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 |
|---|---|
| Paper code | MATH304 |
| Subject | Mathematics |
| EFTS | 0.15 |
| Points | 18 points |
| Teaching period | Semester 1 (On campus) |
| Domestic Tuition Fees (NZD) | $955.05 |
| International Tuition Fees | 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
- 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). - Graduate Attributes Emphasised
- Critical thinking.
View more information about Otago's graduate attributes. - Learning Outcomes
- Demonstrate in-depth understanding of the central concepts and theories.
