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    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
    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

    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

    Semester 1

    Location
    Dunedin
    Teaching method
    This paper is taught On Campus
    Learning management system
    Other

    Lecture

    Stream Days Times Weeks
    Attend
    A1 Tuesday 11:00-11:50 9-16, 18-22
    Thursday 12:00-12:50 9-16, 18-22
    Friday 10:00-10:50 9-15, 18-22

    Tutorial

    Stream Days Times Weeks
    Attend
    A1 Wednesday 12:00-12:50 9-16, 18-22
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