Physics 221A : Course Outline
The subject matter can roughly be divided along the lines of ODEs versus PDEs. The ODE (Ordinary Differential Equations) material will cover dynamical systems, bifurcations, nonlinear oscillators, and chaos. I will assume you have some familiarity with Hamiltonian mechanics from Physics 200AB or the equivalent. The PDE (Partial Differential Equations) material will treat front propagation, pattern formation, solitons, and shock waves.
In addition to not paying much attention to the course catalog, I'm also not going to pay much attention to the course texts, by Manneville and by Cross and Greenside. However, these are both really good books and interested students might consider purchasing a copy. I'll instead be following my lecture notes, which are available through the course web site. A list of relevant texts is provided in chapter 0 of the notes.
Course Web Site
Lecture notes and reading assignments, important announcements, homework assignments and solutions will all be available through the course web site. Please check it regularly to see if there is new material. I am updating my lecture notes as we go along, and I will indicate on the lecture notes page the date, time, and size (in pages) of the most recent upload for each chapter.
There should be a problem set every one or two weeks. Problem sets will not be printed out for you, but rather will be available through the course website. You are encouraged to discuss the problem sets with your fellow students. I suggest that you initially try to do the problems by yourselves, so that you can more accurately identify your confusions and honestly assess your weaknesses. Then, before you write up your assignment, get together with some of your fellow students to talk over the problems and hammer out the details. I will try to prepare solution sets in a timely manner.
Your grade will be determined by the following formula: 50% homework, 40% final project, 10% intangibles. The latter category includes things like class participation, personal hygiene, laughing at my jokes, etc.
Rather than a final exam, there will be a final project. You should write a paper 10 to 12 pages in length (including references). Email me your completed assignment by the due date (TBA). During the scheduled final exam time, you will present your final project to the rest of the class. You may collaborate with one other classmate. Here is a potential list of topics from which you may choose (contact me if you have other ideas):
1. Vehicular traffic modeling and jamming
2. Pattern formation
4. Dynamical chaos
5. Spread of epidemics
6. Bacterial patterns and chemotaxis
7. Evolutionary dynamics
8. Hydrodynamic instabilities
9. Flame fronts
10. Effect of noise on nonlinear dynamics
11. The complex Ginzburg-Landau equation
12. Solitons in optical fibers
13. Spiral waves
14. Synchronization in the presence of noise
15. Numerical simulation of pattern formation