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 a fundamental mathematical tool for the study of systems that change over time and are used in most areas of science, engineering and mathematics.
About this paper
Paper title | Partial Differential Equations |
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Subject | Mathematics |
EFTS | 0.15 |
Points | 18 points |
Teaching period | Semester 1 (On campus) |
Domestic Tuition Fees ( NZD ) | $1,040.70 |
International Tuition Fees | Tuition Fees for international students are elsewhere on this website. |
- Prerequisite
- MATH 203
- Recommended Preparation
- COMO 204
- 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
For more information, contact MATH and COMO200-300 Level Advisor Jörg Hennig.
- Teaching staff
- Paper Structure
The main topics are:
- Metric spaces and topological concepts such as compactness and completeness in infinite dimensions.
- Normed spaces and bounded linear operators, Banach spaces, dual spaces.
- Sequence spaces and Lp-function spaces including null sets, almost everywhere equivalence, and Monotone and Dominated Convergence Theorems.
- Hilbert spaces including separability, orthogonal projections, orthonormal bases, reconstructions formula, Fourier basis and Fourier series with applications.
- 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.