Acknowledgments
Preface
To the Teacher
Contents
0- Modeling Basics: Purpose, Resolution, and Resources
1- Discrete Dynamical Systems
1.1 Basic Recurrence Relations
1.2 Spreadsheet Simulations
1.3 Difference Equations and Compartmental Analysis
1.4 Closed-Form Solutions and Mathematical Analysis
1.5 Variable Growth Rates and the Logistic Model
1.6 Systems of Recurrence Relations
1.7 For Further Reading
1.8 Exercises
1.9 Projects
2- Discrete Stochasticity
2.1 Stochastic Squirrels
2.2 Interpreting Stochastic Data
2.3 Creating Stochastic Models: Simulations
2.4 Model Validation: Chi-Square Goodness-Of-Fit Test
2.5 For Further Reading
2.6 Exercises
2.7 Projects
3- Stages, States, and Classes
3.1 A Human Population Model
3.2 State Diagrams
3.3 Equations From State Diagrams
3.4 A Primer of Matrix Algebra
3.5 Applying Matrices to State Models
3.6 Eigenvector and Eigenvalue Analysis
3.7 A Staged Example
3.8 Fundamentals of Markov Chains
3.9 Markovian Squirrels
3.10 Harvesting Scot Pines: An Absorbing Markov Chain Model
3.11 Life Tables
3.12 For Further Reading
3.13 Exercises
3.14 Projects
4- Empirical Modeling
4.1 Covariance and Correlation -- A Discussion of Linear Dependence
4.2 Fitting a Line to Data Using the Least-Squares Criterion
4.3 R^2: A Measure of Fit
4.4 Finding R^2 for Curves Other than Lines
4.5 Example: Opening The X-Files Again
4.6 Curvilinear Models
4.7 Example: The Cost of Advertising
4.8 Example: Lynx Fur Returns
4.9 Interpolation
4.10 The Statistics of Simple Regression
4.11 Example: Elk of The Grand Totens
4.12 An Introduction to Multiple Regression
4.13 Curvilinear Regression
4.14 For Further Reading
4.15 Exercises
4.16 Projects
5- Continuous Models
5.1 Setting Up the Differential Equation: Compartmental Analysis II
5.2 Solving Special Classes of Differential Equations
5.3 Geometric Analysis and Nonlinear Equations
5.4 Differential Equation Solver
5.5 For Further Reading
5.6 Exercises
5.7 Projects
6- Continuous Stochasticity
6.1 Some Elements of Queueing Theory
6.2 Service at a Checkout Counter
6.3 Standing in Line -- The Poisson Process
6.4 Example: Crossing a Busy Street
6.5 The Single-Server Queue
6.6 A Queueing Simulation
6.7 Pure Birth Process
6.8 For Further Reading
6.9 Exercises
6.10 Projects
Appendices
A- Chi-Square Table
B- F-Table
C- t-Table
D- Mathematica Appendix
References
Index