The course, Mathematical Modeling in Biology requires at least one
semester of calculus, and some sophistication in science.  It covers
(partially) the material of the course for engineers on ordinary differential
equations (427K) with more emphasis on modeling and biological applications;
additional sections on  partial differerential equations and discrete
chaotic  systems  are included.  It is suitable for majors in biology, mathematics,
computer science, chemistry and geology.  Since it does not cover
Fourier series, it is probably not adviseable for either engineering or physics
students I  If you have any doubts about whether you should enroll in the course,
see either Professor Uhlenbeck,  the TA, Dorothy Buck or the math advisor
Gary Hamrick.  While the text is explicitly written for biologists rather than
applied mathematicians, the course will  be of use to math majors with an interest
the applications and uses of mathematics in all fields, as well as a good
course for all scientests to solidify their intuition about calculus.

The course follows an unusual but useful book by the Harvard Professor
Clifford Taubes, who designed  a set of lectures for biologists, explicitly
assuming that they would not know a lot of calculus ahead of time. It
includes with every section on differential equations, an article from
a major scientific journal featuring an application in  one of the sciences,
mostly biology.  However, since I have taught many sections of the
engineering course on this material, we will also add to this material
 a set of computer exercises, which illustrate the power of modern computers
for both visualizing what is happening, and computing stuff that is a mess or
impossible by hand calculation.  The computer work will be kept down to one
short assignment every two weeks, but it is essential.

Professor:  Karen Uhlenbeck  RLM 9.160   512-471-1172    uhlen@math.utexas.edu
        Office hours: M,1-2, 3-4, TH 2-3, F 3-4 and by appointment.
Teaching Assistant:  Dorothy Buck  RLM  11.108  512-475-9178  dbuck@math.utexas.edu
         Office hours (to be announced).
Class:  MWF  2-3    RLM 7.124

Computer accounts on the mathematics department system will be handed out the first week of class.

Work Sessions:   (these are optional, but we will try to schedule one or two optional sessions a week
for  students to obtain help on computer assignements  and homework. These will be scheduled the
first week of classes , and some portion of them will be in the 8th floor computer lab in
RLM. ) No previous knowledge of computing systems is required.  In fact, this is an ideal course
in which to learn about the uses of computers in mathematics.  The free software netmath ,
which is used in the course,  can be very simply and easily  used from the mathematics department
machines or downloadedfrom Professor Schelter's webpage .  We  will attempt to  provide alternative
documentation for using the standard software, mathlab.   Students who want to use other standardized
software can impliment this as part of their project work.

Text:  Modeling Differential Equations in Biology, Taubes,  Prentice Hall*

*The original publication date was August 2000.  Because the publication date is delayed,
we have available in class, and in Professor Uhlenbeck's office, copies of the first
eleven chapters (free!). The new publication date for the entire book is supposedly October.

Course Outline

1. Exponential growth, linear and non-linear equations , stability (1-4)

2.  Sytems and phase plane analysis  (5-6)

3. Vectors, matrices and systems, and stabiltiy(7-11).

4. Partial derivatives, diffusion and separation ofvariables(13-17).

5.  More stability  (17-19).

6.  Waves (21-22)

7.  Periodicity and chaos (23-28).

This is a new course.  Sections 1-3, parts of 4, 5 and 7 have been covered in Uhlenbeck's
usual sections of 427K.  Depth and amount of material in 4-7 will depend on the class. This is
special to this first-time trial offerring of the course, and subject matter is for this one time
negotiable.

Grading:

Grades will be computed as the best five  (500)  grades of the following eight (800):

Quizzes  and homework(100)

Computer assignements   (100)

Minor Project*  (100)

Midterm  (100)

Major Project * (200)

Final  (200)

Graduate students are free to negotiate a grade scheme for the class with the professor.  However, this
must be done within the FIRST TWO WEEKS OF CLASS.   The two      exams will be in-class unless
a majority of the class votes otherwise. Students who are happy with the grade  they  have earned without
the final exam are expected not to take the final.

* Project grades are determined according to standard scientific assessment.  A rough grading sheet
is provided to guide students.  Also, successful projects from many years of 427K can be looked at
in 9.160 as explicit  guidance for the minor project.