Undergraduate Course: Analysis of Nonlinear Waves (MATH11093)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Year 4 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  Fundamental theorem of ordinary differential equations, the contraction mapping principle. Duhamel's formula, PDEs as EulerLagrange equations and Noether's theorem, continuous functions as a normed vector space, completion of a metric space, Lebesgue and Sobolev spaces, Sobolev embedding theorem, existence and uniqueness of solutions, methods for proving blow up.
Aims :
1. To explore the concepts of local and global solutions and of blow up for ordinary and partial differential equations.
2. To introduce the relevant sets of functions to study nonlinear evolution equations and show how they are used.
3. To construct solutions to nonlinear wave equations. 
Course description 
See short description.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Understand local wellposedness.
 Calculate conserved quantities using Noether's theorem.
 Use contraction mapping theorem.
 Demonstrate familiarity with function spaces.
 Understand global existence and blow up and be able to determine which in common cases.

Reading List
Evans, L C, Partial differential equations (American Mathematical Society, 1998)
John, F, Nonlinear wave equations: formation of sigularities (American Mathematical Society, 1990)
Racke, R, Lectures on Nonlinear Evolution Equations: Initial value problems (Vieweg, 1992) 
Contacts
Course organiser  Dr Pieter Blue
Tel: (0131 6)50 5076
Email: P.Blue@ed.ac.uk 
Course secretary  Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk 

