Ordinary Differential Equations II

Course Information, Spring 2007

Text:  L. Perko, Differential Equations and Dynamical Systems    


Prerequisites: Graduate standing , exposure to basic ordinary differential equations and linear algebra; Mth 545 is not a prerequirement

Exams and Grading:

Course grade will be determined based on homework and mid-term and final exams.  The exams will be of the take home variety.

The topics that will be covered are:

Invariant manifolds - center manifold
Normal form theory
Gradient and Hamiltonian systems
The Poincare map
Periodic solutions and Floquet theory
The Stable manifold theorem for periodic orbits
Poincare-Bendixson theory
Structural stability
Bifurcations at nonhyperbolic equilibrium points


Computer Requirements

The use of computer algebra systems such as MATHEMATICA, MAPLE, and Scientific Notebook is encouraged.  Some MATHEMATICA and/or MAPLE notebooks will be provided and demonstrated in the class. Most of the exams may require the substantial use of  MAPLE or MATHEMATICA.

Instructor: M. Kulenovic


Online information: or

Office hours:  

Time: M,W: 4:30 - 5:45