Ordinary Differential Equations, Fall 2013
Instructor: Boris Botvinnik
Class meets MWF 10:00-10:50, Deady 303
Office: Fenton 304.
(Please always include a correct e-mail return address.)
Office Hours: MW 1:00-1:50 pm,
Elementary Differential Equations, by Boyce and DiPrima,
1. Background and Goals. Differential equations are
used to describe processes that vary continuously
with respect to
time. In applications, one often knows some relationship between an
(or system of functions) and its derivatives, and
uses this relation to determine the original function.
covers the basic theory of ordinary differential equations. This
includes stability theory
and the existence and uniqueness of
solutions, and techniques of solutions for linear systems of
2. Exams. There will be a midterm in-class exam on
Friday, November 1st, 10:00-10:50 a final exam on
Homework problems will be assigned
every week and are due in class on Wednesday on
the material of the
previous week. No late homework will be accepted.
4. Grading. The
grading distribution will be as follows:
Midterm Exam: 25%
Final Exam: 50%
5. Weekly Schedule:
1. Systems of first order
linear differential equations. Read 7.1, 7.2, 7.3.
2. Linear systems
with constant coefficients. Read 7.4, 7.5, 7.6.
matrices and eigenvalues. Read 7.7, 7.8, 7.9.
4. Existence and
uniqueness theorems. Read 2.4, 2.8.
5. Stability and the phase
plane. Read 9.1, 9.2
6. Almost linear systems, MIDTERM. Read 9.3
7. Applications to population dynamics. Read 9.4, 9.5
8. Liapunov's second method. Read Chapter 9.6.
9. Periodic solutions, limit cycles,
and chaos. Read Chapter 9.7, 9.8.