Welcome to the Home Page for Mathematics 427K-H for Spring 2007. 

This course follows calculus.  We do differential equations and linear algebra and the connection between them.  The graphics obtainable using simple computer software, especially dfield and dplane, give nice pictures and help mathematicians understand the conceptual link between matrix computations, the behavior of differential equations, and give anintuition about what calculus is all about.  There is even a little chaos towards the beginning of the course.

Your Professor is Karen Uhlenbeck.  Her e-mail is  uhlen@math.utexas.edu.  The Teaching Assistant for this course will be Carl Mautner.  Click here to find the office hours for both.

Detailed information about the course including a tentative syllabus and grading  policy  is available on the first day handout. Please read this to be sure you belong in this section of 427K and that you understand what is expected of you in the course. Here is a synopsis of the important information: 1.This is an honors course. Students will be expected to do simple proofs. 2.Professor Uhlenbeck asks that each student come to her office at least once before April 1 for a brief discussion (about the course, about math in general or about life in general). 3. We will be using standard mathematical software (matlab, maple). You can obtain an account in the computer lab  RLM 7.122. 4. An important part of the course is the project. If you do not wish to do a project or use mathematical software to solve problems, it would be wise to enroll in another section of 427K.

Firstday handout (here)

Preliminary list of references on reserve in APM library(here).  At the moment these are mostly applications, as that is what I emphasized in past classes.  I will add some theory books. These should go on reserve soon.

Computer information (here).

Project information (here).

Ideas for project topics(here).

Schedule of Lecture Topics (click here).

Remarks on the first exam.

Project grade form is here.

Remarks on the second exam.


First assignment (January 26)

Second assignment(February 2)

Third assignment(February 9)
          If you are interested in computing the difference equations yourself, here is a set of exercises and a program which will help you.  There is also some stuff about finding roots and computing with matrices we will use later, if you feel like playing with it ahead of time.

Fourth Assignment (February 22)

Fifth Assignment (March 2)  There is information about the computer programs added to the computer page.   There are also some sample problems for the matlab program ode45.

Sixth Assignment (March 23)

Seventh Assignment (April 2)

Eighth Assignment (April 11)

Ninth Assignment  ((April 23)

Tenth Assignment ((May 2)