Math 490, Partial Differential Equations and Mathematical Biology, Spring 2004

Instructor: Professor Junping Shi
Office: Jones Hall 122
Office Hour: MWF 2-3pm 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 410 (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. All quizzes, test answer keys and practice tests will be available at the section website, also the answers to even number homework problems. 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:   MWF 12-12:50pm, Tucker 131.

Textbook: There is no printed textbook for the course. Lecture notes will be given to you in class, and also available online. Copies of other reading material (selected chapters from other books, selected research papers) will also be distributed in class when needed.

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 will be used in some homework assignments and  in your semester project. Maple is available on all university Win-2000 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.

Course Grade:

Test #1 15%
Test #2 15%
Homework 40%
      Project and 
Total 100%
Percentage Letter grade
90-100 A
80-90 B
70-80 C
60-70 D
below 60 F
Your letter grade will be calculated according to the formula above. Scores of tests, homework and presentations will be available on Blackboard website (certainly you can only find your own scores) once they are available.

Tests and Final Exam: We will have two take-home exams during the semester. Each test accounts for 15 points in the semester grade. (total 30%) You will have one week for the take-home tests.

Homework: Homework will be assigned for every lecture (the list will be available from course webpage) and will be collected once a week (sometimes once in 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: Research groups two or three people will be formed to conduct projects involving modeling some real world problems using R-D equations, and subsequent analysis and computing on the model will follow. In the week before spring break, your group will give a presentation on a paper published by othe people about diffusion model; and in the last week of class, your group will report some your own research on a subject using the reaction-diffusion models. Each member in the group should at least do the presentation once. Your group will also write a short paper for the topic of the second presentation. Successful projects will also be presented in Undergraduate Research Conference next fall (for junior students).