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MA 532-001 Fall 2008

Ordinary Differential Equations I

Mathematics

### Material on Test 2

Test 2 is Wednesday Nov. 19. In the Meiss text, it will cover linear stability and nonautonomous linear systems, but not Floquet theory (2.7 - 2.8); existence and uniqueness (Chapter 3); flows (4.1 - 4.3); Liapunov functions and omega-limit sets (4.5 - 4.6, 4.9).

Things you should be able to do:

- Derive and use the variation of parameters formula; use Lemma 2.9 in Meiss (Homework 6, problem 3; Homework 8, problem 1).
- Find all solutions of an initial value problem when the Existence-Uniqueness Theorem does not apply (Homework 7, problem 1).
- Show that a mapping is a contraction, and use the Contraction Mapping Theorem (Homework 7, problem 3).
- Use the Existence-Uniqueness Theorem (Homework 7, problem 4; Homework 8, problem 2).
- Verify the properties of a flow (Homework 8, problems 3 and 4).
- Use Lyapunov functions and the Lasalle Invariance Principle (Homework 9, problems 1 - 5).
- Use the notion of omega-limit set (Homework 9, problem 6).

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Last modified Tue Nov 11 2008

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