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MA 732-001 Spring 2013

Ordinary Differential Equations II

Mathematics

*Ordinary Differential Equations* by Schaeffer and Cain | Feedback on text

*Ordinary Differential Equations and Dynamical Systems* by Gerald Teschl

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### Material on Midterm

The midterm is Friday March 22. It will cover Homeworks 1 - 4.

Things you should be able to do:

- Use polar coordinates to analyze degenerate equilibria in the plane (Homework 1, problems 1 - 3).
- For maps between Banach spaces, use the definition of derivative, and calculate derivatives using the generalized product rule and chain rule (Homework 2, problems 1, 3).
- Use the Contraction Mapping Theorem and the Contraction Mapping Theorem with Parameters (Homework 2, problems 4, 5; Homework 4, problem 1).
- Use center manifold reduction with a one-dimensional center manifold (Homework 3, problems 3, 4, 5).
- For a periodic differential equation of the form x' = f(t,x), with x in R and f 2pi-periodic in t, use the graph of the Poincare map and linearization to show existence and stability of 2pi-periodic solutions. (Homework 4, problems 2 - 5.)

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Last modified Wed Mar 20 2013

Send questions or comments to schecter@ncsu.edu