Lectures: 9.30am-10.45am on Tue., Thr., in Math 1311.

Prerequisites: MATH 405, and MATH 410, or an equivalent.

Textbook: "Principles of Differential Equations" by Nelson G. Markley, 2004.

Additional References:

• V. Arnold, "Ordinary Differential Equations", MIT Press 1992..
• P. Hartman, "Ordinary Differential Equations", Birkhauser 1982.
• V. Arnold, "Mathematical Methods of Celestial Mechanics", Springer-Verlag 1978.

Description: MATH 670 is an introduction to some important aspects of modern dynamical systems theory, and qualitative theory of differential equations. The main topics are: existence and uniqueness theorems, asymptotic behavior of solutions and stability, linear systems with constant coefficients, Floquet theory of periodic linear systems, Liapunov theory of stability, planar systems with Poincare-Bendixon theorem, linearization, and invariant manifolds.

Assignments: Homework must be submitted on the date assigned. Homework must be prepared without consulting any other person. You may however consult any written reference. In this case you should cite the reference. Results taken from the reference should be (re)stated to the notation used in the course. Explanation should be given in complete English sentences. Written work must be legible and clear.

Exams: The midterm will be scheduled during a regular class (1h15min long). Currently, the mid-term is scheduled for October 23, 2007. You are allowed with one-sided cheat sheet. The final exam will be 3-hour long, and currently it is scheduled for December 18, 2007, 9.30am-11.30am December 14, 8am-11am. For the final exam you are allowed with a two-sided cheat sheet.

Grading:

• 25%: homeworks
• 25%: midterm
• 50%: final exam