|Course Title:||Ordinary Differential Equations|
|Course Number:||MATH 6410 - 1|
|Place & Time:||M, W, F at 2:00 - 2:50 in JWB 308|
|Office Hours:||11:45 - 12:35 M, W, F, in JWB 224 (tent.) and by appointment|
|Prerequisites:||Math 5210, its equivalent or consent of instructor.|
|Main Text:||Ordinary Differential Equations by Thomas Sideris, Atlantis Press 2013. ISBN 978-94-6239-020-1|
|Supplementary Notes:||Christopher Grant, Theory of Ordinary Differential Equations, pdf, Solutions.
List of additional supplementary materials used in the course: M6414Supplement.html .
In this first semester of a year long graduate course in differential equations, we shall focus on ordinary differential equations and dynamical systems. The second semester, Math 6420 taught by P. Bressloff, will emphasize partial differential equations. In this course, along with the Math 6420, we shall try to cover the syllabus for the qualifying exam in differential equations. Although some mathematical sophistication is required to take the course, and it moves at the blazing speed of a graduate course, I shall provide any background materials needed by the class. If you are unsure about background material, I EXPECT YOU TO ASK ME so I know what needs covering.
We shall follow Siders's text covering the behavior of solutions: existence and uniqueness, continuous dependence on data; and dynamical systems properties: long time existence, stability theory, Floquet theory, invariant manifolds and bifurcation theory. We shall discuss as many applications as we can.
I recently chose Sideris for the main text. Let us say that this text is "recommended," but you should own at least some of the better texts (Amann, Barriera-Valls, Chicone, Hartman, Kong, Perko, Schaeffer-Cain, Teschl) suitable for the course. The two other new books that I was trying to choose from included Kong, and Schaeffer-Cain. Siders is a no-nonsense book that proves all of the theorems and covers almost exactly Utah's course. Kong is a very readable, non-pretentious book aimed more at the first year student which omits some desirable material. Schaeffer-Cain is a chatty, amusing, readable but verbose treatment that has plenty of examples and exercises and a shallow learning curve, but doesn't cover some important material.
Topics include (depending on time):
In addition, the student's performance will be reported to the Graduate Committee, which decides the continuation of financial support annually. Ultimately, the learning will also be measured by the Differential Equation Qualifying Examination.
Last updated: 7 - 13 - 17