Ordinary Differential Equations II
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
Hopf bifurcations
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
e-mail: kulenm@math.uri.edu
Online information: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm
Office hours: 
Time: M,W: 4:30 - 5:45
Room: