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1. What is Modeling

1.1 Models and Reality

1.2 Properties of Models

1.3 Building a Model

1.4 An Example

1.5 Another Example Problems

1.6 Why Study Modeling?

Part I. Elementary methods

2. Arguments from Scale

2.1 Effects of Size Costs of Packaging Speed of Racing Shells Size Effects in Animals Problems

2.2 Dimensional Analysis Theoretical Background The Period of a Perfect Pendulum Scale Models of Structures Problems

3. Graphical Methods

3.1 Using Graphs in Modeling

3.2 Comparative Statics The Nuclear Missile Arms Race Biogeography: Diversity of Species on Islands Theory of the Firm Problems

3.3 Stability Questions Cobweb Models in Economics Small Group Dynamics Problems

4. Basic Optimization

4.1 Optimization by Differentiation Maintaining Inventories Geometry of Blood vessels Fighting forest Fires Problems

4.2 Graphical Methods A Bartering Model Changing Environment and Optimal Phenotype Problems

5. Basic Probability

5.1 Analytic Models Sex Preference and Sex Ratio Making Simple Choices Problems

5.2 Monte Carlo Simulation A Doctor's Waiting Room Sediment Volume Stream Networks Problems A Table of 3000 Random Digits

6. Potpourri Desert Lizards and Radiant Energy Are Fair Election Procedures Possible? Impaired Carbon Dioxide Elimination Problems

Part 2. More Advanced Methods

7. Approaches to Differential Equations

7.1 General Discussion

7.2 Limitations of Analytic Solutions

7.3 Alternative Approaches

7.4 Topics Not Discussed

8. Quantitative Differential Equations

8.1 Analytical Methods Pollution of the Great Lakes The Left Turn Squeeze Long Chain Polymers Problems

8.2 Numerical Methods Towing a Water Skier A Ballistics Problem Problems The Heun Method

9. Local Stability Theory

9.1 Autonomous systems

9.2 Differential Equations Theoretical Background Frictional Damping of a Pendulum Species Interaction and Population Size Keynesian Economics More Complicated Situations Problems

9.3 Differential-Difference Equations The Dynamics of Car Following Problems

9.4 Comments on Global Methods Problem

10. More Probability Radioactive Decay Optimal Facility Location Distribution of Particle Sizes Problems

Appendix. Some probabilistic Background

A.1 The Notion of Probability

A.2 Random Variables

A.3 Bernoulli Trials

A.4 Infinite Events Sets

A.5 The Normal Distribution

A.6 Generating Random Numbers

A.7 Least Squares

A.8 The Poisson and Exponential Distributions

References A Guide to Model Topics Index

1.1 Models and Reality

1.2 Properties of Models

1.3 Building a Model

1.4 An Example

1.5 Another Example Problems

1.6 Why Study Modeling?

Part I. Elementary methods

2. Arguments from Scale

2.1 Effects of Size Costs of Packaging Speed of Racing Shells Size Effects in Animals Problems

2.2 Dimensional Analysis Theoretical Background The Period of a Perfect Pendulum Scale Models of Structures Problems

3. Graphical Methods

3.1 Using Graphs in Modeling

3.2 Comparative Statics The Nuclear Missile Arms Race Biogeography: Diversity of Species on Islands Theory of the Firm Problems

3.3 Stability Questions Cobweb Models in Economics Small Group Dynamics Problems

4. Basic Optimization

4.1 Optimization by Differentiation Maintaining Inventories Geometry of Blood vessels Fighting forest Fires Problems

4.2 Graphical Methods A Bartering Model Changing Environment and Optimal Phenotype Problems

5. Basic Probability

5.1 Analytic Models Sex Preference and Sex Ratio Making Simple Choices Problems

5.2 Monte Carlo Simulation A Doctor's Waiting Room Sediment Volume Stream Networks Problems A Table of 3000 Random Digits

6. Potpourri Desert Lizards and Radiant Energy Are Fair Election Procedures Possible? Impaired Carbon Dioxide Elimination Problems

Part 2. More Advanced Methods

7. Approaches to Differential Equations

7.1 General Discussion

7.2 Limitations of Analytic Solutions

7.3 Alternative Approaches

7.4 Topics Not Discussed

8. Quantitative Differential Equations

8.1 Analytical Methods Pollution of the Great Lakes The Left Turn Squeeze Long Chain Polymers Problems

8.2 Numerical Methods Towing a Water Skier A Ballistics Problem Problems The Heun Method

9. Local Stability Theory

9.1 Autonomous systems

9.2 Differential Equations Theoretical Background Frictional Damping of a Pendulum Species Interaction and Population Size Keynesian Economics More Complicated Situations Problems

9.3 Differential-Difference Equations The Dynamics of Car Following Problems

9.4 Comments on Global Methods Problem

10. More Probability Radioactive Decay Optimal Facility Location Distribution of Particle Sizes Problems

Appendix. Some probabilistic Background

A.1 The Notion of Probability

A.2 Random Variables

A.3 Bernoulli Trials

A.4 Infinite Events Sets

A.5 The Normal Distribution

A.6 Generating Random Numbers

A.7 Least Squares

A.8 The Poisson and Exponential Distributions

References A Guide to Model Topics Index

Library of Congress subject headings for this publication: Mathematical models