Simon Fraser University Department of Mathematics
Fall 2003
Course Information
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Nonlinear Dynamics and Bifurcation This course is an introduction to the study of dynamical systems. Nonlinear differential equations and iterative maps arise in the mathematical description of numerous systems throughout science and engineering, for instance in physics, chemistry, biology, economics, and elsewhere. Such systems may display complicated and rich dynamical behaviour, and we will develop some linear and nonlinear mathematical tools for their analysis, and consider models in such fields as population biology, ecology, and mechanical and electrical oscillations. Our emphasis throughout will be on the qualitative behaviour of the models, in particular, on the prediction of qualitative change in the nature of the dynamics as a system parameter varies (bifurcation). Reading List:In addition to the prescribed text by Strogatz, you may find some of the following books useful; they are all available in the library reserves:
Course Policies and General Information:Prerequisites:This course will depend most strongly on a previous course in ordinary differential equations (Math 310) and linear algebra (Math 232), in addition to the standard calculus sequence. Homework: Homework problems will be assigned weekly; they will be posted on the web by Wednesday, and due the following Wednesday at the beginning of class; you can also hand them in in the Mathematics Homework Box 15a (9000 level of Shrum Science Centre). Problems may be listed earlier; however, I reserve the right to make changes until one week before the due date. You are encouraged to work together and discuss problems with each other (or use the WebCT discussions utility), but solutions must be worked out and submitted individually; you are responsible for your own homework. Please work neatly and clearly and explain your reasoning, and produce neat and clearly labelled graphs when appropriate. A random selection of the problems will be marked every week. The lowest (nonzero) score will be dropped before computing the homework average, and all homework assignments will count equally toward the final homework grade. In addition to the homework problems, I have suggested exercises. These are optional, but I encourage you to look at them; they are usually chosen as a review, a simpler introduction to the basic ideas of a section, an alternative perspective to the ideas discussed in class, or additional practice. Exams and Grading: There will be two midterm exams in class, on October 20 and November 19; and a project at the end of the semester. The (tentative) overall grading policy is as follows:
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