Ordinary Differential Equations II

Course Information, Spring 2013

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 (50%) and mid-term exam and final project (50%).  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

Applications to Mathematical Biology


Computer Requirements

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


Illness Due to Flu

The nation is experiencing a widespread influenza-like illness. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify me of your status, and we will communicate through email, at We will work together to ensure that your questions regarding the material are answered and that you have a proper amount of time to complete your assignments.


The Centers for Disease Control and Prevention has posted a few simple methods to reduce the transmission of the flu virus. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequent washing or sanitizing of your hands; avoiding touching your eyes, nose, and mouth; and staying home when you are sick. For more information please view or The URI Health Services web page,, will carry advice and local updates.

Interesting links: 

Hal Smith's web page

Instructor: M. Kulenovic

Office: Lippitt 202D; Ph. 44436


Online information: or

Office hours:  MW: 1-2; F: 11-12.

Time: W, F: 3 - 4:15

Room: Lippitt 201