Overview
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 direct expressions of the laws of Nature. Partial differential equations (PDEs), in particular, typically describe how quantities change with both space and time. They are used in many areas of science, finance, engineering and mathematics. In MATH 304, you will learn the origin of common PDEs, a range of methods to solve them and approximate their solution numerically, and some important qualitative properties of their solutions. This paper is ideal for anyone wanting to explore the topic using a methods-oriented/hands-on approach.
About this paper
| Paper title | Partial Differential Equations |
|---|---|
| Subject | Mathematics |
| EFTS | 0.15 |
| Points | 18 points |
| Teaching period | Semester 1 (On campus) |
| Domestic Tuition Fees ( NZD ) | $1,103.10 |
| International Tuition Fees | Tuition Fees for international students are elsewhere on this website. |
- Prerequisite
- MATH 203, COMO 204
- Schedule C
- Arts and Music, Science
- Notes
- The temporary prescription note aims to resolve a transitional issue in the fairest way possible for students. For students to plan programme pathways they need to plan to take COMO204 in their current year for the upcoming year but updated paper prerequisites will not be published for the upcoming year until semester two of the current year. The prerequisites for the upcoming year would therefore be published after it is too late for current students to have taken COMO204 in the current year. Fully enforcing the prerequisite from 2026 will disadvantage students who could not know that it was becoming a prerequisite. Delaying the change will delay the problem for one year, at which point it will reoccur for the cohort of 2026.We propose using a temporary prescription note for one year advising interested students to contact the department to discuss their eligibility so that course advice can be provided and enrolment by special permission considered.
- Eligibility
This paper is particularly relevant for students majoring in Mathematics, Statistics, Physics, Energy Management, Marine Science, Zoology, Economics, or any other field in which the natural world can be described by differential equations.
- Contact
For more information, contact MATH and COMO 200 to 300-level Advisor Jörg Hennig.
- Teaching staff
- Paper Structure
The main topics are:
- Derivation of common PDEs
- Method of characteristics for first-order PDEs and d'Alembert's formula for the wave equation
- Fourier series and the method of separation of variables
- Qualitative analysis of PDEs
- Green's function method and the Fourier transform
- Teaching Arrangements
Three lectures and one tutorial per week.
- Textbooks
Course reader: MATH 304 course notes will be made available chapter-by-chapter during the semester via Blackboard. These notes are the main reference for this paper.
Supporting textbooks (ebooks freely available via the University library):
- Olver, P.J. (2020). Introduction to Partial Differential Equations. Springer
- Griffiths, D.F., Dold, J.W. and Silvester, D.J. (2015). Essential Partial Differential Equations: Analytical and Computational Aspects. Springer
- Graduate Attributes Emphasised
- Critical thinking.
View more information about Otago's graduate attributes. - Learning Outcomes
- Ability to solve a range initial/boundary-value problems involving partial differential equations
- Demonstrate in-depth understanding of central concepts in the theory of partial differential equations
- Assessment details
- Five written assignments (20%)
- Two in-class tests (20%)
- Tutorial attendance (10%)
- Final exam (50%)