Ordinary Differential Equations I

Course Information,

Spring 2019

Text:  F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, 2006


Supplementary texts:

J. Hale and H. Kocak, Dynamics and Bifurcation, Springer, 1996

Linda Allen, An Introduction to Mathematical Biology, Pearson, 2006


Prerequisites: Graduate standing, exposure to basic ordinary differential equations and linear algebra;

Exams and Grading:

Course grade will be determined based on homework (40%) and mid-term exam and final project or final exam (60%).  The exams will be of the take home variety.

The topics that will be covered are:

Existence and Uniqueness theorems
Stability Theory of ODE

Oscillation Theory of ODE
The Poincare map
Periodic solutions and Floquet theory
Bifurcations for first and second order ODE

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.


Interesting links: 

Hal Smith's web page

Instructor: M. Kulenovic

Office: Lippitt 202D; Ph. 44436

Online information: or

Office hours:  TuWTh: 11-12 and by appointment.

Time: TTh: 2 - 3:15

Room: Lippitt 201