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MA 532-001 Fall 2012

Ordinary Differential Equations I

Mathematics

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

*Ordinary Differential Equations and Dynamical Systems* by Gerald Teschl

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### Homework Assignments

#### Assigned Tuesday, Aug. 21

Homework 1: Sec. 1.8, problems 3c, 3d, 5, 6, 7. **Due Friday Aug. 31**. For instructions on how to submit, go here and scroll down to Homework.

More problems may be added later this week.

Problem 3d: What happens to your solution when x (not t) approaches 0?

Problem 5 refers to equation 1.39 in the text. Warning: equation 1.47 is upside down (numerator and denominator should be exchanged). You should derive the equation L(x,y)=c by solving 1.47 by separation of variables. Then you should check your answer by checking that if (x(t),y(t)) is any solution, then (d/dt)L(x(t),y(t))=0.

Problem 6a: You can do this by showing that x_{partic}(t) - x(t) satisfies the homogeneous equation.

Problem 6d: You can use Maple or something similar to make the graph.

#### Assigned Friday, Aug. 31

#### Assigned Sunday, Sep. 9 and Monday, Sep. 10

Homework 3: Prove Lemma 2.2.3 parts (i)-(iii) and Lemma 2.2.4. Note that the statement of Lemma 2.2.4 continues onto the next page. Also: Problem 5(a) in Sec. 2.6.

**Due Friday Sep. 14**.

In Lemma 2.2.3, ||A|| is the operator norm given by (2.12), in which you should interpret |x| as any norm on R^d (so it satisfies the properties listed in Lemma 2.2.2).

In Lemma 2.2.4, |x| is the Euclidean norm, and ||A|| is the operator norm.

In Problem 5(a), don't use Jordan form. Follow the hint, and compute the exponential as an infinite series. You should recognize the sum.

#### Assigned Friday, Sep. 14

#### Assigned Tuesday, Sep. 18

#### Assigned Wednesday, Oct. 10, corrected Tuesday, Oct. 16

#### Assigned Saturday, Oct. 20; corrected Monday, Oct. 29; extended Tuesday, Oct. 30

#### Assigned Friday Nov. 16

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Last modified Fri Nov 16 2012

Send questions or comments to schecter@ncsu.edu