Math 410(510), Mathematical Models in Biology, Fall 2001

Instructor: Professor Junping Shi
Office: Jones Hall 122
Office Hour: TR  9:30-11am   W 4-5pm or by appointment
Phone: 221-2030
Course Description

This course introduces many mathematical models in biology. The increasing use of mathematics in biology is inevitable as biology becomes more quantitative. We use the mathematical tools like difference equations, differential equations to model various biological phenomena, and we also introduce the basic analytical method based on calculus and algebra, qualitative analysis based on elementary geometry and computer aid numerical method to completely analyze some basic models. These mathematical tools will be useful for life sciences major students in any quantitative and qualitative analysis in the future. Biological applications include various population growth models (Malthus, Logstic, competion, predator-prey, cooperating), epidemic models, chemostat, HIV virus models, enzyme kinetics,
and others. The prerequisites of the course are Math 111 and 112 (Calculus I and II). Math 211 (multivariable calculus) and 212 (linear algebra) are not needed, but we will learn some material on these subjects during the course. There is a large overlap between this course and Math 302 (Differential Equations), but this course emphasizes applications in biology while Math 302 also includes applications to physics, chemistry and eigeneering. This course has a sequal course Math 490 (Partial Differential Equations and Mathematical Biology) in Spring 2002, where models involving both time and spatial variables will be introduced. (In this course, spacial variables are not considered.)

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:   Tuesday and Thursday, 8:00-9:20am, Morton Hall 001

Prerequisites: Math 111 and Math 112

Textbook: Mathematical Models in Biology, By Leah Edelstein-Keshet, First Edition, 586 pp, 1988.
While this book is excellent in introducing many mathematical biology models, most mathemtics parts are poorly written, maybe not suitable for beginners. I will write some mathematical notes to complement the textbook. We will roughly cover the first seven chapters, but some will be skipped and some will be added.

References: some material of the course will from these books, you don't have to buy these books.
 Mathematical biology, Murray, J. D. Second edition. Biomathematics, 19. Springer-Verlag, Berlin, 1993. 767 pp. ISBN: 3-540-57204-X (This is an encyclopedia in mathematical biology. If you like to learn more on math biology some day, this is a must-have book.) ($45 from
Modeling Differential Equations in Biology, Clifford Henry Taubes. Prentice Hall PTR, 2000, 1st ed., 479pp. ISBN: 0130173258. (This is another newer textbook, which has a lot of original biology articles to read. Maybe not good as textbook, but definitely good reference.) ($85 from
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Steven Strogatz. 1st ed., 512pp. ISBN: 0738204536. Perseus Books Group, 2000. (An excellent book in the mathematical area of dynamical system, but has a lot of applications including biology. ($35 from
Differential Equations, Paul Blanchard, Robert L. Devaney, Glen R. Hall. First Edition. 732pp. ISBN: 0534345506, 1998. (This is the textbook of Math 302) ($105 from

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 possibly in your semester project. Maple is available on all university Win-2000 network computers, please visit webpage for lab information. Tutorial for Maple will be given on the course webpage later. Graphing calculator is not necessary for this course, though a simple scientific calculator may be useful for some numerical calculations. Any calculator (but not laptop computer or handheld computer) is allowed in quizzes, tests and final exam.

Email address: I find that email is a good way to leave messages, but it is not a good way to get help on your homework. For help with the mathematics in this course, I encourage you to visit me in my office. If you miss class, do not send me email asking for answers to questions that were covered in class.

Course Grade:

Test #1 15%
Test #2 15%
Test #3 15%
Homework 20%
      Project     10%
Final Exam 25%
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 finals will be available on CourseInfo website (certainly you can only find your own scores) once they are available. A possible extra credit up to 5% will be awarded by the instructor(extra credit point in tests, challenging homework problems, creative project, etc.)

Tests and Final Exam: We will have three exams during the semester, one in-class and two take-home, and the final exam will be held December 18th, Tuesday, 1:30-4:30pm, Morton Hall 001. Please note the date of the final and make your travel plans now! University policy states that you must take the final at the scheduled time.
Make-up tests will not be given, except in cases of officially approved absences or for substantiated medical reasons. In some extreme cases, if you are forced to miss the test, you must notify me within three (3) days of the date of the test, preferably before the test is given. An excuse from your doctor or other appropriate authorities must be presented at that time. Each test accounts for 15 points in the semester grade. (total 45%) The final exam will be comprehensive and  accounts for 30% in the semester grade. All exams (tests and final) will be closed book, closed notes, but calculators (TI-82 or TI_83(+)) will be allowed.

Homework: Homework will be assigned for every lecture (the list is available from course webpage) and will be collected.  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: A semester long project is to choose one of your favorite topics as an application of differential equation techniques from this course. Your work should include mathematical modeling, analytic computation, qualitative analysis and numerical computations. The final product is a report (or webpage) to be submitted in November 29th. (a week before the last day of the class) Your report should be typed (mathematical notations are hard to type, although Microsoft Word has this function, or LaTex is a better option for this propose, but if you don't want to do that, you can hand write the mathematical part). Your report should record all your works, including possible graphic illustrations. If you choose to write a webpage, again mathematical notations are hard to put online (although possible). But webpage is a better way to include exciting animations and colorful graphs. You can choose the topic of your project, or you can choose one from a list of possible topics provided by the instructor on the course webpage. In any case, you should submit a title and a 200 word abstract by email to the instructor by October 21st.

Helps for Maple: Helps for using software Maple are very easy to get online. But if you prefer to get help in person, Professor Sid Lawrence will be in Jones 203 on Tuesday through Friday from 10:30 AM to 12:30 PM to help any student in any math class with a Maple problem.

Attendance of the class: Attendance of the class and lab is necessary for your success in this class. Attendance will not be strictly enforced, but if your absence of one class or lab is confirmed (for example, you are not presented when your assignment is given back or you miss a quiz), then 0.3% will be deducted from your semester grade for each absence.