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 undergraduates, including
physics majors, and other students with preparation in introductory
physics and in solving
differential equations (ordinary and partial).
Grades: Grades will be assigned according to the
following weighted average:
Problem Sets (assigned every one to two weeks): 30%
Midterm exam and Final exam: 20% each
Final Project: 30%
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.
Exam Policy:
No collaboration on exams is allowed.
No books, notes or calculators are allowed.