Math 557 Fall 2014
Ordinary Differential Equations and Dynamical Systems
Michael W. Smiley
Professor of Mathematics
Office: 458 Carver Hall
Office phone/voice mail: 294-6420
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.
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.
Ordinary Differential Equations
and Dynamical Systems ,
by Gerald Teschl .
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
Theory of Ordinary Differential Equations, by Earl Coddington and Norman
Levinson, McGraw-Hill, 1955.
Asymptotic Behavior and Stability Problems in Ordinary Differential
Equations (2rd edition), by Lamberto Cesari, Springer, 1963.
Ordinary Differential Equations, by Philip Hartman,
John Wiley & Sons, 1964.
The Qualitative Theory of Ordinary Differential Equations, An
Introduction, by Fred Brauer and John Nohel, Dover, 1969.
Ordinary Differential Equations, by Jack Hale, Wiley-Interscience, 1969.
Texts on Dynamical Systems
Applications of Centre Manifold Theory, by Jack Carr, Springer, 1981.
Geometric Theory of Dynamical Systems, An Introduction, by Jacob Palis,
Jr. and Welington de Melo, Springer, 1982.
Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector
Fields, by John Guckenheimer and Philip Holmes, Springer, 1983.
More Recent Texts on Differential Equations
Ordinary Differential Equations, by Richard Miller and Anthony Michel,
Academic Press, 1982.
Nonlinear Ordinary Differential Equations, by Roger Grimshaw, Blackwell
Scientific Publiching, 1990.
Differential Equations, Introduction and Qualitative Theory
(2nd. edition), by Jane Cronin, Dekker, 1994.
Ordinary Differential Equations, by Wolfgang Walter, Springer, 1998.
Ordinary Differential Equations with Applications, by Carmen Chicone,
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
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.
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
Maintain by the instructor, last updated: September 29, 2014.