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

1. Chapter One (Introduction)
2. Chapter Two (Scale, Proportion and Dimensional Analysis)
3. Chapter Three (Linear Programming) (Updated Sep 25)
4. Chapter Four (Nonlinear Programming)(Updated Oct 21 2003)
5. Chapter Five (Data Fitting)
6. Chapter Six (Difference Equations)

Handouts from Class:

• Course Syllabus and Outline of Topics
• Chapter 1
• Class Notes, Chapter 1
• Case Study 1 (From Sociology): I Will if You Will. This is also an introduction to Chapter 2
• Chapter 2
  • Adventures in Modeling: A Universal Scaling Law for Biology?
  • Class Notes, Dimensional Analysis Revised Sep 21, 2003
  • Exercise Solutions, Dimensional Analysis Notes
• Exam 1
• Overview for Exam 1
• Solutions to questions from Overview 1
• Chapter 3
  • Maple Lab- Linear Algebra and Linear Programming
  • Introduction to Linear Programming
  • Details: Rocket Launch with Air Resistance
  • Maple Worksheets
  • Basic Targeting Problem
  • Targeting with Air Resistance
  • Targeting with Air Resistance and Soft Landing
• Chapter 4
  • Introduction to Nonlinear Programming Class Notes
  • Maple Worksheets
  • Draw a tangent line to a space curve
  • Example 4-6 from Text
  • Example 4-7 from Text
  • Example 4-8 from Text
  • Example 4-10 from Text
  • Example 4-10, continued
• Exam 2
  • Exam 2 Review Questions
  • Exam 2 Review Solutions
• Chapter 5 (Curve Fitting)
• Class Notes for Ch 5
• Matlab and Lab info:
  1. Homework Assignment for Chapter 5
  2. Lab Instructions
  3. A Note about Handwriting
  4. Cubic Splines in Matlab
• Data and Functions
• Matlab function for the Median-Median Line
• Walla Walla Weather data: October 1-Nov 1, 2003 Three columns- Max, Median, Min daily temperatures
• Enzyme Data Set 1
• Enzyme Homework Data Set
• Population of the United States, 1900-1990. In two column format- Year and Population (in number of persons).
• An image of John Hancock's signature
• Some digitized data from John Hancock's signature
• Homework data file: Handwriting
• 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.
• The original graph
• The data as a text file. The first column is the year, second column is for the Hare, third column is for the Lynx

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Exam 3 Materials

• Exam 3 (in PDF)
• ExamData1.mat To download this, right-click and "save link as..."
• Sample Maple Worksheet

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Projects

• Projects Outline
• NFL data as an M-file Download this to a local file, then run nfldat in Matlab. This will produce 4 arrays of data, corresponding to the 4 sets of data in the handout (NFL, Old NFL QBs, NCAA, and Draft).
• Sample Linearization Maple Worksheet (For the three way predator-prey)
• Sample M-file for plotting an orbit (Predator-Prey)
• Blackjack:
1. Main program, blackjack.m
2. Helper program, my_card_value.m
3. Helper program, dealer_card_value.m

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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

• An Introduction to Matlab
• A Summary Sheet of Matlab Commands
• A Sample Matlab Function
• A Sample Matlab Script
• Matlab File with data for Kepler's Third Law
• Matlab File with data on Mammals: Mass versus Heart Rate
• Intergroup (synthetic) data

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