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MA 732-001 - Ordinary Differential Equations II

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MA 732-001 Spring 2009

Ordinary Differential Equations II

Mathematics

### Material on Test 2

Test 2 is Wednesday April 15. In the Meiss text, it will cover Section 6 and what we have done in Sections 8 (roughly 8.1, 8.2, 8.4, 8.6).

Things you should be able to do:

- Use center manifold reduction when the center manifold is 2-dimensional. (Homework 6, problem 3.)
- Use polar coordinates to analyze degenerate equilibria in the plane. (Homework 6, problems 2 and 3.)
- Use the Poincare-Bendixson Theorem. (P. 241, problems 10 and 12; Homework 8, problem 1.)
- Use Bendixson's criterion. (Homework 8, problem 3c.)
- Analyze planar differential equations near the "circle at infinity." (Homework 9, problem 1d.)
- Draw phase portraits, put together what we've done to draw conclusions. (Homework 6, problem 1; Homework 8, problem 3; Homework 9, problem 1.)
- Prove bifurcation theorems. (Homework 9, problem 2.)
- Use center manifold reduction for bifurcation problems. (Homework 9, problem 3; Homework 10.)

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Last modified Tue Apr 21 2009

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