This course is the second semester of a graduate level introduction to differential equations with emphasis on qualitative methods for nonlinear systems.
Topics for the second semester will include: periodic orbits and Floquet theory, Euler and Morse indices of restpoints, homoclinic points and the Melnikov integral, omega limit sets, attractors and other interesting topics.
Ordinary Differential Equations with Applications, by Carmen Chicone. I will not follow the book very closely but it is good to have something to read and this seems to be a good book.
Grades will be based on several homework assignments throughout the semester.