e-mail: ostapyuk@math.uni.edu
Office: WRT 305
Office phone: 319-273-2432
Office hours: TBA

Class schedule: M W F noon-12:50 pm, room: Wright 08. Labs will be held in WRT 110.
All changes in schedule, if any, will be posted on this page.

Textbook: A First Course in Chaotic Dynamical Systems: Theory and Experiment, by Robert L. Devaney,  ISBN: 0-201-55406-2.

Class Syllabus

Homework

Mathematica programs

The Dynamical Systems and Technology Project (from R. Devaney web-page) - check it for images of Julia and Mandelbrot sets.

Click here to learn how to download Mathematica software  (scroll down to "Mathematica")

Exam and Lab dates will appear below at least one week in advance.


Final exam will be on Monday, April 30th  from 1 pm to 2:50 pm in WRT 08. Final Exam will be comprehensive. This is open book exam, you may use any books, notes, calculators or laptops.

Before the exam, review your midterm exam and all homework assignments (labs, while may be helpful, are not directly related to the exam problems).

Things to know for the exam:

• How to iterate functions and compute orbits of the given point;
• Discuss the behavior of the orbit (e.g. whether it is fixed, periodic, etc.);
• How to find fixed points and 2-cycles and describe their behavior (attracting, repelling, neutral) analytically (i.e. by computing derivatives and solving equations);
• How to find fixed points and 2-cycles and describe their behavior (attracting, repelling, neutral) graphically (i.e. by using graphical analysis);
• Chaotic systems; conjugations ans semiconjugations;
• Schwarzian derivatives (including chain rule), relationship to critical points and basins of attraction;
  
• Fractals: definition, how to find area and/or perimeter as a limit, topological and fractal dimension, self-similarity, magnifying factors.

Final review before Final Exam will be during the last class on the semester, on Friday, April 27th. Be ready to ask questions during review.

Lab #6 will be on Wednesday, April 25th  noon - 12:50 pm (regular class time) in WRT 110.

Due to snowstorm, the class on Wednesday, April 18th had been canceled. Lab #5 will be on Friday, April 20th  noon - 12:50 pm (regular class time) in WRT 110.

Lab #4 will be on Monday, March 26th  noon - 12:50 pm (regular class time) in WRT 110.

Midterm Exam Solutions
Midterm Exam statistics: min. 30, max. 96, mean 71.14, median 77.

Midterm Exam will be on Wednesday, Feb 28th  noon-12:30 pm  (regular class time) in WRT 08 (regular room). The exam will cover chapters 3-6. This is open book exam, you may use any books, notes, calculators or laptops.

Things to know for the exam:

• How to iterate functions and compute orbits of the given point;
• Discuss the behavior of the orbit (e.g. whether it is fixed, periodic, etc.);
• How to find fixed points and 2-cycles and describe their behavior (attracting, repelling, neutral) analytically (i.e. by computing derivatives and solving equations);
• How to find fixed points and 2-cycles and describe their behavior (attracting, repelling, neutral) graphically (i.e. by using graphical analysis);
• How to do all of the above for piecewise-defined function (e.g. tent function);
• How to compute fixed points, 2-cycle, describe their type for (simple enough) one-parameter families; recognize bifurcations; provide graphical analysis, sketch phase portraits for parameter value before, at, and after bifurcation value; sketch bifurcation diagrams.

Lab #3 will be on Friday, Feb 16th  noon - 12:50 pm (regular class time) in WRT 110.


Lab #2 will be on Friday, Feb 2nd  noon - 12:50 pm (regular class time) in WRT 110.


Lab #1 will be on Friday, Jan 19th noon - 12:50 pm (regular class time) in WRT 110. You do not have to prepare anything, but make sure you login and password works on lab computers, or, if you are going to use your own laptop, that Mathematica or other software of your choice is installed and working.