Postgraduate Course: MIGSAA Advanced PDE 1 (MATH12006)
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
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Academic year 2023/24, Not available to visiting students (SS1)
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Quota: None |
Course Start |
Semester 1 |
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 )
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Assessment (Further Info) |
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Coursework: 100% |
Feedback |
Not entered |
No Exam Information |
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 |
Special Arrangements |
*Only students of the MIGSAA CDT may take this course* |
Keywords | Not entered |
Contacts
Course organiser | Prof Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk |
Course secretary | Ms Isabelle Hanlon
Tel: (0131 6)50 5955
Email: i.hanlon@ed.ac.uk |
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