Math 361 - Chaos and Dynamical Systems

Spring Semester, 2007-2008

Go straight to the syllabus.

This course is about dynamics--the mathematics of how things change with time. Dynamics has evolved from its origins in the calculus of Newton and Leibniz to a modern theory of dynamical systems relevant to areas of science including physics, astronomy, biology, chemistry, engineering, medicine, ecology, and economics. We will look at the main concepts and applications of dynamical systems and, in particular, a type of motion now called "chaos".

CLASS INFORMATION:

• Meeting time: MWF 12:00-12:50 AM
• Meeting room: Glatfelter 203

OFFICE AND OFFICE HOURS:

• Office: Glatfelter 202A
• Office hours: MWF 11:00-12:00 and by appointment

TELEPHONE NUMBER AND E-MAIL:

• Telephone: 337-6630
• E-mail: jfink@gettysburg.edu
• WWW page: http://cs.gettysburg.edu/~jfink/courses/ma361.html

EXAM DATES:

• Exam 1: Wednesday, February 27
• Exam 2: Wednesday, April 16
• Final Exam: Saturday, May 10, 1:30-4:30 PM

PREREQUISITES:

• Mathematics 225 (grade of C or better) or permission of instructor

TEXTBOOK:

• Chaos: An Introduction to Dynamical Systems by Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke
  ISBN 978-0-387-94677-1
• Any printing may be used. Later printings are essentially the same as earlier printings but with errors and typos fixed.

COURSE CONTENT:

• Topics from Chapters 1, 2, 3, 4, 5, 7, 8, and 9
• Detailed syllabus

GRADING POLICY:

• Your grade will be determined by your scores on the following:
  • homework (1/6);
  • two exams (1/6 each);
  • project (1/6);
  • final exam (1/3).
• ***There will be no make-up exams and late work will not be accepted.***

HOMEWORK:

• Homework will be assigned, collected, and graded.
• Assignments may include material that will not be discussed in class. You are expected to learn this material on your own and to make use of the resources available to you to complete the assignments.
• Grading will be based both on mathematical content and on the quality of your write-up. NEATNESS COUNTS! Show all work necessary to justify your solutions. Answers alone are not sufficient.
• You may work with other students on the homework; in fact, I encourage that. However, your write-up should be your own.

TEAM PROJECT:

• The project will be a team effort with each team consisting of two students.
• For a topic, you may choose any Challenge or Lab Visit in the textbook. See the Introduction in the book for descriptions of the Challenges and Lab Visits.
• The project is not intended to take an unreasonable amount of time, but it is unlikely that you will complete the project in a single sitting. Thus, your team should begin work on the project well in advance of the due date. You will probably find that shorter work sessions spread over several days are the best way to attack the project.
• To get you started early on the project, you must select your teammate and topic by Friday, April 11.
• Projects will be presented in class at the end of the semester.

COURSE SOFTWARE:

• Although you can write your own computer programs to explore dynamics through numerical simulations, it is much simpler to use existing software packages.
• Many packages are available, along with general purpose computing environments such as MATLAB and Mathematica.
• For discrete dynamical systems, we will use the applets developed by Robert Devaney at Boston University.
• For continuous dynamical systems, we will use MATLAB and associated ODE software developed by John Polking of Rice University.