Math 557     Fall 2008

Catalog Description

Math 557, Ordinary Differential Equations. (3-0) Cr. 3. Prereq: Math 266 or 267, 307 or 317, 415 or 465. First semester of a full year course. The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, topics from dynamical systems and two-point boundary value problems.

Textbook

The Qualitative Theory of Ordinary Differential Equations, An Introduction , by F. Brauer and J. Nohel .

List of References

Classic Texts on Differential Equations

1. Theory of Ordinary Differential Equations, by Earl Coddington and Norman Levinson, McGraw-Hill, 1955.
2. Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (2rd edition), by Lamberto Cesari, Springer, 1963.
3. Ordinary Differential Equations, by Philip Hartman, John Wiley & Sons, 1964.
4. Ordinary Differential Equations, by Jack Hale, Wiley-Interscience, 1969.

Texts on Dynamical Systems

5. Applications of Centre Manifold Theory, by Jack Carr, Springer, 1981.
6. Geometric Theory of Dynamical Systems, An Introduction, by Jacob Palis, Jr. and Welington de Melo, Springer, 1982.
7. Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, by John Guckenheimer and Philip Holmes, Springer, 1983.

More Recent Texts on Differential Equations

8. A First Course in the Qualitative Theory of Differential Equations, by James H. Liu, Prentice Hall, 2003.
9. Ordinary Differential Equations, by Richard Miller and Anthony Michel, Academic Press, 1982.
10. Nonlinear Ordinary Differential Equations, by Roger Grimshaw, Blackwell Scientific Publiching, 1990.
11. Differential Equations, Introduction and Qualitative Theory (2nd. edition), by Jane Cronin, Dekker, 1994.
12. Ordinary Differential Equations, by Wolfgang Walter, Springer, 1998.
13. Ordinary Differential Equations with Applications, by Carmen Chicone, Springer, 1999.
14. Basic Theory of Ordinary Differential Equations, by Po-Fang Hsieh and Yasutaka Sibuya, Springer, 1999.

Copies of references 2,3,4,5,6,7,8,10,11 can be obtained from the instructor.

Grading Policy

Course grades will be determined from student performance on homework assignments. There will be four to six homework assignments.

Disability Resources

Iowa State University complies with the American with Disabilities Act and Section 504 of the Rehabilitation Act. If you have a disability and require accommodations, please contact the instructor early in the semester so that your learning needs may be appropriately met. You should contact the Disability Resources office for information on appropriate policies and procedures. The Disability Resources office is located on the main floor of the Student Services Building, Room 1076; their phone is 515-294-6624.

Homework Assignments

Homework 1 (in pdf format)

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Maintain by the instructor, last updated: September 4, 2008