Concepts of Mathematical Modeling

ISBN-10: 0486435156
ISBN-13: 9780486435152
Edition: 2004
Authors: Walter J. Meyer
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Description: Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in  More...

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Book details

List price: $26.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 8/13/2004
Binding: Paperback
Pages: 448
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.232
Language: English

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 ed.

Preface
The Scope of Mathematical Modeling
Models, Mathematical and Otherwise
Steps in Building a Mathematical Model
Approximate and Limited Models--Gravity, Rockets, and Raindrops
Macro and Micro Population Models I--Exponential Growth
Macro and Micro Population Models II--The Leslie Matrix
Macro and Micro Population Models III--Family-Planning Models
Descriptive and Prescriptive Models--Inventory Policy
The Relation of Models to Data
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
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
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
Simulation versus Analytic Solution--Queueing Up in the Doctor's Waiting Room
Discrete versus Continuous Models
Introduction to Difference Equations
Exponential Population Growth--Difference and Differential Equations
Logistic Population Growth--Difference and Differential Equations
Equilibrium, Stable and Unstable
Stability of Linear Difference Equations--Commodity Prices and Cobweb Analysis
Stability of Some Nonlinear Difference Equations--Logistic Population Growth
Deterministic versus Stochastic Models--Forecasting Epidemics
An Outline of Probability
A Day in the Life of an Epidemic--Stochastic and Deterministic Views
The Lifetime of a Deterministic Epidemic
The Lifetime of a Simple Stochastic Epidemic
Appendix
Answers to Selected Exercises
Index

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