MAU34210 Linear partial differential equations
| Module Code | MAU34210 |
|---|---|
| Module Title | Linear 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
- Explicit methods: separation of variables, method of characteristics, quasilinear equations, fully nonlinear equations, second-order PDE.
- Wave equation: d'Alembert's formula, conservation of energy, reflection method, uniqueness of solutions, inhomogeneous equation.
- Heat equation: heat kernel, maximum principle, uniqueness of bounded solutions, stability of solutions, inhomogeneous equation.
- Laplace equation: maximum principle, rotational invariance, Dirichlet problem for rectangles and disks, Poisson formula.
Recommended Reading
- An introduction to partial differential equations by Pinchover and Rubinstein.
- Applied partial differential equations by Alan Jeffrey.
- Partial differential equations, an introduction by Walter Strauss.