University of Utah
Department of Mathematics

Math 5470/6440   Nonlinear Dynamics and Chaos
M W F     9:40-10:30     WBB 617 

Text:  Nonlinear Dynamics and Chaos  by  Steven Strogatz

Instructor:   Elena Cherkaev
Office: LCB 206   ph: 581-7315   email: elena@math.utah.edu
Office hours: M 11am-noon and by appointment


Tentative Course Outline

Part I

Aug 23-
Sept 15
 Flows on the line
 Bifurcations
 Flows on the circle
 Aug 23-30
 Sep  1-11
  Sep 13-15
Part II
 
Sept 18-
   Oct 20
 Linear systems
 Phase plane
 Limit Cycles
 Bifurcations
 Sep 18 - 25
 Sep27-Oct2
 Oct 4-11
 Oct 13-20
Part III
 
Oct 23-
   Dec 6
 Lorentz equations
 1D Iterated maps
 Fractals
 Strange attractors
 Oct 23-30
 Nov 1-8 
 Nov 10-20
 Nov 22 - Dec 6
Dec 11  Final exam

   8am-10am



Labor Day holiday:
Monday, September 4
Fall break
Thurs.-Fri., October 5-6
Thanksgiving break
Thurs.-Fri., November 23-24

Course description Chaos is everywhere around us from fluid flow and the weather forecast to the stock exchange and striking geometric images. The theory of nonlinear dynamical systems uses bifurcations, attractors and fractals to describe the chaotic behavior of real world things. The course gives an introduction to chaotic motions, strange attractors, fractal geometry. The emphasis of the course is on applications:
  • Mechanical vibrations
  • Chemical oscillators
  • Superconducting circuits
  • Insects outbreaks
  • Genetic control systems
  • Chaotic waterwheels 
  • Chaotic communications

The course is addressed to senior undergraduate and graduate students in mathematics, science, and engineering.  Prerequisites: Calculus and Differential Equations.

Grades:  Your percentage grade will be computed as follows:
75% for the homeworks; 15% for the project; 10% for the final