Welcome to the Home Page for Mathematics 427K-H for Spring  2010. 

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 the matlab programs dfield, pplane and ode45, 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 students an   intuition as to what calculus is all about. 

Your Professor is Karen Uhlenbeck.  Her e-mail is  uhlen@math.utexas.edu.  The teaching assistant for the course is Su Chen.  Her e-mail is schen@math.utexas.edu  She has office hours  M-W 10-11 and F 2-3 in room RLM 9.116.

Office hours for professor Uhlenbeck are M:3-4, W 2:15-3:15 and Th 11:30-12:30.  You are very much encouraged to make an appointment or drop in if my office hours are not convenient for you.The office number is RLM 9.160. Send an e-mail or call Lizbeth Lynch at 471-6237 to make an appointment or leave a message.

The text for this course is different from the text being used in most of the other sections of 427-K.  It is "Differential Equations with Boundary Value Problems" (2nd edition) by Polking, Bogess and Arnold. It is cheaper than the usual text.  A package with a new book, solution manual and matlab manual is available at a few dollars over the cost of the book alone from the Co-op.  Used versions are available on-line for considerably less. It has been used as a text at Rice University for a long time, hence there are used copies on the market.  You are not required to have the solution manual or the matlab manual, although you might find them useful.

We will cover most of Chapters 2-4,7-10 and parts of 11-13.

Detailed information about the course including a tentative syllabus and grading  policy  will be 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. It also contains information on how the course is to be graded, the schedule for the homework and exams, etc. 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 Spring Break 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. 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. Some of the software is available free from Polking's web site at Rice University. &4- An important part of the course is the project. Both project outlines 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.

Here is the list of lectures, sections of the book we are covering and exercises from the text (which are not to be handed in). It will be updated weekly.

Assignments and date to be handed in:

Due Jan 27: assignment 1

Due Feb 3:assignment 2
Feb 2: Notes on linearization

Due Feb 10: assignment 3

Due Feb 24: assignment 4

Due March 3:assignment 5

Feb 25: cheat sheet on ode45

Due March 10 assignment 6

Due March 24 assignment 7

Due March 31  assignment 8

March 31  2nd exam

April 9  first project submission and project information

April 14  assignment 9

April 21 assignment 10

April 28 assignment 11

 May 4  3rd exam