Math 5470 - 1   Chaos Theory                                          January 11, 2016
Math 6440 - 1   T, Th  9:10 - 10:30  in LS 101.

Homepage:       http://www.math.utah.edu/~treiberg/M5470.html

Instructor:     A. Treibergs, JWB 224, 581 - ­8350.
                Office Hours: MW 11:45-12:45, T10:45-11:45 (tent.) & by appt.
                E-mail: treiberg@math.utah.edu

Prerequisites:  "C" or better in MATH 2250 OR MATH 2280 OR consent of instructor. 
                
Texts:          Stephen H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to 
                Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) 
                2nd ed., Westview Press; 2014.  ISBN-13: 978-0813349107
 
Grading
    Homework:   To be assigned weekly. Homework will be due Fridays and will be collected
                in class. Papers turned into my mailbox in the math mail room (JWB 228) by 
                4:00 PM Fridays before I leave will be regarded as being turned in on
                time. Homework that is late will receive half credit.

Term Project:   Students will write a short mathematical paper on an approved topic of
                their choice. This paper will allow students to explore in some detail a
                mathematical theory or a model from science or engineering beyond what's
                covered by lectures. Students will meet individually with the instructor
                to discuss an outline of their proposed project. Project outlines must be
                approved by Mar. 10. Completed projects are due the last day, Apr. 26.

       Exams:   Exams will be closed book except that you will be allowed 
                to bring a "cheat sheet," an 8.5" x 11" piece of paper with 
                notes on both sides. Your text, notes, homework papers, 
                calculators laptops, tablets, phones, text messaging devices,
                and other books will not be allowed.

       Midterms:   There will be two in-class one-hour midterm exams on Thursdayss 
                   Feb. 18 and Mar. 31.  

       Final Exam: Wed., May 4, 8:00 - 10:00 AM. Half of the final will be devoted to
                   material covered after the second midterm exam. The other half will be
                   comprehensive. Students must take the final to pass the course.

Course grade:   Two midterms 40% + Project 10% + HW 20% + final 30%.

Withdrawals:    Last day to drop a class is Jan. 22. Last day to add a class is Jan. 22.
                Until Mar. 4 you can withdraw from the class with no approval at all.
                After that date you must petition your dean's office to be allowed to
                withdraw.

ADA:            The University of Utah seeks to provide equal access to its programs, 
                services and activities for people with disabilities. If you will need 
                accommodations in this class, reasonable prior notice needs to be given
                the Center for Disability Services, 162 Olpin Union Building, 
                581-5020 (V/TDD). CDS will work with you and the instructor to make
                arrangements for accommodations. All information in this course can be
                made available in alternate format with prior notification to the Center
                for Disability Services  (www.hr.utah.edu/oeo/ada/guide/faculty/)

Faculty and Student Responsibilities:
               All students are expected to maintain professional behavior in the 
               classroom setting, according to the Student Code, spelled out in the
               Student handbook. Students have specific rights in the classroom as
               detailed in Article III of the Code. The Code also specifies proscribed
               conduct (Article XI) that involves cheating on tests, plagiarism and/or
               collusion, as well as fraud, theft, etc. Students should read the Code
               carefully and know they are responsible for the content. According to the
               Faculty Rules and Regulations, it is faculty responsibility to enforce
               responsible classroom behaviors, beginning with verbal warnings and 
               progressing to dismissal from class and a failing grade. Students have 
               the right to appeal such action to the Student Behavior Committee.
               Faculty must strive in the classroom to maintain a climate conductive to
               thinking and learning (PPM 6-316). Students have a right to support and
               assistance from the University in maintaining a climate conducive to 
               thinking and learning (PPM 6-400).

Note:          The syllabus is not a binding legal contract. It may be modified by the 
               instructor when the student is given reasonable notice of the
               modification.
                              

Course Description: 
               Chaos is everywhere around us from fluid flows, weather forecasting, stock 
               prices and fractal images. The theory of nonlinear dynamical systems uses
               bifurcations, attractors and fractals to describe the chaotic behavior in
               the real world. The course gives an introduction to chaotic motions,
               strange attractors, fractal geometry:

               We shall generally follow Strogatz' text. We will emphasize applications
               taken from various subjects like mathematical biology, engineering,
               geometry and physics. Occasionally we'll refer to other texts. Topics
               include (depending on time):

                     Mechanical Vibrations
                     Chemical Oscillators
                     Superconducting Circuits
                     Insect Outbreaks
                     Genetic Control Systems
                     Chaotic Water Wheel
                     Noisy Communications