Math 457: Discrete Dynamical Systems

Information for Spring 2008

Instructor: Daniel Dugger
Office: 320 Fenton
E-Mail: ddugger@math.uoregon.edu
Phone: (541)-346-4790

Office Hours: M 11-12, T 10:30-11:30, F 9-10.

Textbook: A First Course in Chaotic Dynamical Systems: Theory and Experiment, by Robert L. Devaney.

Syllabus: There will be two midterms and a final exam. Homework assignments are due each Wednesday, including the last week of class (dead week). Grades will be calculated based on the following percentages:

Homework: 20%
Midterm 1: 25%
Midterm 2: 25%
Final: 30%

Reading assignments and homework for each week will be posted on this web page. You are expected to have read the indicated material and done the exercises BEFORE class meets, and to bring questions about the material into class for discussion. The exercises for the week should be turned in each Wednesday.

Exam #1 will be on Friday, April 25, in class.

Here is a review sheet for the first exam.

Exam #2 will be on Friday, May 23, in class.

Here is a review sheet for the second exam.

The final will be on Friday, June 13, 10:15-12:15, in 301 Deady.

Here is a review sheet for the third part of the course.

Computer tools

Reading assignments and homework:

For Wednesday, April 2: Read chapter 2; you may enjoy reading chapter 1 as well, but we will not use it in class. Also do the following:

For Friday, April 4: Read chapter 3. Turn in the Mathematica worksheet.

The homework to be turned in next Wednesday is here.

For Monday, April 7: Read chapter 4.

For Wednesday, April 9: Read sections 5.1-5.4. Turn in the homework from the above worksheet.

For Friday, April 11: Re-read the proof of the attractive fixed point theorem; also read section 5.5. Start the homework due next Wednesday (the date on the top of the worksheet should be April 16th, not April 13th). Note that the last problem requires Mathematica, and may also take a little thought. Don't save it until the last minute! You might want to use the file iter2.m rather than typing in the code yourself. This is an ASCII file, and you can download it into your home directory or perhaps copy it directly to a Mathematica window. If you don't know how to do this, it might be faster to just enter the code by hand---it's not long.

For Monday, April 14: Read Sections 6.1 and 6.2.

For Friday, April 18: Read Sections 7.1 and 7.2. The homework due next Wednesday is here. Again, ignore the "April 20" due date written at the top---the homework is due next Wednesday, April 23rd.
Here is the file plot.m which has Mathematica code for drawing colored graphs like I did in class. This might be useful in Problem #4 on the homework. The command "Cplot[{x,x^2,x^3}]" will plot the three functions y=x, y=x^2, and y=x^3 in different colors. Use "Cplot[{f[x],f[f[x]]}]" if you want to plot f and its second iterate. You can also use a command like "Iplot[{1,2,3}]", which will plot f, f^2, and f^3 (assuming you have first defined f).

For Wednesday, April 23: Look over the review sheet for Exam #1. Bring any questions you have to class, for us to talk about. We can also go over questions on the homework assignment. If there are no questions, I will continue lecturing on the Cantor set.

The homework due next Wednesday is here.

For Friday, May 2: Re-read all of Chapters 7 and 8. This will mostly be a summary of everything we've been talking about for the past couple of weeks.

The homework due next Wednesday is here.

For Friday, May 9: Read Chapters 9 and 10. Review complex numbers in Chapter 15.

The homework due next Wednesday, May 14, is here.

For Monday, May 12: Read Sections 16.1 and 16.2.

For Friday, May 16: NO CLASS TODAY. Read Sections 17.1-17.5. The homework due next Wednesday, the 21st, is here. Please note that the due date listed at the top of this worksheet is, as usual, incorrect.

For Wednesday, May 21: NO HOMEWORK DUE. Read Sections 16.3 and 17.1 (again).

For Monday, June 2: Make sure you've read all of Chapter 17. There will be no homework due this week, as it's Dead Week.