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Unit of study_

PDEs and Waves - MATH3078

Year - 2020

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.

Classes
3x 1 hour lectures; 1x1 hour laboratory /wk

Assessment
Final exam (70%), 2 assignments (15%+15%). To pass the course, students must achieve at least 50% on the final exam.

Assumed knowledge
[MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22]

Pre-requisites

12 credit points of MATH2XXX units of study

Prohibitions

MATH3978 or MATH4078

Details

Faculty: Science

Semester 2

24 Aug 2020

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 28 Sep 2020
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
Unit of Study coordinator: Prof Georg Gottwald
HECS Band: 2
Courses that offer this unit

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