Lectures: MWF 3:30 pm-4:20 pm in Porter Hall room A19

Professor: Robert Pego

• Office: 6130 Wean Hall
• Phone: (412)268-2553
• email: rpego AT cmu.edu
• Office hours: after class, T 3:30 and by arrangement

Assignments:

• Problems due W 2/6: pdf
• Problems due M 3/3: pdf
• Problems due W 3/26: pdf
• Syllabus for the midterm test (handed out W 4/2): pdf
• Problems due W 4/30: pdf

• Ordinary Differential Equations with Applications by Carmen Chicone, 2nd ed., Springer-Verlag, 2006.
  Has a modern selection and treatment of topics close to the approach we will take in the course.
  The classic sources below are more comprehensive within their scope, however.

Classic reference books:

• Theory of Ordinary Differential Equations by E. Coddington and N. Levinson, McGraw-Hill, 1955.
• Ordinary Differential Equations by P. Hartman, Birkhauser, 1982 (reprint of the 2nd ed., 1973).

Additional/supplementary texts (less advanced or comprehensive)

• Differential Equations, Dynamical Systems, and an Introduction to Chaos by M. Hirsch, S. Smale and R. Devaney, Elsevier 2003
• Nonlinear dynamics and Chaos by S. Strogatz, Perseus, 2001
• Lectures on Ordinary Differential Equations by Witold Hurewicz, MIT Press, 1958 (Dover 2002)

References/Links:

• Gohberg, Israel and Goldberg, Seymour,
  A simple proof of the Jordan decomposition theorem for matrices.
  Amer. Math. Monthly 103 (1996), no. 2, 157--159. (text available online)
• DSWeb online dynamical systems magazine

Course Description:  

Outline of topics (pdf)   The course is a fundamental introduction to the qualitative theory of ordinary differential equations (ODE), particularly emphasizing geometric and dynamical systems ideas. We develop basic infrastructure for analyzing solutions of ODE (theorems on existence and uniqueness, dependence on parameters, continuation), study questions of stability and instability (using Liapunov functions, linearization, Floquet theory, dichotomies), develop geometric methods (Poincare-Bendixson index theory, attractors and flows, invariant manifold theorems) and study generic structure (normal forms, basic bifurcation theory). Much motivation comes from applications in many areas of science and engineering.

Grading: Based on approx. 6 homework sets and a midterm and final exam.

Homework will be posted online at http://www.math.cmu.edu/~bobpego/21630/ .

Academic integrity requires that your tests and homework solutions are your independent work and not copied from other sources. On homework you are encouraged, however, to discuss with others and consult other resources to improve your understanding.

Make-up tests are only possible in the case of a documented medical excuse, a university-sanctioned absence (e.g., participation in a varsity sporting event), or a family emergency. Please contact me at the earliest time possible to schedule a make-up.