Postgraduate Course: MIGS: Elliptic and Parabolic PDEs (MATH11210)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 15 |
ECTS Credits | 7.5 |
| Summary | This course covers parabolic and elliptic equations. Useful methods to study solutions such as travelling wave and similarity solutions are developed and nonexistence and multiplicity results for solutions of nonlinear elliptic problems are studied by a variety of methods. Different concepts and tools are developed such as maximum principles, blow up and comparison theorems. One striking result that will be proved is that positive solutions of autonomous semilinear elliptic problems on a ball must be radially symmetric.
The remaining lectures are on variational formulation of elliptic PDEs. The material includes an introduction to the Sobolev function spaces, Sobolev embedding and trace theorems.
- Analysis of parabolic and elliptic PDEs (including existence, uniqueness, maximum principles, energy estimates, monotone iteration, regularity, eigenfunctions)
- Variational theory of PDEs
- Sobolev embeddings and trace theorems |
| Course description |
The aim is to learn new things to get a broad education in the area as a basis for a wide range of PhD projects and for post-PhD employment. Unless otherwise noted, the details of the content of these courses can be found on the Scottish Mathematical Sciences Training Centre web site www.smstc.ac.uk
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
|
| Academic year 2022/23, Not available to visiting students (SS1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
150
(
Lecture Hours 20,
Programme Level Learning and Teaching Hours 3,
Directed Learning and Independent Learning Hours
127 )
|
| Assessment (Further Info) |
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
100% coursework |
| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Thoroughly understand the analytical concepts and methods developed in the uniqueness and existence theorems for solutions of PDEs.
- Apply finite element approximations to solve PDEs.
|
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Prof Benedict Leimkuhler
Tel:
Email: B.Leimkuhler@ed.ac.uk |
Course secretary | Mrs Katy Cameron
Tel: (0131 6)50 5085
Email: Katy.Cameron@ed.ac.uk |
|
|
University Homepage