Math 372 - Fall 2009
Dynamical Systems: Syllabus

Contact:
Instructor: Dennis Pixton
Email: dennis at math.binghamton.edu
Office: LN2245
Office hours: M 3:30 - 4:30; TWF 1:10 - 2:10.

If you can't meet me during my scheduled hours just check with me after class, or send email, to arrange a meeting time.

Prerequisites: Calculus II (Math 222) and Linear Algebra (Math 304). You need to know how to calculate with matrices, especially eigenvalues and eigenvectors, and you need to know how this is related to diagonal forms for matrices. This will be very important after the first couple of weeks of the class.

Course outline: We will cover the first five chapters, and part of the sixth as time allows, from the online notes. The most recent version of the notes is available on the course home page. The main topics, corresponding to the chapters, are:

1. Discrete population models
2. Continuous population models
3. Discrete Linear models
4. Linear models: continuous version
5. Non-linear systems
6. Chaotic systems

Learning objectives: Students will learn to:

• Develop dynamical systems to model problems from biology, physics, and other areas.
• Solve simple dynamical systems; apply computer methods to solve and visualize more complex systems.
• Apply tools from Calculus and Linear Algebra to analyze discrete and continuous dynamical systems. Especially important will be connections between eigenvalues and eigenvectors and the long term behaviour of dynamical systems.
• Set up, analyze, and interpret phase portraits of linear and non-linear systems of differential equations, in low dimensions.
• Use graphical and symbolic methods to represent and interpret chaotic dynamical systems.

Grading: There will be two midterms and a final, and you will also have a homework grade. I will drop the lowest of these scores, leaving 3 grades. The grades will be recorded on a 0-4 scale, corresponding approximately to letter grades. Your course grade will be based on the average of these scores. Later in the semester I may propose "projects" which will count towards your grade. Any such projects will be optional.

My basic expectation is that you will turn in serious work on a significant number of homework assignments. Full credit for half the assigned homework will be sufficient for a B as your homework grade. Approximately one fourth of the assigned homework will be sufficient for a C.

Attendance: Attendance is required at all classes. This includes the Tuesday meeting, which is a regular class, not a discussion session. After 3 unexcused absences I will penalize you for missed classes. Each missed classes will cost you one tenth of a grade. For example, 20 missed classes will reduce an A- to a C-.

Academic honesty: You are encouraged to work with others in the class on homework, to talk with me about it, and to consult other sources. You need to identify any part of your homework that is based on collaboration with others in the class, or that is substantially based on other sources. If you acknowledge your collaboration or outside sources then there will be no penalty. If you do not acknowledge collaboration or outside sources then you are in violation of University rules on academic honesty. The penalties for such violation can be severe: see the Student Academic Honesty Code.