# MATH304 Partial Differential Equations

Introduction to the theory of partial differential equations by discussing the main examples (Laplace equation, heat equation, wave equation and transport equations) and their applications.

Differential equations are a fundamental mathematical tool for the study of systems that change over time and are used in most areas of science, engineering and mathematics.

Paper title Partial Differential Equations MATH304 Mathematics 0.15 18 points Semester 1 (On campus) \$955.05 Tuition Fees for international students are elsewhere on this website.
Prerequisite
MATH 202 and MATH 203 and (COMO 204 or MATH 262)
Restriction
MATH 362
Recommended Preparation
MATH 301
Schedule C
Arts and Music, Science
Eligibility
This paper is particularly relevant for students majoring in Mathematics, Statistics, Zoology, Economics, Design or any other field in which the natural world is being modelled by differential equations.
Contact

florian.beyer@otago.ac.nz

Teaching staff

Dr Florian Beyer

Paper Structure
Main topics:
• The transport equation (initial value problem, characteristics)
• The Poisson equation (harmonic functions, mean value theorem for harmonic functions, maximum principle, Green's function, boundary value problem)
• The wave equation (d'Alembert formula, energy methods, domain of dependence, finite propagation speed, Initial boundary value problem)
• Non-linear first order PDE (characteristics, conservation laws, shocks)
Teaching Arrangements
Five lectures a fortnight
One tutorial per week.
Textbooks
Lecture Notes: Lecture notes will be made available chapter-by-chapter during the semester on the resource webpage. These lecture notes are the main reference for this paper.

Book: Partial differential equations/Lawrence C. Evans (on reserve in the library).
Critical thinking.
Learning Outcomes
Demonstrate in-depth understanding of the central concepts and theories.

## Timetable

### Semester 1

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Tuesday 12:00-12:50 9-14, 16, 18-22
Thursday 09:00-09:50 9-14, 16-22
Friday 10:00-10:50 10, 12, 17, 19, 21

#### Tutorial

Stream Days Times Weeks
Attend
A1 Tuesday 16:00-16:50 9-14, 16, 18-22