Introduction to the theory of pdes for applied mathematics (MAGIC056)
There are no announcements
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
Spring 2010 (Monday, January 11 to Friday, March 19)
(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
No syllabus information is available yet.
No bibliography has been specified for this course.
No assessment information is available yet.
No assignments have been set for this course.
Files marked L are intended to be displayed on the main screen during lectures.
Please log in to view lecture recordings.