Concepts of mathematical modeling

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Concepts of mathematical modeling / Walter J. Meyer

資料種別:: 図書
出版情報:: New York : McGraw-Hill, c1984
形態:: xi, 440 p. ; 25 cm
著者名:: Meyer, Walter J. (Walter Joseph), 1943- <DA02636061>
ISBN:: 9780070417472 [0070417474]
書誌ID:: BA04413254

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主題:

Mathematical models

言語:

英語

目次情報:

Preface

The Scope of Mathematical Modeling / Chapter 1：

Models, Mathematical and Otherwise / 1：

Steps in Building a Mathematical Model / 2：

Approximate and Limited Models--Gravity, Rockets, and Raindrops / 3：

Macro and Micro Population Models I--Exponential Growth / 4：

Macro and Micro Population Models II--The Leslie Matrix / 5：

Macro and Micro Population Models III--Family-Planning Models / 6：

Descriptive and Prescriptive Models--Inventory Policy / 7：

The Relation of Models to Data / Chapter 2：

Sources of Error--Underground Exploration of the Earth

Adjusting Data I (The Easy Way)--The Mean and the Maximum Likelihood

Adjusting Data II (The Hard Way)--Miscellaneous Methods and Examples

Testing Models--Weighted-Voting Games

Putting the Facts in Order--Mendeleev and the Periodic Table

Evaluation of Mathematical Models / Chapter 3：

A Bird's-Eye View of Evaluation--College Enrollment

Descriptive Realism--Simple Linear Regression

Descriptive Realism--Correlation Is Not Causation

Accuracy--Multiple Linear Regression

Precision--Malthus and the Dismal Theorem

Generality and Fruitfulness--From Astrology to Technology with Kepler and Newton

Robustness--The Ups and Downs of Ancient Astronomy

Optimization / Chapter 4：

Classical Optimization

Linear Programming--Formulation and Graphical Solution

An Outline of the Simplex Method

Integer Programming--The Knapsack and Traveling Salesman Problems

The Transportation Problem

Combinatorial Optimization--The Chinese Postman Problem

Choosing the Mathematics for the Model / Chapter 5：

Simulation versus Analytic Solution--Queueing Up in the Doctor's Waiting Room

Discrete versus Continuous Models

Introduction to Difference Equations / 2A：

Exponential Population Growth--Difference and Differential Equations / 2B：

Logistic Population Growth--Difference and Differential Equations / 2C：

Equilibrium, Stable and Unstable / 2D：

Stability of Linear Difference Equations--Commodity Prices and Cobweb Analysis / 2E：

Stability of Some Nonlinear Difference Equations--Logistic Population Growth / 2F：

Deterministic versus Stochastic Models--Forecasting Epidemics

An Outline of Probability / 3A：

A Day in the Life of an Epidemic--Stochastic and Deterministic Views / 3B：

The Lifetime of a Deterministic Epidemic / 3C：

The Lifetime of a Simple Stochastic Epidemic / 3D：

Appendix

Answers to Selected Exercises

Index

Preface

The Scope of Mathematical Modeling / Chapter 1：

Models, Mathematical and Otherwise / 1：

Steps in Building a Mathematical Model / 2：

Approximate and Limited Models--Gravity, Rockets, and Raindrops / 3：

Macro and Micro Population Models I--Exponential Growth / 4：

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