#### Math 172 (section 1), Fall 2005 Mathematical Modeling for the Life Sciences MWF, 9:05 AM - 9:55 AM, Davis 209

Instructor: Bob Murphy LeConte 400H Mon. (2:30 PM - 3:30 PM), Wed. (2:30 PM - 3:30 PM), or by appointment. 777-4713 murphy This course has its own web page. You can find it at http://www.math.sc.edu/~murphy/teaching/ A grade of C or better in Math 122, 141, or an equivalent course to be approved by the instructor. Elementary Mathematical Modeling: A Dynamic Approach by James Sandefur. It may also be useful to use your math 122 or 141 textbook to review some of the calculus needed for this course. Each student is required to have a graphing calculator. My instructions will predominantly be for the TI-83 and TI-84. If you have another calculator, it will be your responsibility to make sure it has the features you will need in this course and learn how to use those features.

Overview: You will possibly find that this course is very different from other math courses that you have taken. We will be less concerned with the mechanical aspects of computation, and more concerned with why we want to do these calculations. We form a mathematical model of a changing real world situation, such as population growth, use a variety of methods to analyze it, and then interpret our calculated results in the context of the original problem. We will solve problems by using a blend of numerical, graphical, and analytic methods (manipulation of formulas). Modeling is more comprehensive than problem solving; we will learn how models are built, not just how to use them. Finally, in the real world, solutions must be communicated effectively, both in writing and orally, and you will get a lot of practice doing this.

Course Content: We begin with an introduction to discrete models and in particular to difference equations, which are the main focus of your text. We supplement chapter 1 of the text with calculus-based continuous models in which derivatives are used instead of differences. We will learn a little bit about matrices and vectors, which will simplify things later on, and then go on to chapter 2, with a more extended discussion of matrix models for population projections. At this point chapter 3 will be a piece of cake; we skip all but the end of chapter 4, but replace it with a calculus-based treatment of the sine and cosine functions to learn how to model oscillatory behavior (which occurs very often in nature, both at the chemical level and the ecological level). We then follow chapters 5 and 6 of the text with few digressions. If time permits we'll take a look at chapter 7. All along we will work with tables of data, or verbal descriptions of problems, to build our models, and we will use our calculators to make educated guesses about the qualitative behavior of the solutions to make predictions such as whether a population will boom, go extinct, or fluctuate. You will be expected to gradually recognize for yourself when the use of technology is appropriate, and when hand computation and exact algebra or calculus is called for.

Work Load: There will be daily reading and homework, 10 quizzes, 3 tests, and 1 cumulative final exam. You should expect to work at least 6-9 hours per week, outside of class.

Grading: No make-ups will be given for any quizzes or tests. Your two lowest quiz scores will be dropped. No test scores will be dropped, and the final exam score will not be dropped. If your final exam score, when scaled to be out of 100 points, is higher than one of your test scores, then the scaled final exam score will replace your lowest test score. This can only be done for one test. The final exam score itself cannot be replaced by any other score. The final exam will be cumulative.
 Quizzes: 80 points (these will be based on the daily homework assignments) Test 1: 100 points (Monday, Sept. 26) Test 2: 100 points (Monday, Oct. 24) Test 3: 100 points (Monday, Nov. 21) Cumulative Final Exam: 120 points (Wednesday, Dec. 7, 9:00 AM - Noon, Davis 209) TOTAL: 500 points

Attendance: You are expected to come to every class on time and stay until the end of class.