Fall 2009 Syllabus

Math 343 Mathematical Modeling (3 hours)

 

Instructor:  William Harris                                                                 Office:  120 ASC

Email:  wharris@georgetowncollege.edu                                             Phone:  863-7921

Instructor’s Web Site:  www.georgetowncollege.edu/departments/mpc/harris

Course Web Site:  scholar.georgetowncollege.edu

 

Office Hours:  11:00-11:30 MWF; 2:00-3:00 MWF; 1:00-2:00 TR; also by appt.

 

Course Description:  An introduction to the study of modeling real-world phenomena, with an emphasis on applications to science.  Topics include modeling using difference equations and differential equations, simulation, matrix modeling and Markov chains, and dimensional analysis.

 

Prerequisite:  MAT125. 

 

Text:  Giordano, Frank R., Fox, William P., Horton, Steven B., and Weir, Maurice D., A First Course in Mathematical Modeling, 4th edition, Brooks/Cole, 2009.

 

Course Objectives:  To introduce students to the process of formulation, analysis and verification of mathematical models which reasonably describe real-world situations.  To introduce students to a variety of models in biology, chemistry, and physics.  To introduce students to software tools that aid in the modeling process.

 

Requirements of Course:

 

1)      Homework assignments.  I will assign problems, more or less daily, based on recent class work.  You should expect homework to be collected 10-12 times over the course of the semester.

 

2)      Projects.   I will regularly assign projects or extended explorations.  Some of these will be completed individually, and some will be done in groups.  I expect to assign 4 or so individual projects and 3-4 group projects.  The projects will form a major part of your evaluation in the course.

 

3)      Field Trip.  On Monday, October 19, we will tour the facilities at Oak Ridge National Laboratory, in Tennessee.   This will be a roughly 8:00am to 8:00pm experience.  Attendance is required.

 

4)      Exams.  There will be two in-class exams during the semester; they will occur approximately in weeks 6 and 12.  The final exam will come in two parts:  an individual take-home section, and a group project, which will include a written report and a 30-minute oral presentation during the final exam period (9-11am, Tuesday, December 15).   The take-home and the report are both due at 9am on the 15th.

 

Course Outline:  We will cover material from Chapters 1-7 and 11-13 of the text.  Additional topics will be addressed as time permits.           

 

 

Evaluation:                 Homework:                              25%

Projects:                                   35%

Exams:                                     20%

Take-home Final:                     10%

Final Project:                            10%

 

I would expect grades to be assigned according to the following scale: 

A:  91-100;  A/B:  88 up to 91;  B: 81 up to 88;  B/C:  78 up to 81;  C:  70 up to 78; 

D: 60 up to 70;  F:  below 60.   I reserve the right to adjust this scale slightly at the end of the semester.

 

Technology:  We will make regular use of technological tools in this course.  You will be introduced to Vensim Simulation Software, which will allow you to construct models and visualize the changes in the quantities being modeled, and to Matlab, a technical computing/programming environment.  We will likely make occasional use of Microsoft Excel, as well.  Prior experience with programming is not expected, but it would extremely beneficial!

 

Attendance:  I will be taking daily attendance.  I’m not expecting this to be a problem, but obviously, if you are repeatedly absent, we’ll have to talk about it.

 

Cheating:  In a word, DON’T.  Please make sure you have read and understand the school policies on “Academic Honesty” in your college Catalog.  Recall also that there is an Academic Honor Code present on this campus.  If you are caught cheating in this course, you will be dealt with appropriately.

 

Bibliography:

 

Allman, Elizabeth S., and Rhodes, John A., Mathematical Models in Biology:  An Introduction, Cambridge University Press, 2004.

 

de Vries, Gerta, et. al.,  A Course in Mathematical Biology:  Quantitative Modeling with Mathematical and Computational Methods, Society for Industrial and Applied Mathematics, 2006.

 

Hannon, Bruce, and Ruth, Matthias, Dynamic Modeling, 2nd ed., Springer-Verlag, 2001

 

Maki, Daniel, and Thompson, Maynard, Mathematical Modeling and Computer Simulation, Brooks/Cole, 2006.

 

Meerschaert, Mark M., Mathematical Modeling, 3rd ed., Academic Press, 2007.

 

Modeling Resource CD, Consortium for Mathematics and Its Applications, 2004.

 

Mooney, Douglas, and Swift, Randall, A Course in Mathematical Modeling, Mathematical Association of America, 1999.

 

Shiflet, Angela B., and Shiflet, George W., Introduction to Computational Science:  Modeling and Simulation for the Sciences, Princeton University Press, 2006.