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 |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| 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. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Metric Spaces (MATH10049)
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
| Not being delivered |
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% |
Special Arrangements
| None |
Additional Information
| Academic description |
See short description. |
| Syllabus |
See short description. |
| Transferable skills |
Not entered |
| 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) |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | ANLW |
Contacts
| Course organiser | Dr Pieter Blue
Tel: (0131 6)50 5076
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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