MATH 440 - Mathematical Modeling

Spring Semester, 1997
MW 7:00-8:15
Room 205, Gosnold Hall

Objectives:

• demonstrate the applicability of mathematics in the formulation, analysis and interpretation of models in the study of concrete problems;
  
• introduce students to problems which require effort for precise formulation;
  
• introduce students to problems whose treatment could require topics drawn from any mathematics course in the student's background;
  
• demonstrate the use of appropriate technologies in the solution of mathematical models; and
  
• give students practice in the oral and written communication of mathematical ideas.
  

Instructor:	BRIAN BRADIE
Office:	Gosnold Hall, Room 119
Office Phone:	594 - 7944
Department Phone:	594 - 7914
E-mail	bbradie@pcs.cnu.edu
Homepage:	www.pcs.cnu.edu/~bbradie/home.html

Office Hours:

Monday	4:00-5:00, 8:30-9:00
Tuesady	1:30-2:30
Wednesday	4:00-5:00, 8:30-9:00
Thursday	1:30-2:30
	... and ... always available by appointment

References:

Beltrami, Mathematics for Dynamic Modeling , Academic Press, 1987
Dreyer, Modeling with Ordinary Differential Equations , CRC Press, 1993
Fowkes and Mahoney, An Introduction to Mathematical Modeling , Wiley, 1994
Meerschaert, Mathematical Modeling , Academic Press, 1993
Mesterton-Gibbons, A Concrete Approach to Mathematical Modeling , Wiley, 1995

If you are interested in further references, or references which contain more advanced
models, check out the course web site listed above or see me.

Grading:

Homework 20%
Class Participation 10%
Mini-Projects 15% each (3 mini-projects)
Final Project 25%

Prerequisites:

MATH 320 - Ordinary Differential Equations

Many, though not all, of the models which we discuss in this course will involve ordinary differential equations (ODEs). It will be assumed that you are familiar with the basic analytical procedures for solving first and second order ODEs.

Homework:

A variety of different homework assignments will be made throughout the semester. Some assignments will require modifying a model covered in class, others the development of a different model, others the analysis of a model and still others will focus on the interpretation/validation of the model's results. Each assignment should be completed individually, and a detailed solution should be submitted. Enough detail should be included so that someone unfamiliar with the problem you are dealing with could still follow your work. One student will be selected to present his/her solution to the class. This selection will be made when the assignment is given so that there will be no surprises.

Mini-Projects:

There will be three (3) "mini-projects", of 1-1/2 to 2 weeks in duration, assigned during the semester. These projects will focus on a portion of the modeling process - the portion of focus may change with each project. Each of these projects will be completed in groups, to be designated when the assignment is made. Each group will submit a report detailing their solution to the problem and will also make a short presentation (roughly 15 minutes in length) to the class. Tentatively, these mini-projects will deal with population dynamics, determination of proper dosages of medication and Monte Carlo simulation.

Final Project:

During the final 4-5 weeks of the semester, a final modeling project, which will focus on the entire modeling process, will be completed. The final project may be completed individually or in groups of two people, and the topic of the project will be selected by the individual/group. As with the mini-projects, a report detailing the solution of the problem will be submitted and a presentation of the results will be made.

Helpful Hints and Suggestions:

• Review your class notes on a regular basis. It would be to your advantage, early in the semester, to establish the habit of reviewing your class notes between class periods --- especially before attempting the homework problems.
  
• The items regarding homework which were mentioned in the homework section above are worth repeating. Work homework problems as soon after class as possible. Don't forget the item immediately above --- review your class notes before attempting homework problems. Working problems on a CONSISTENT basis will be one of your best means of testing your understanding and developing/honing your modeling skills.
  
• When working homework problems keep the following simple thought in mind: Show, don't tell. You need to keep in mind that your objective is not to "get the right answer," but rather to derive the correct solution. For grading purposes, you will earn credit for the work which you show. An answer, even the correct answer, unsupported by clear work and/or derivations will be worth no credit.
  
• If there is material which you do not understand and/or you just feel like you need help, ASK!!!
  

Students with Disabilities:

Any student who believes that she or he is disabled should make an appointment to see me to discuss your needs. In order to receive an accommodation, your disability must be on record in the Office of Career & Counseling Services (telephone 594-7047, CC-146).