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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Analysis of Nonlinear Waves (MATH11093)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryFundamental 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Metric Spaces (MATH10049) OR Hilbert Spaces (MATH10046)
Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Understand local wellposedness.
  2. Calculate conserved quantities using Noether's theorem.
  3. Use contraction mapping theorem.
  4. Demonstrate familiarity with function spaces.
  5. 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)
Additional Information
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsANLW
Contacts
Course organiserDr Pieter Blue
Tel: (0131 6)50 5076
Email: P.Blue@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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