Introduction to the Mathematical Theory of Diffraction
University of Manchester – Department of Mathematics
PhD Course, Spring 2026
Lectures
| Lecture |
Topics |
Notes |
Video recordings (Youtube) |
| 1 |
Governing equations; Laplace operator; Green’s function of Helmholtz equation; plane waves; plane wave decomposition; far-field asymptotics |
PDF |
Part 1 Part 2 |
| 2 |
Mathematical statement of diffraction problem; boundary conditions; Sommerfeld radiation condition; limiting absorption principle; Meixner series |
PDF |
Part 1 Part 2 |
| 3 |
Ray approximation; geometric theory of diffraction; canonical problems; Half-plane problem (problem statement) |
PDF |
Part 1 Part 2 |
References
Recommended literature for the course:
- J. B. Keller – Geometrical Theory of Diffraction
- V. A. Fock – Electromagnetic Diffraction and Propagation Problems
- D. S. Jones – Acoustic and Electromagnetic Waves