# 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.
• 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
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.