Thinking with models · Mathematical Models in the Physical, Biological, and Social Sciences by Alexander, Joyce M. -- Read -- Imperial Library of Trantor

Index

Cover Page Title Page Copyright Page Dedication Preface Contents Part I. Methodology

Chapter 1. An Overview

1.1. Introduction 1.2. Problems: Identification, Formulation, and Solution

1.2.1. Guidelines on Formulating the Problem 1.2.2. Guidelines on how to solve the Problem 1.2.3. Impact of the Solution

1.3. Mathematical Models and their Applications

1.3.1. The Process of Solving 1.3.2. Equilibrium and Stability

1.4. The Modeling Process 1.5. Why Structuring and Solving should be separated Problems References Bibliography

Chapter 2. Three Basic Themes: Counting, Estimation, and Structuring

2.1. Introduction 2.2. Counting 2.3. Results of Estimation 2.4. Counting and Estimation and their use in Probability 2.5. Structuring 2.6. Proving Problems References Bibliography

Part II. Framework

Chapter 3. Equations

3.1. Introduction 3.2. Algebraic Equations 3.3. Diophantine Algebraic Equations 3.4. Ordinary Differential Equations 3.5. Partial Differential Equations 3.6. Difference Equations 3.7. Differential Difference Equations 3.8. Delay–Differential Equations 3.9. Differential–Difference–Delay Equations 3.10. Integral Equations 3.11. Integro–Difference and Integro–Differential Equations 3.12. Stochastic Differential Equations 3.13. Functional Equations Problems References Bibliography

Chapter 4. Optimization

4.1. Introduction 4.2. Unconstrained Minima 4.3. Constrained Problems

4.3.1. Lagrange Multipliers 4.3.2. Unknown Number of Variables

4.4. Linear Programming 4.5. Nonlinear Programming 4.6. Multistage Optimization (Dynamic Programming) 4.7. Calculus of Variations 4.8. Theory of Optimal Control 4.9. Stochastic Optimization 4.10. Game Theory Problems

Chapter 5. Probability and Stochastic Processes

5.1. Introduction 5.2. Applications of the Theory of Probability 5.3. Applications of the Theory of Stochastic Processes Problems Bibliography

Part III. Applications

Chapter 6. Physical and Biological Applications

6.1. Introduction 6.2. Natural Sciences 6.3. Oxygen and Blood Circulation 6.4. Medical Application 6.5. Muscular Control 6.6. Weight Control 6.7. Cellular and Genetic Applications 6.8. Models Related to the Nervous System 6.9. Evolution 6.10. Social Biology Problems References Bibliography

Chapter 7. Social and Behavioral Applications

7.1. Introduction 7.2. Courts and Justice 7.3. Academic Activities 7.4. Communication and News Transmissions 7.5. Population and Pollution 7.6. Economic Models 7.7. Conflict Resolution 7.8. Learning Problems References Bibliography

Chapter 8. Hierarchies and Priorities

8.1. Introduction 8.2. Paired Comparisons 8.3. Calculation of the Weights and Priorities 8.4. Hierarchies in Decision Making 8.5. Weighting through the Hierarchy 8.6. The Forward and Backward Processes in Planning and in Conflict Analysis 8.7. Design of a Transport System for the Sudan: Priorities—Investment 8.8. Rationing Energy to Industries: Optimization 8.9. Oil Prices in 1985

8.9.1. The Problem 8.9.2. How to Compute Price Increases 8.9.3. Computation of Oil Price in 1985 8.9.4. Analysis of the Results for 1985

8.10. Architectural Design Problems References

Index Back Cover References Bibliography