End of Semester - Thanks for a very interesting poster session!
Complete List of Homework Problems
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).
In this course we will proceed from simpler to more complicated (and more interesting!) systems. We begin with one-dimensional flows, their steady states, stability and bifurcations, and then observe the far more complicated dynamics, including chaos, that may occur in one-dimensional maps. Phase-plane analysis in two dimensions reveals the possibility of oscillations and limit cycles, and we study their bifurcations. As time permits, we will also investigate higher-dimensional dynamical systems, deterministic chaos and strange attractors.
Instructor: Ralf Wittenberg
Office: K-10536; Tel: 291-4792
E-Mail: ralfw@sfu.caOffice Hours: Monday, 2:30-3:30pm in K-10536; Wednesday 2:30-3:20pm in AQ 5016 (until 4:30pm in K-10536); or by appointment (preferably by e-mail) Lecture: Monday, Wednesday, Friday 12:30-1:20pm
Location: AQ 2104Web Page: http://www.math.sfu.ca/~ralfw/math467w03
WebCT page
Library course reserves - online lecture notes and reserve booksText: Steven H. Strogatz,
"Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering"
Westview Press.
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 on Fridays, and due the following Friday in class; you can also hand them in by 3:00pm in the Mathematics Homework Box 11b (9000 level of Shrum Science Centre). Problems may be listed on the web 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.
Exams and Grading:
There will be two midterm exams in class, on February 14 and March 28; and a project at the end of the semester. The (tentative) overall grading policy is as follows:
First Lecture | Friday, January 3 | AQ 5030 |
Midterm Exam 1 | Friday, February 14 | In class |
Midterm Exam 2 | Friday, March 28 | In class |