Unit of study_

# MATH3978: PDEs and Waves (Advanced)

### 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

#### Science

 Prerequisites: ? A mark of 65 or greater in 6cp from (MATH2X21 or MATH2X65 or MATH2067) and a mark of 65 or greater 6cp from (MATH2X22 or MATH2X61) None MATH3078 or MATH4078 [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 structured PDEs
• LO5. calculate solutions or perform analysis of classical nonlinear PDEs
• LO6. synthesise solution methods and equations analysis to classify 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.

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Session MoA   Location Outline
Semester 2 2024
Normal day Camperdown/Darlington, Sydney
Session MoA   Location Outline
Semester 2 2025
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Session MoA   Location Outline
Semester 2 2020
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Remote
Semester 2 2022
Normal day Camperdown/Darlington, Sydney
Semester 2 2022
Normal day Remote
Semester 2 2023
Normal day Camperdown/Darlington, Sydney

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### Modes of attendance (MoA)

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