Math 8501 --- Fall 2001

Theory of Ordinary Differential Equations

MW 10:10-11:00 in Vincent Hall 2

Description:

This course will be a one-semester graduate level introduction to differential equations with emphasis on qualitative methods for nonlinear systems. If there is sufficient interest it will be followed in the spring by Math 8502 -- Dynamical Systems and Differential Equations, which will explore further topics.

Understanding the modern theory of dynamical systems requires a lot of ideas from many parts of mathematics. I hope to cover both the differential equations theory itself and these background ideas in a way which can be understood not only by math graduate students but by any mathematically inclined student with a solid knowledge of linear algebra, advanced calculus and elementary differential equations.


Topics for the first semester will include: basic existence and uniqueness theory, theory of linear systems, dynamics near equilibria including Hartman's theorem and the stable manifold theorem, dynamics near periodic orbits including Floquet theory and the stable manifold theorem. In addition we spend a good deal of time on (interesting) examples to illustrate and apply the theory.

Text:

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:

Homework 2/3
Final Exam 1/3