Math 6308   Ordinary differential Equations II.  Spring 2018

 Schedule: 1:30 - 2:45 pm  TR Classroom: Skiles 255 Office: Skiles  102A Phone: 404-894-4750 Email: zengch@math.gatech.edu Webpage: www.math.gatech.edu/~zengch Office hours: 10:05 - 11am W & 12:30 - 1:25pm R

Syllabus

Instructor: Chongchun Zeng

Prerequisites: MATH 2552&4541, or permission of the instructor

Participation: Attendence in classes is mandatory. Students are expected to read the materials before and/or after the classes. It is suggested that you start to work on homework problems right after they are assigned.

Main reference book: Ordinary differential equations with applications, Carmen Chicone, 2nd edition, Springer. (Homework will mainly come from this book.)

Materials:  In this semester, we will develop the qualitative theory for systems of nonlinear ordinary differential equations. After a brief review of the material covered in Math 6307, the main subjects include invariant manifold theory, bifurcation theory, normal forms, periodic orbits and homoclinic orbits. The topics are among

• Invariant manifolds: existence, uniqueness, smoothness, and other properties of invariant manifolds and invariant foliations.

• Basic bifurcations: saddle-node, transcritical, pitch-fork, and Hopf bifurcations.

• Periodic orbits: Poincare map, persistence, period-doubling, and periodic orbtis in Hamiltonian systems.

• Homoclinic orbits: Melnikov method, Smale-Birkhoff theorem, etc.

• 1 take-home final exam 40%: `open-textbook' and `open-notes', must be entirely independent work.
• 4 homework, 15% each: homework will be assigned at the end of each lecture and then put on this webpage in the below. You may discuss the homework problems with other students in this class, but you should write down the solutions and complete the homework independently. On each collecting day, the homework is due in the classroom at the beginning of the lecture. The corresponding assignment includes all the problems assigned in previous weeks, but after the last assignment. Some selected problems from each assignment will be graded and the score will be given based on both the graded problems and the completion of the whole assignment. The exact homework collecting dates are:

1/25(Thu.), 2/15(Thu.), 3/8(Thu.), 4/5(Thu.)

Homework assignments:

• Homework Assignment #1 (due Thu. 1/25):
• Assigned on Tue. 1/9:  P159, 2.30;  P163,  2.34;  P193, 2.86, 2.87
• Assigned on Thu. 1/11:  P228, 3.2;  P233, 3.5, 3.7
• Homework Assignment #2 (due Thu. 2/15):
• Homework Assignment #3 (due Thu. 3/8)
• Assigned on Tue. 2/13:  Page 347,  4.4, 4.5
• Assigned on Thu. 2/22:  Page 558,  8.9
• Homework Assignment #4 (due Thu. 4/5)
• Assigned on Tue. 3/6: Page 564,  8.18, 8.19
• Assigned on Tue. 3/13:  P373,  5.2
• Assigned on Tue. 3/27:  P382,  5.9