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|
|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.|
- MATH 202 and MATH 203 and (COMO 204 or MATH 262)
- MATH 362
- Recommended Preparation
- MATH 301
- Schedule C
- Arts and Music, Science
- 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.
- 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.
- 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
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.