MAGIC058: Theory of Partial Differential Equations

Course details

A core MAGIC course


Spring 2018
Monday, January 22nd to Friday, March 16th; Monday, April 23rd to Friday, May 4th


Live lecture hours
Recorded lecture hours
Total advised study hours


15:05 - 15:55
15:05 - 15:55


Please note that there is no lecture on Monday 22 January 2018. The first (rather introductory) lecture will be on Tuesday 23 January 2018 at 3pm.


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.


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


  • 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


  • AT

    Dr Alice Thompson

    University of Manchester


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

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


The assessment for this course will be released on Monday 7th May 2018 and is due in by Sunday 20th May 2018 at 23:59.

The assessment for this course will be via a single take-home paper in May 2018 with 2 weeks to complete and submit online. There will be six questions, each worth 20 marks. You will need to complete the equivalent of three questions to pass.

Please note that you are not registered for assessment on this course.


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