# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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# Undergraduate Course: Analysis of Nonlinear Waves (MATH11093)

 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 Euler-Lagrange 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.
 Pre-requisites Students MUST have passed: Metric Spaces (MATH10049) OR Hilbert Spaces (MATH10046) Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites None High Demand Course? Yes
 Not being delivered
 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.
 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)
 Course URL https://info.maths.ed.ac.uk/teaching.html Graduate Attributes and Skills Not entered Keywords ANLW
 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
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