Advanced PDEs (L.7) (866G1)
Advanced Partial Differential Equations (L.7)
Module 866G1
Module details for 2023/24.
15 credits
FHEQ Level 7 (Masters)
Library
Indicative reading and resource list:
Evans, Lawrence C. Partial differential equations, 2nd ed. : Providence, R.I. : American Mathematical Society, 2010. ISBN: 978-0-8218-4974-3.
Salsa, Sandro, Partial differential Equations in Action: From Modelling to Theory (Universities), Springer Verlag, 2010. ISBN-13: 978-8847007512.
Module Outline
The students will be introduced to modern theory of linear and nonlinear Partial Differential Equations. Starting from the theory of Sobolev spaces and relevant concepts in functional analysis, they will treat the linear second-order elliptic, parabolic, and hyperbolic equations (Lax-Milgram theorem, existence of weak solutions, regularity, maximum principles), e.g., the potential, diffusion, and wave equations that arise in inhomogeneous media. The emphasis will be on the solvability of equations with different initial/boundary conditions, as well as the general qualitative properties of their solutions. They then turn to the study of nonlinear PDEs, focusing on calculus of variation, in particular the direct method.
Module learning outcomes
Have a comprehensive understanding of Sobolev spaces and properties of Sobolev functions and be able to apply central theorems to partial differential equations (PDEs).
Investigate elliptic equations of the second order by applying existence and uniqueness theorems of weak solutions, critically evaluate regularity and maximum principle.
Critically evaluate and deploy established techniques in the theory of parabolic equations of the second order and time-dependent, linear equations.
Critically evaluate and interpret the theory of calculus of variations, in particular explain the concept of a minimiser and evaluate the regularity of minimisers.
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 30.00% | |
| Coursework components. Weighted as shown below. | ||
| Problem Set | T2 Week 8 | 16.67% |
| Problem Set | T2 Week 11 | 50.00% |
| Problem Set | T2 Week 3 | 16.66% |
| Problem Set | T2 Week 5 | 16.67% |
| Coursework | 10.00% | |
| Coursework components. Weighted as shown below. | ||
| Portfolio | T2 Week 11 | 100.00% |
| Unseen Examination | Semester 2 Assessment | 60.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring Semester | Lecture | 1 hour | 11111111111 |
| Spring Semester | Lecture | 2 hours | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Prof Michael Melgaard
Assess convenor, Convenor
/profiles/36956
Please note that the University will use all reasonable endeavours to deliver courses and modules in accordance with the descriptions set out here. However, the University keeps its courses and modules under review with the aim of enhancing quality. Some changes may therefore be made to the form or content of courses or modules shown as part of the normal process of curriculum management.
The University reserves the right to make changes to the contents or methods of delivery of, or to discontinue, merge or combine modules, if such action is reasonably considered necessary by the University. If there are not sufficient student numbers to make a module viable, the University reserves the right to cancel such a module. If the University withdraws or discontinues a module, it will use its reasonable endeavours to provide a suitable alternative module.