Vaughn Climenhaga

Associate Professor
Department of Mathematics
University of Houston


Math 6324

Ordinary Differential Equations


Announcement:  The final exam is scheduled for Thursday, December 13, 2012.  It will be held in the regular lecture room (SEC 202) from 11am-2pm.

Office hours during final exam week:  Wednesday Dec 12, 9am-12pm and 2pm-4pm. 

I will also be available Monday Dec 10 from 2-3pm and Tuesday Dec 11 from 10am-12pm.  You may pick up your last homework assignment during any of these times (if I do not put it in your mailbox).



I have written up the proof of the stable manifold theorem into a more legible form than the one in my handwritten notes - the link to a pdf file is at the right, or you can see the (identical) notes on my blog.



From the syllabus This course is an introduction to differential equations. We cover linear theory: existence and uniqueness for autonomous and non-autonomous equations; stability analysis; stable and unstable manifolds; Floquet theory and elementary bifurcation theory. We will also cover topics such as quasiperiodic motion; normal form theory; perturbation theory and classical mechanics.
  • Lectures are Tuesdays and Thursdays, 11:30am-1pm in SEC 202.
  • My office is PGH 651A.  Office hours are 9:30-10:30am on Tuesdays and 10:30-11:30am on Wednesdays, or by appointment at other times.

Textbooks:


You are not required to buy a textbook for this course - the notes from lectures will be the primary reference.  However, the book
will be useful to have, and closely mirrors the topics we will cover.  Another useful text is
Of the two, Hirsch-Smale is more accessible and more directly useful for this course.  I have placed both books on reserve in the library (2 day loan period).

At a similar level to Hirsch-Smale's book, but rather more concise and with less explanation of the preliminaries from linear algebra, real analysis, etc., is

The following three books are good references and also lead into more advanced topics:

Coursework:

There will be one midterm (worth 20 points), a final exam (30 points) as well as 2 to 4 take-home problem sheets (to make up 50 points in total).  These will be announced in class several weeks in advance and will also be posted on this website.