Course Title: Ordinary Differential Equations
Course Number: MATH 6410 - 1
Instructor: Andrejs Treibergs
Home Page:
Place & Time: M, W, F, 2:00 - 2:50 in JWB 308
Office Hours: 10:40-11:30 M, W, F, in JWB 224 (tent.)
Main Text: Lawrence Perko, Differential Equations and Dynamical Systems, Springer 1991.

We shall basically follow the text. But much of the material is standard and widely available. Therefore, students might be able to get by without owning the text, although the majority of the problems will come from the text. I'll provide references and put copies in the math library. I will also cover additional topics that were suggested in consultation with Professors Adler, Dobson and Keener. Come to class for details and references. Here is a partial list of alternative sources that cover the material.

I have tried several different texts for this course: Amann, Perko, Chicone, Liu and Cronin. Perhaps not so unexpectedly, the texts the students liked the best, Perko and Liu, are not the ones I liked the best, Amann and Chicone. None of the texts perfectly suits the material we teach at the University of Utah. Grant's notes as far as they go are modeled on the course he took as a graduate student here at Utah. All the texts cover about two thirds of the course, and the rest has to be supplemented. The authors all have their hobby horses, and they discuss their favorite special topics beyond what would be appropriate for a beginning course.

This course is designed to be a balance of application and theory that is optimized for the needs of students at Utah, be they interested is applied mathematics, mathematical biology, numerical analysis, probability, differential equations or geometric analysis. As mathematicians, it is our prerogative and, indeed duty, to understand why theorems work, so that we may modify or code them as we encounter them in the future. However, only a minimal amount of doing proofs will be required. Besides the general understanding why any of the theorems hold, I will only require that students know completely the proofs of two things: local existence and linearized stability at a rest point.

The choice of topics in Math 6410 varies slightly from instructor to instructor, although the variance is far less than you might think hearing old graduate student gossip. One only needs to look at previous syllabi, or the Differential Equations Preliminary Exams derived from these courses over the last decade to see that they are very consistent. Schmitt and Thompson's notes designed for this course spins toward nonlinear functional analysis. A course based on Jordan & Smith's, Verhulst's and Glendenning's texts spins towards perturbation methods.

Texts Suitable for an Undergraduate Course in ODE's.

Texts Suitable for a Graduate Course for Students who have not Studied Measure Theory.

Texts Suitable for a Graduate Course for Students who have Studied Measure Theory.

Specialist's Books on Specific Topics. Unsuitable for Math 6410.

Last updated: 5 - 4 - 12