Math 488    Fall 2005  

			Introduction to Dynamical Systems
			(Nonlinear Ordinary Differential Equations)
        
                            Professor J. Duan 
                            E1 Room 115B   
                            Tel: 567-5335 
	                      E-mail: duan@iit.edu 
 

Class Hours: Tuesdays and Thursdays  in E1  
Office Hours: Tuesdays and Thursdays or by appointment in E1

 
This is an introductory course in nonlinear dynamical systems with
applications for undergraduate students. This course provides a
coherent treatment of   basic ideas, methods and techniques in
this area. Students will learn nonlinear differential equations
along the way, i.e., in the context of mathematical models.
Throughout the course, many examples of nonlinear differential
equations will be used to illustrate basic concepts and
approaches.

Applying the ideas and methods of nonlinear dynamical systems
theory to scientific and engineering problems has been a
thoroughly interdisciplinary effort.
 
Topics include:

 1. Examples of differential equations as mathematical models,
equilibrium solutions,
plane autonomous systems and linearization, phase portraits;

 2. Periodic solutions, perturbation methods;

 3. Linear stability, asymptotic stability,  Poincare stability and Liapunov
 stability;
 
 4. Bifurcations and invariant manifolds:
Saddle-node, pitchfork, Hopf, period-doubling, 
homoclinic and heteroclinic bifurcations;

  5. Chaos:  sensitive dependence on initial conditions; 

  6. Applications: 
chemical, physical and biological systems;
electrical and mechanical systems; 
chaotic signal masking and telecommunications;
fluid dynamics; geophysical and environmental flows;
mixing and transport phenomena;
control of chaotic systems
 
Textbook Book: 

S. H. Strogatz, Nonlinear Dynamics and Chaos --- with Applications to Physics, Biology, Chemistry, and Engineering.