Undergraduate Course: Elliptic Partial Differential Equations (MATH10089)
Course Outline
School | School of Mathematics |
College | College of Science and Engineering |
Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
SCQF Credits | 10 |
ECTS Credits | 5 |
Summary | 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. |
Course description |
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.
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Information for Visiting Students
Pre-requisites | None |
Course Delivery Information
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Academic year 2015/16, Available to all students (SV1)
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Quota: None |
Course Start |
Semester 1 |
Timetable |
Timetable |
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 )
|
Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
Additional Information (Assessment) |
Coursework 5%, Examination 95% |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
|
Main Exam Diet S1 (December) | MATH10089 Elliptic Partial Differential Equations - Visiting Students | 2:00 | |
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Academic year 2015/16, Part-year visiting students only (VV1)
|
Quota: None |
Course Start |
Semester 1 |
Timetable |
Timetable |
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 )
|
Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
Additional Information (Assessment) |
Coursework 5%, Examination 95% |
Feedback |
Not entered |
No Exam Information |
|
Academic year 2015/16, Part-year visiting students only (VV2)
|
Quota: None |
Course Start |
Semester 1 |
Timetable |
Timetable |
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 )
|
Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
Additional Information (Assessment) |
Coursework 5%, Examination 95% |
Feedback |
Not entered |
No Exam Information |
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.
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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 |
Additional Information
Graduate Attributes and Skills |
Not entered |
Keywords | EPDE |
Contacts
Course organiser | Dr Martin Dindos
Tel:
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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© Copyright 2015 The University of Edinburgh - 27 July 2015 11:35 am
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