Math 557     Fall 2014

Ordinary Differential Equations and Dynamical Systems


A Quick Link to Homeworks and Solutions

A Quick Link to Lecture Notes

Important Announcements

Go Cyclones

Instructor

Michael W. Smiley
Professor of Mathematics
Office: 458 Carver Hall
Office phone/voice mail: 294-6420
email: mwsmiley@iastate.edu
office hours: MWF 11-12 & 1:30-2:30; and by appointment

Email, Office Hours, and Grades

The office hours are intended to be used to help students with questions about mathematical problems. They can also be used to discuss exam scores and a student's progress in the course. Email will not be used for these purposes. As a standard policy, no grades or exam scores will be sent out to students via email or over the phone.

Catalog Description

Math 557. Ordinary Differential Equations and Dynamical Systems. (3-0) Cr. 3. F. Prereq: 415 or 501. The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, linearization, dynamical systems, bifurcations, and chaotic behavior.


Textbook

Ordinary Differential Equations and Dynamical Systems , by Gerald Teschl .


Course Policies

This is a graduate course that develops the theory of ordinary differential equations. Students will learn the theoretical foundations of the cornerstone topics of the subject that are listed in the catalog description above. Applications to specific problems will be discussed so that students will be able to apply their knowledge of the subject to problems they encounter as they continue their studies and start to conduct mathematical research. The assessments of student learning will be mainly in the form of homework assignments that will be posted below. At the discretion of the instructor there could be announced exams. Students can discussed the problems in the homework assignments with classmates, but should submit solutions to the problems that are written up as their own independently prepared work. Homework assignments will be given explicit due dates. In the event that a student is unable to turn in an assignment by the due date, the student should discuss the circumstances of the event with the instructor.


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. The Qualitative Theory of Ordinary Differential Equations, An Introduction, by Fred Brauer and John Nohel, Dover, 1969.
  5. Ordinary Differential Equations, by Jack Hale, Wiley-Interscience, 1969.
  6. Texts on Dynamical Systems

  7. Applications of Centre Manifold Theory, by Jack Carr, Springer, 1981.
  8. Geometric Theory of Dynamical Systems, An Introduction, by Jacob Palis, Jr. and Welington de Melo, Springer, 1982.
  9. Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, by John Guckenheimer and Philip Holmes, Springer, 1983.
  10. More Recent Texts on Differential Equations

  11. Ordinary Differential Equations, by Richard Miller and Anthony Michel, Academic Press, 1982.
  12. Nonlinear Ordinary Differential Equations, by Roger Grimshaw, Blackwell Scientific Publiching, 1990.
  13. Differential Equations, Introduction and Qualitative Theory (2nd. edition), by Jane Cronin, Dekker, 1994.
  14. Ordinary Differential Equations, by Wolfgang Walter, Springer, 1998.
  15. Ordinary Differential Equations with Applications, by Carmen Chicone, Springer, 1999.
  16. Basic Theory of Ordinary Differential Equations, by Po-Fang Hsieh and Yasutaka Sibuya, Springer, 1999.

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


Grading Policy

Course grades will be determined from student performance on homework assignments and possibly one or two exams that would correspond to a midterm and/or final exam. There will be four to six homework assignments, and at most two exams.


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 and Solutions


Homework 1


Homework 1 Solutions


Homework 2


Lecture Notes


An Existence Theorem Under a Lipschitz Condition



Maintain by the instructor, last updated: September 15, 2014.