Syllabus UTK – M531 – Ordinary Differential Equations I Fall 2004, Jochen Denzler, TR 11:10–12:25, Ayres 309B

Book(s): I don’t adapt an official course textbook, because neither covers the full variety of intended material. The course philosophy is closest to Chicone’s book. Walter’s book contains relevant material not in Chicone. They are on course reserve in the library. See the book info posted on-line for more details.

Course contents (531+532): Existence, uniqueness etc (dynamical systems perspective). Linear systems. Stability (linear and non-linear). Possibly invariant manifolds. Poincaré Bendixson. Sturm-Liouville; eigen- and boundary value problems, and variational methods. Power series methods. (Not necessarily in this order.)

Exams: There will be one midterm exam, and a final during the official exam period.

Total grade: 30% homework, 30% midterm, 40% final.

Homework: Will be assigned on a flexible schedule, and in various forms: some formally graded, some to be presented at the blackboard.

Course Philosophy: The course blends classical ODE material with more modern qualitative methods (dynamical systems point of view.) This latter will be stressed early in the course, since it is traditionally neglected in the sophomore course, but highly relevant for current research. Abstract notions like Banach spaces will be introduced to provide conceptual clarity and conciseness, but always with a focus on concrete, practical questions. Rigorous proofs are a core part of the course, but some additional facts will be given without proofs to get a rich and coherent theory in short time.

Office hours: I am posting regular office hours on my website, but am available for drop-in or appointments. You may call my cell phone 789-8031.

Diverse Prerequisites: Participants with education at different undergraduate programs may have different backgrounds. I welcome questions and am available for individual help where needed. You must initiate the contact in this case. As I am teaching this course the first time, I am not good in anticipating when you may lack some material that I might assume. I then prefer to use my time to just help you out, rather than to concoct a slalom around poles posted by “presumed– prerequisite–astrology”. And anyways, you’ll learn more that way.