MATH304 Partial Differential Equations

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

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

Dr Florian Beyer

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.

Timetable