MAGIC058: Theory of Partial Differential Equations

Course details

A core MAGIC course

Semester

Spring 2019
Monday, January 21st to Friday, March 29th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Timetable

Mondays
15:05 - 15:55
Tuesdays
15:05 - 15:55

Announcements

The two first two lectures (Monday 21st and Tuesday 22nd January 2019, at 3pm) are cancelled. These will be replaced by two extra lectures at 4pm on Tuesday 29th January and Tuesday 12th February.

Description

This course is intended to provide an introduction to the theory of partial differential equations (pdes).
Definitions and examples are given of first, second and higher order pdes and also systems of first order pdes. The focus is on developing practical methods that will be applicable in applied mathematics.

Prerequisites

No prior knowledge of PDEs is required, but experience with vector calculus and general undergraduate methods courses would be very helpful.

Syllabus

  • Notation, definitions. Symbol of a pde and of systems.
  • Examples from applied mathematics.
  • Method of characteristics for first order PDEs
  • Classification of second order PDEs, and reduction to normal form
  • Wave equation and separation of variables
  • Fourier series and Fourier transforms
  • Sturm-Liouville systems
  • Nonlinear PDEs

Lecturer

  • AT

    Dr Alice Thompson

    University
    University of Manchester

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

  • An Introduction to Partial Differential Equations, 2nd. edition (M. Renardy and R.C. Rogers, )

Assessment

Description

The assessment for this course will be via a single take-home paper issued on 28 April 2019 and due by 12 May 2019. There will be five questions each with equal weight; you will need to answer the equivalent of 2.5 questions perfectly to pass.

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Files

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Lectures

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