Undergraduate Course: Analysis of Nonlinear Waves (MATH11093)
Course Outline
School |
School of Mathematics |
College |
College of Science and Engineering |
Course type |
Standard |
Availability |
Available to all students |
Credit level (Normal year taken) |
SCQF Level 11 (Year 4 Undergraduate) |
Credits |
10 |
Home subject area |
Mathematics |
Other subject area |
None |
Course website |
None |
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Course description |
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 Delivery Information
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Delivery period: 2010/11 Semester 2, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: None |
Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
No Classes have been defined for this Course |
First Class |
First class information not currently available |
Summary of Intended Learning Outcomes
1. Understand local wellposedness.
2. Ability to calculate conserved quantities using Noether's theorem.
3. Ability to use contraction mapping theorem.
4. Familiarity with function spaces.
5. Understand global existence and blow up and the ability to determine which in common cases. |
Assessment Information
Examination 100% |
Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
Not entered |
Contacts
Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Mrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk |
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copyright 2010 The University of Edinburgh -
1 September 2010 6:19 am
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