# Introduction to Mathematical Modeling

Fall 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.
- Chapter One (Introduction)
- Chapter Two (Scale, Proportion and Dimensional Analysis)
- Chapter Three (Linear Programming) (Updated Sep 25)
- Chapter Four (Nonlinear Programming)(Updated Oct 21 2003)
- Chapter Five (Data Fitting)
- Chapter Six (Difference Equations)

## 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.

## Exam 3 Materials

## Projects

## 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**