Welcome to the Home Page for Mathematics 427K-H for Spring 2009.

This has as a prerequisite a year of calculus, although some students will have taken some vector caculus and/or linear algebra. In the course we study differential equations and systems of differential equations and their applications. We use and develop as tools matrix algebra, elementary complex numbers and, of course, lots of calculus. The graphics obtainable using simple computer software, especially dfield and dplane, give nice pictures and help mathematicians understand the conceptual link between matrix computations, differential equations and simple applications, especially growth and decay of physical entities. This gives many stdents an intuition as to 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 Orit Davidovich.

Office hours are M 1:15-2:00, W 10-10;50 F 2-3:15 and by appointment or drop-in. Office number is RLM 9.160. Call Lizbeth Lynch at 471-6237 to make an appointment or leave a message.

The unique number for the course is 56905 and the class is in RLM 6.104.

Office hours are M 1:15-2:00, W 10-10;50 F 2-3:15 and by appointment or drop-in. Office number is RLM 9.160. Call Lizbeth Lynch at 471-6237 to make an appointment or leave a message.

The unique number for the course is 56905 and the class is in RLM 6.104.

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. Grades are high, and the competition is stiff. &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, about the project and/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. My understanding is that if you log in with your UTEID the math system automatically allows you to get a math account. There are proctors there who will help you. Of course, you can do your homework anyhow and anywhere. This is for those of you, like me, who are computer amateurs. Don't worry about the computer aspect. I do all the computer homework, and if I can do it, you can do it. &4. An important part of the course is the project. Both sample projects, and the project grade sheet will be available to guide you.

Projects may be done in groups or two or three individuals. 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)

List of lectures, book chapters and exercises (here).

Notes on linearization.

Remarks on the first exam. This will be held February 10 in the TA classroom.

Remarks on projects. View ideas about project topics.

Information on ode45 progam

Remarks on the second exam. This will be held March 27 in the lecture room.

Updated Project information (here).

Updated ideas for project topics(here).

Project grade form for 2009(here).

The third midterm in on Wednesday May 6 in the lecture room. Here are the sections which will be covered.

Projects are due Monday, May 11

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. I also have books in my office which can be signed out.

Computer information from 07(here).

Assignments:

First assignment (due Thursday January 29)

Second assignment (due Thursday February 5)

Extra credit assignment three due Monday Feb16.

Homework 3 due Thursday February 19

Homework 4 due Thursday February 26.

Extra Credit L due Monday March 2.

Homework 5 due Thursday March 5.

Homework 6 due Thursday March 12.

Homework 7 due Thursday March 26.

Homework 8 due Thursday April 9

Homework 9 due Thursday April 16

Extra Credit 9 due Monday April 20

Homework 10 due Thursday April 23

Homework 11 due Thursday April 30.