Undergraduate Course: Elliptic Partial Differential Equations (MATH10089)
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 10 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | The aim of the course is to give an introduction to elliptic partial differential equations and their applications in geometry, material sciences, biology and finance. The student will learn about important concepts such as the notion of a weak solution, the maximum principle as well as important theoretical results, for example the Krylov-
Safonov theorem. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 1, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
15/09/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | MATH10089 Elliptic Partial Differential Equations | 2:00 | |
Summary of Intended Learning Outcomes
1. Reformulate equations of divergence form through integral identities using partial integration.
2. Evaluate or estimate the maximum and minimum of solutions of elliptic equation using the maximum principle.
3. Infer regularity of solutions from that of given data.
4. Explicitly compute the (radially) symmetric solutions and Green/Poisson kernels for the Laplace operator.
5. Estimate first and second order derivatives of solutions via integral norms of solution itself.
6. Compare qualitative properties of weak and viscosity solutions. |
Assessment Information
| Coursework 5%, Examination 95% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Examples of elliptic PDEs and various types of weak solutions.
Weak differentiability, Sobolev spaces and classical solutions.
Harmonic functions: Mean value theorem, Greens function Poisson kernel.
Maximum principle for general linear equations.
Divergence form equations, Caccioppoli's inequality, Morrey's theorem in two dimensions.
Non-divergence form equations, strong and viscosity solutions.
Aleksandrov's maximum principle.
Krylov-Safonov's theorem. |
| Transferable skills |
Not entered |
| Reading list |
Recommended :
E. Landis, Second Order Equations of Elliptic and Parabolic Type, AMS 1998
Qing Han, Fanghua Lin, Courant Institute Lecture notes, NYU, 2011
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 2011 |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | EPDE |
Contacts
| Course organiser | Dr Martin Dindos
Tel:
Email: M.Dindos@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
|
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