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Index
DOVER BOOKS ON MATHEMATICS
Title Page
Copyright Page
PREFACE
Table of Contents
CHAPTER 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 1 - ELEMENTARY METHODS
CHAPTER 2 - ARGUMENTS FROM SCALE
2.1. EFFECTS OF SIZE
2.2. DIMENSIONAL ANALYSIS
CHAPTER 3 - GRAPHICAL METHODS
3.1. USING GRAPHS IN MODELING
3.2. COMPARATIVE STATICS
3.3. STABILITY QUESTIONS
CHAPTER 4 - BASIC OPTIMIZATION
4.1. OPTIMIZATION BY DIFFERENTIATION
4.2. GRAPHICAL METHODS
CHAPTER 5 - BASIC PROBABILITY
5.1. ANALYTICAL MODELS
5.2. MONTE CARLO SIMULATION
CHAPTER 6 - POTPOURRI
Desert Lizards and Radiant Energy
Are Fair Election Procedures Possible?
Impaired Carbon Dioxide Elimination
PROBLEMS
PART 2 - MORE ADVANCED METHODS
CHAPTER 7 - APPROACHES TO DIFFERENTIAL EQUATIONS
7.1. GENERAL DISCUSSION
7.2. LIMITATIONS OF ANALYTICAL SOLUTIONS
7.3. ALTERNATIVE APPROACHES
7.4. TOPICS NOT DISCUSSED
CHAPTER 8 - QUANTITATIVE DIFFERENTIAL EQUATIONS
8.1. ANALYTICAL METHODS
8.2. NUMERICAL METHODS
CHAPTER 9 - LOCAL STABILITY THEORY
9.1. AUTONOMOUS SYSTEMS
9.2. DIFFERENTIAL EQUATIONS
9.3. DIFFERENTIAL DIFFERENCE EQUATIONS
9.4. COMMENTS ON GLOBAL METHODS
CHAPTER 10 - STOCHASTIC MODELS
Radioactive Decay
Optimal Facility Location
Distribution of Particle Sizes
PROBLEMS
APPENDIX SOME PROBABILISTIC BACKGROUND
REFERENCES
A GUIDE TO MODEL TOPICS
INDEX
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