# Introduction to Mathematical ModelingFall 2003

This course explores the process of building, analyzing and interpreting mathematical descriptions of real-world processes. The course introduces basic techniques, which may include such topics as data fitting, modeling with functions, discrete dynamics, differential equations, and simulation modeling.

### The Textbook: Mathematical Modeling, A Comprehensive Introduction, By Michael J. Kirby and Gerhard Dangelmayr

This textbook is in DRAFT FORM. It is included below as a courtesy to the students at Whitman in Math 250, and may be pulled off the web as the semester progresses. Students: Please do not print more copies than you need- I will be passing out hardcopy in class.

## Handouts from Class:

• Course Syllabus and Outline of Topics
• Chapter 1
• Chapter 2
• Exam 1
• Chapter 3
• Chapter 4
• Exam 2
• Chapter 5 (Curve Fitting)
• Chapter 6, Difference Equations
• Class Notes
• The Famous Canadian Lynx-Hare Data

• NOTE about the data: I have not been able to verify this data, but this is the data (or rather the graph) that is always cited. This particular set of data came from scanning in the graph from Odum's "Fundamentals of Ecology", p. 191 which is often cited. Odum says that his graph is taken from MacLulich's "Fluctuations in the numbers of varying hare", 1937, which is not widely available. Some authors caution that this data is actually a composition of several time series, and should probably not be analyzed as a whole, and that some of the lynx data was actually missing. It is said that the data was collected from Hudson's Bay historical records, and does not reflect animal populations, but rather the number of pelts turned in for trading (a large number of which came from Native Americans- mentioned because there were some medical outbreaks during these years which could account for skewed data). The data is presented here with these cautions.

## Matlab Material

NOTE: There are two methods of inputting data in Matlab. Some data files have a .m suffix, while others have a .mat suffix. For example, if I want to load the data in the filename data1.m, in Matlab I would type only data1 If the data is data1.mat, in Matlab I would type load data1