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

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.

Tentative Course Outline and Homework Schedule

Part I
Aug 23-
  Sept 15		  Flows on the line
 Bifurcations
 Flows on the circle		  Aug 23 - 30
 Sep  1 - 11
 Sep 13 - 15		  Hw 1 - Sept 18
Part II 
Sept 18-
   Oct 20		  Linear systems
 Phase plane
 Limit Cycles
 Bifurcations		  Sep 18 - 25
 Sep 27 - Oct 2
 Oct 4 - 11
 Oct 13 - 20		  Hw 2 - Oct 4
 Hw 3 - Oct 18
 Hw 4 - Nov 1
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		  Hw 5 - Nov 15
 Hw 6 - Nov 29
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

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