Ordinary Differential Equations I
Text: F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, 2006
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
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.
Instructor: M. Kulenovic
Office: Lippitt 202D; Ph. 44436
Online information: www.math.uri.edu/courses or www.math.uri.edu/~kulenm
Office hours: TuWTh: 11-12 and by appointment.
Time: TTh: 2 - 3:15
Room: Lippitt 201