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General


This course is part of the MAGIC core.

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.

Semester

Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)

Timetable

  • Mon 15:05 - 15:55
  • Tue 15:05 - 15:55

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


Alice Thompson
Email Alice.Thompson@manchester.ac.uk
Phone 0161-3068951
Photo of Alice Thompson


Students


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Bibliography


An Introduction to Partial Differential Equations, 2nd. editionM. Renardy and R.C. Rogers


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Assessment



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Recorded Lectures


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