Introduction
 

This course is a graduate-level introduction to nonlinear dynamics: we examine linear and and nonlinear instabilities in mathematical, physical, chemical and biological systems that evolve in time. It is also appropriate for upper division undergraduate physics majors.

 

Grades: Grades will be assigned according to the following weighted average:

• Problem Sets (assigned every one to two weeks): 40%
• 20 minute quiz approximately every 3 weeks: 25%
• Final Project: 35%


 
  Prerequisites
 
• Exposure to the mathematics covered in MTH 111.
• Exposure to the physics covered in PHY 51 and 52.
• SOME experience with a programming language like Basic, FORTRAN, or C.

  Topics
 
• Overview of Chaos and Dynamical systems
• One-dimensional flows
• Bifurcations
• Two-dimensional flows
• One-dimensional maps
• Strange attractors and fractal dimensions
• Dynamical properties of chaotic systems
• Phase space, manifolds, Lyaponov exponents, time series analysis, control
• Special topics
• Applications

  Academic Integrity
• Homework Assignments:  Collaborating on the problem sets by discussing approaches is OK, but please remember that you learn from these mostly by struggling through them for yourself. Do not let others solve them for you. Also, it pays to start early; sleeping on a problem is often a useful step when confused.

 
• Exams:  No collaboration on quizzes is allowed. You may not access any quizzes, tests, or finals from previous years. You may discuss the general concepts and get advice from advanced students. No books, notes or calculators are allowed during quizzes.