| lecture 1: generalities | commented slides | pdf version of the slides |
| lecture 2: traffic flow and method of characteristics | commented slides | pdf version of the slides |
| lecture 3: viscous shocks | commented slides solution exercice 1a, 1srt tutorial solution exercice 1d, 1srt tutorial solution exercice 2.3, 1srt tutorial |
pdf_version_of the slides |
| lecture 4: advection-diffusion and KdV | commented slides | pdf version of the slides |
| lecture 5: NLS | recorded lecture | properly drafted typed notes |
| lecture 6: reaction-diffusion | typed_notes |
| Handwritten notes for the course I (Mainly nonlinear advection equation and the method of characteristics) |
pdf (15 pages) |
| Handwritten notes on flood waves (not discussed during the course) These are meant to give a physical illustration of the use of the method of characteristics different from traffic flow theory. |
pdf (4 pages) |
| Illustration of the importance of the subject: cf the video showing a flood submerging a bridge in less than 3mns (St Jean du Gard, 19/09/2020, cortesy of E. Pratlong) | submersion wave |
| Handwritten notes for the course II (Mainly advection-diffusion and Korteweg-de Vries equations) |
pdf (14 pages) |
| When, as in KdV equation, dispersion dominates over viscosity, after wave breaking, a dispersive shock wave is formed, such as seen e.g., on Dordogne river | Mascaret de St Pardon |
| TUTORIAL #1 | TUTORIAL #2 |
| solution_tuto1 | solution_tuto2 |
previous exams
| 2017-2018 | exam | solution |
| 2018-2019 | exam | solution |
| 2019-2020 | exam | solution |
| 2020-2021 | exam | solution |