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 including
Hopf bifurcation
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: MWF: 10-11
Time: W, F: 2 - 3:15
Room: Lippitt 201