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.
- Re-assessment, if needed, consists of 100% exam.
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 problems, Noether's theorem, second variation, Legendre's condition.
- Conservation laws: transport equation, method of characteristics, Burgers' equation, weak solutions, Rankine-Hugoniot jump condition, Oleinik entropy condition.
Recommended Reading
- Calculus of variations by Gelfand and Fomin (chapters 1-5).
- Partial differential equations by L.C. Evans (chapter 3).