial differential equations (PDEs) arising in Physics, Chemistry, Biology and Mathematical Finance. The focus is mainly on linear equations but some important examples of nonlinear equations and related phenomena re introduced as well. After an introductory lecture, we proceed with first-order PDEs and the method of characteristics. Here, we also nonlinear transport equations and shock waves are discussed. Then the theory of the elliptic equations is presented with an emphasis on eigenvalue problems and their application to solve parabolic and hyperbolic initial boundary-value problems. The Maximum principle and Harnack's inequality will be discussed and the theory of Green's functions.
Unit details and rules
Managing faculty or University school:
Science
| Study level | Undergraduate |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
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Prerequisites:
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[A mark of 65 or greater in 6 credit points from (MATH2X21 or MATH2X65 or MATH2067) and a mark of 65 or greater 6 credit points from (MATH2X22 or MATH2X61)] or [12 credit points from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3979)] |
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Corequisites:
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None |
| Prohibitions:
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MATH3078 or MATH3978 |
| Assumed knowledge:
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(MATH2X61 and MATH2X65) or (MATH2X21 and MATH2X22) |
At the completion of this unit, you should be able to:
- LO1. employ foundational techniques to analyze and solve a range of different types of partial differential equations
- LO2. explain how classical PDEs are derived and their application in different types of problems
- LO3. solve classical 2nd-order linear differential equations and apply appropriate boundary and initial conditions
- LO4. apply the theory of orthogonal polynomials to solve a range of different PDEs
- LO5. calculate solutions or perform analysis of classical nonlinear PDEs
- LO6. synthesise solution methods and equations analysis to classify complex solutions of nonlinear PDEs
- LO7. Communicate mathematical analysis accurately, completely, and correctly using algebraic, computational, or graphical methods, in a typeset manner when appropriate.
Unit availability
This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.
The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.
| Session | MoA ? | Location | Outline ? |
|---|---|---|---|
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Semester 2 2025
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Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Modes of attendance (MoA)
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