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Description

Description: Introduction to the theory of pdes for applied mathematics
Outline Syllabus: Systems of first order pdes and single pdes of higher order, examples from continuum mechanics
Symbol of a pde and of systems; characteristics; existence, uniqueness and continuous dependence on the data; well- and ill-posedness.
(Brief exposition of necessary functional analysis, e.g. operator theory, distributions, Sobolev spaces, see below *).
Weak and strong solutions.
Maximum principles for elliptic and parabolic pde's, existence of solutions.
Linear elliptic pde's, coercivity/energy estimates; Lax-Milgram lemma, Garding's inequality, existence and uniqueness of weak solutions.
Evolutionary pde's - abstract parabolic initial value problems, energy methods, uniqueness and existence.
Nonlinear elliptic pde's, monotone operators, existence of a weak solution.
Systems of hyperbolic equations; Symmetrisable systems; well-posedness.
Introduction to semi-group methods.
Prerequisites
Undergraduate courses on real analysis and partial differential equations (methods courses) will be assumed without explicity mention. * Functional analysis is more problematic (as applied mathematics students may not have taken such options) but time constraints prevent assuming no prior knowledge. Probably the best way forward is to present some necessary functional analysis briefly during the lectures and to provide ädditional" notes online and together with careful page references to books covering the material in the hope that students who have little or no functional analysis will wish to learn more in ßelf-study" as a means to coming to a deeper understanding of the "theory" of pde's

Semester

Spring 2010 (Monday, January 11 to Friday, March 19)

Timetable

  • Thu 12:05 - 12:55
  • Fri 10:05 - 10:55

Prerequisites

(eg other courses which this course fits in with)
Other Magic courses will/may provide useful pre-requisites:
MAGIC003: Introduction to Linear Analysis
MAGIC018: Linear Differential Operators in Mathematical Physics

Syllabus

No syllabus information is available yet.

Lecturer


David Harris
Email david.harris@manchester.ac.uk
Phone (0161) 306 3683


Students


Photo of Hanefa Al-Qasmi
Hanefa Al-Qasmi
(Manchester)
Photo of Faris ALZAHRANI
Faris ALZAHRANI
(Cardiff)
Photo of Andrew Bailey
Andrew Bailey
(Birmingham)
Photo of Ruediger Borsdorf
Ruediger Borsdorf
(Manchester)
Photo of Susanne Claus
Susanne Claus
(Cardiff)
Photo of Samuel Durugo
Samuel Durugo
(Loughborough)
Photo of Nigel Harrison
Nigel Harrison
(Liverpool)
Photo of Charlotta Howarth
Charlotta Howarth
(Reading)
Photo of Imran Khan
Imran Khan
(Manchester)
Photo of Qifeng Liao
Qifeng Liao
(Manchester)
Photo of Yi-Ping Lo
Yi-Ping Lo
(Loughborough)
Photo of Michael MARNELL
Michael MARNELL
(Cardiff)
Photo of Stephen Rickaby
Stephen Rickaby
(East Anglia)
Photo of Chris Rowlatt
Chris Rowlatt
(Cardiff)
Photo of Catherine Saunders
Catherine Saunders
(Manchester)
Photo of Kathleen Scott
Kathleen Scott
(Manchester)
Photo of Thomas Shearer
Thomas Shearer
(Manchester)
Photo of Phillip Taylor
Phillip Taylor
(Manchester)
Photo of Thomas Wieber
Thomas Wieber
(Leeds)
Photo of Yiqian Zhou
Yiqian Zhou
(Liverpool)


Bibliography


No bibliography has been specified for this course.

Assessment



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No assignments have been set for this course.

Recorded Lectures


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