Math 490, Partial Differential Equations and Mathematical Biology, Spring 2009

Instructor: Professor Junping Shi
Office: Jones Hall 122
Office Hour: T,W,Th 11-12,  or by appointment
Phone: 221-2030
Course Description

Reaction-diffusion (R-D) systems are some of the most widely used models  in situations where spatial dispersal plays significant role. We will learn some theory of reaction-diffusion equations in the context of models in mathematical biology. Applications to be discussed in class include spatial spread of genes and of diseases, random dispersal of population, random and chemotactic motion of microorganisms, cellular maturation, pattern formations in developmental biology and morphogenesis, and animal coat patterns (why zebra has the stripes......). While introducing many biology models, we will also develop related mathematical theory and methods like, diffusion mechanism, waves, bifurcation theory, Turing's instability mechanism. Computation and simulation of solutions will be used throughout the class. (We are going to use software Maple, but no prior knowledge is required.)
The prerequisites of the course are Math 111, 112 (Calculus I and II), and Math 302 (Differential equations) or Math 345 (Mathematical Models in Biology). Math 211 (multivariable calculus) and 212 (linear algebra) are not needed, but we will learn some material on these subjects during the course.

Course Webpage:
We have a course webpage with tons of extra material, including java applets graphing the solutions, animations, background of many models, online tutorial of differential equations. Check the section website at least once a week for new course information. A lot of files are available in Adobe Acrobet (pdf) format. If you do not know how to view or print these files, please ask your instructor or computer lab assistant for help.

Meeting Times and places:   T, Th 2-3:20pm, Washington 304.

Textbook: The material will come from a lot of different sources, but mainly two books:                              

Applied Partial Differential Equations, by J. David Logan (Springer 2008)
Lectures notes on reaction-diffusion models,
By Junping Shi. (copies will be available as handouts)

Computer and Calculators: Computer demonstrations will be given in classes sometime, and browsing differential equations related webpages is a fun thing to do and is necessary for your success in this course. Computer software Maple and Matlab will be used in some homework assignments and  in your semester project. Maple and Matlab are available on all university Windows network computers, please visit webpage for lab information. Graphing calculator is not necessary for this course, though a simple scientific calculator may be useful for some numerical calculations occationally.

Course Grade:

Participation and discussion
Project & Presentation 1
Homework 30%
      Project & Presentation 2
Project paper
Total 100%
Percentage Letter grade
90-100 A
80-90 B
70-80 C
60-70 D
below 60 F

Homework: Homework will be assigned for some lectures (the list will be available from course webpage) and will be collected every two or three weeks.  Not all problems will be graded, but all answer keys will be given to you on the website. It is your responsibility to check your answers and make sure you do them correctly. No late homework will be accepted for any reason.

Project and Presentation: Two projects will be assigned during the semester. In each project, you will be assigned to some reading material, and you need to present the material in class. The presentation is about 30-45 minutes. Some projects may require you to perform some calculations and simulations. You can choose to work individually, or in a group of two (collaborating on two projects). A variety of topics will be selected by Prof. Shi, and you can choose your favarite ones. You will also write a short paper based on your one or two presentations.