MAU34204 Partial differential equations
| Module Code | MAU34204 |
|---|---|
| Module Title | Partial differential equations |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Paschalis Karageorgis |
| Module Prerequisites |
MAU11404 Techniques in theoretical physics OR
MAU23205 Ordinary differential equations |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 10% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Module Content
- Calculus of variations: functional, variation, extremals, Euler-Lagrange equation, Beltrami identity, brachistochrone, catenary, natural boundary conditions, isoperimetric constraints.
- Conservation laws: transport equation, Burgers' equation, method of characteristics, weak solutions, Rankine-Hugoniot jump condition, Oleinik entropy condition.
- Green's functions: Green's identities, Laplace equation, Dirichlet principle, fundamental solution, rotational symmetry, solution in half space, Poisson formula.
Recommended Reading
- Gelfand and Fomin, Calculus of variations (Sections 1-6 and 12).
- Pinchover and Rubinstein, An introduction to partial differential equations (Chapter 2).
- Walter Strauss, Partial differential equations: an introduction (Section 6.1, Chapter 7).