# Math 420/520,
Ordinary Differential Equations, Fall 2013

**
Instructor: Boris Botvinnik**
** Class meets MWF 10:00-10:50, Deady 303**
** Office: Fenton 304. **
** Phone: 346-5636. **
** E-mail:
botvinn@math.uoregon.edu
(Please always include a correct e-mail return address.)**
** Office Hours: MW 1:00-1:50 pm,**
** Web Page:
http://darkwing.uoregon.edu/~botvinn/420_F13.html **
** Elementary Differential Equations, by Boyce and DiPrima,
9th edition. **
** 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
unknown function

(or system of functions) and its derivatives, and
uses this relation to determine the original function.

This course
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
equations.
** 2. Exams.** There will be a midterm in-class exam on
Friday, November 1st, 10:00-10:50 a final exam on

Monday, December
9th, 10:15-12:15.
** 3. Homework. **
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. Final Exam Review. ** Here are two hand-outs:
The first one
The second one
** 5. Grading. ** The
grading distribution will be as follows:
Homework: 25%
Midterm Exam: 25%
Final Exam: 50%
** 6. 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.
3. Fundamental
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.
10. Review.