MAT452 Introduction to Chaos and Nonlinear Dynamics

Instructor: Professor Juan Lopez

Fall 2008: TTh 10:30-11:45, ECG315, SLN: 75984

Office: 640 Goldwater Center
Office Hours: Tu 3:00-4:00
 Phone: (480) 965-8843
E-mail: lopez@math.asu.edu
URL: math.asu.edu/~lopez

Overview:

This is an introductory course to nonlinear dynamics and chaos, with an emphasis on applications. We shall start with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. Throughout we shall emphasis applications, including mechanical vibrations, lasers, biological rhythms, chemical oscillators, and fluid flows.

Text Book:

S. H. Strogatz Nonlinear Dynamics and Chaos (1994: Perseus Books).

Pre-requisites: Differential Equations (M274/M275) and Linear Algebra (M242/M342/M343).

Suggested problems from Strogatz:

Ch. 2: 2.1.1, 2.1.2, 2.2.1, 2.2.4, 2.2.5, 2.2.10, 2.2.13, 2.3.3, 2.4.1, 2.4.3, 2.4.5, 2.4.8, 2.5.3, 2.6.1, 2.7.1, 2.7.3., 2.8.3, 2.8.4, 2.8.5.

Ch. 3: 3.1.4, 3.1.5, 3.2.4, 3.2.6, 3.2.7, 3.4.4, 3.4.5, 3.4.6, 3.4.7, 3.4.8, 3.4.14, 3.4,16, 3.6.2, 3.6.3, 3.6.4, 3.6.6.

First Project

This syllabus is tentative and should not be considered definitive. The instructor reserves the right to modify it to meet the needs of the class. It is the student's responsibility to attend class and to make note of any change.

ACADEMIC DISHONESTY: In the ``Student Academic Integrity Policy'' manual, ASU defines ``Plagiarism'' [as] using another's words, ideas, materials or work without properly acknowledging and documenting the source. Students are responsible for knowing the rules governing the use of another's work or materials and for acknowledging and documenting the source appropriately,'' You can find this definition at:
http://www.asu.edu/studentaffairs/studentlife/judicial/academic_integrity.htm#definitions
Academic dishonesty, including inappropriate collaboration, will not be tolerated. There are severe sanctions for cheating, plagiarizing and any other form of dishonesty.