Postgraduate Course: MIGS: Advanced PDE 1 (MATH12027)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 12 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 15 |
ECTS Credits | 7.5 |
| Summary | The course will cover the basic techniques and methods needed for a rigorous understanding of Elliptic and Parabolic Equations. Furthermore we will study the basic functions space needed for the analysis of partial differential equations. |
| Course description |
i. Holder and Lp spaces, Arzela-Ascoli, Divergence Theorem and Gronwall's inequality.
ii. Laplaces equation, Harmonic functions and basic properties, Fundamental solutions.
iii. Sobolev Spaces and their properties, Schwartz space and the Fourier Transform.
iv. Elliptic equations: Dirichlet problem, Lax-Milgram, Fredholm Alternative, Interior and boundary regularity.
v. Parabolic equations: Heat equation, general second order equations and weak solutions. Galerkin approximation.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Thoroughly understand foundational function spaces used in the study of basic partial differential equations.
- Demonstrate familiarity with Elliptic and Parabolic Partial Differential Equations and their properties.
- Demonstrate a concrete understanding of basic concepts and tools needed to analyse Elliptic and Parabolic Differential Equations rigorously.
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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:
Email: Katy.Cameron@ed.ac.uk |
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