Detailed course information and support will be provided through Moodle pages. For questions about the course, do not hesitate to contact Dr. Ilday via email.

This course is an introduction to nonlinear dynamics, with applications to physics, optics, engineering, biology, and chemistry. We will emphasize analytical methods, numerical techniques, and geometric thinking. Topics to be discussed include one-dimensional systems, bifurcations, synchronization, nonlinear
oscillators, discrete maps, period doubling, fractals, strange attractors, and chaos.
The course is designed for graduate students and accesible to a range of backgrounds, including physics, mathematics, chemistry, material science and electrical engineering. Senior undergraduate students with good preparation should be able to follow. Familiarity with mathematical software packages, such as Matlab, Maple and Mathematica will help.

 

Instructor: F. Omer Ilday (www)

Office: SA-224 (phone: 1076x)
Office Hours: To be determined

Lectures: To be determined

Grading (tentative)
Homeworks (about 10 sets)
 %25
Midterm exam
 %25
Attendance/participation %10
Final exam (take-home)
 %40

Textbook (required):
Nonlinear Dynamics and Chaos by Strogatz (Addison-Wesley, 1994)
  Topic
 Book Chapters
1
 One-dimensional systems and elementary bifurcations (2 weeks)
1-4
2
 Two-dimensional systems; phase plane analysis (1 week)
5-6
3
 Nonlinear oscillators, limit cycles and their bifurcations (2.5 weeks)
7-8
4
 Lorenz equations and chaos (2.5 weeks)
9
5
 Iterated mappings, period-doubling route to chaos, renormalization (2 weeks)
10
6
 Fractals and strange attractors (2 weeks)
11-12
7
 More advanced topics, if time permits
TBD

 

Accessed at least times several since August 18, 2009.