MTH 545/URI
Ordinary
Differential Equations I
Course
Information,
Fall 2016
Text:
J. Hale and H. Kocak, Dynamics
and Bifurcation, Springer, 1996
Supplementary texts:
L. Perko, Differential
Equations and Dynamical Systems
,Springer 2006
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
Basic topics for delay DE
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:
Instructor: M. Kulenovic
Office: Lippitt 202D; Ph. 44436
e-mail: mkulenovic@mail.uri.edu
Online information: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm
Office hours: MWF: 11-12 and by appointment.
Time: M,W: 5 - 6:15
Room: Lippitt
201