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Applied Mathematical Modeling

A Multidisciplinary Approach

Edited by Douglas R. Shier, K.T. Wallenius

Series Editor: Kenneth H. Rosen

Contributors: William F. Lucas, Marc Artzrouni

Published November 11th 1999 by CRC Press – 472 pages

Series: Discrete Mathematics and Its Applications

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Description

The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines.

The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects.

In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter. Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea.

Applied Mathematical Modeling serves as a handbook of in-depth case studies that span the mathematical sciences, building upon a modest mathematical background. Readers in other applied disciplines will benefit from seeing how selected mathematical modeling philosophies and techniques can be brought to bear on problems in their disciplines. The models address actual situations studied in chemistry, physics, demography, economics, civil engineering, environmental engineering, industrial engineering, telecommunications, and other areas.

Reviews

"…scholarly and thought provoking…The book is described as 'a handbook of in-depth case studies' and in this it undersells itself…over 600 pages of delight…a nice mixture of mathematical rigour and scientific analoques and intuition…the mathematical techniques are treated with just the right level of common-sense rigour that I associate with the best applied mathematics teachers…the treatments of some of more awkward topics such as bifurcations in ODEs and Greens functions, are some of the simplest and most transparent I have seen…hundreds of worked examples and exercises. The Special Topics chapter is superb…There are countless references, and the book is literally a gold-mine."

-The Mathematical Gazette, November 2001

Contents

THE IMPACT AND BENEFITS OF MATHEMATICAL MODELING

Introduction

Mathematical Aspects, Alternatives, Attitudes

Mathematical Modeling

Teaching Modeling

Benefits of Modeling

Educational Benefits

Modeling and Group Competition

Other Benefits of Modeling

The Role of Axioms in Modeling

The Challenge

References

REMARKS ON MATHEMATICAL MODEL BUILDing

Introduction

An Example of Mathematical Modeling

Model Construction and Validation

Model Analysis

Some Pitfalls

Conclusion

References

UNDERSTANDING THE UNITED STATES AIDS EPIDEMIC

Introduction

Prelude: The Postwar Polio Epidemic

AIDS: A New Epidemic for America

Why an AIDS Epidemic in America?

A More Detailed Look at the Model

Forays into the Public Policy Arena

Modeling the Mature Epidemic

AIDS as a Facilitator of Other Epidemics

Comparisons with First World Countries

Conclusion: A Modeler's Portfolio

References

A MODEL FOR THE SPREAD OF SLEEPING SICKNESS

Introduction

The Compartmental Model

Mathematical Results

Discussion

Alternative Models

Exercises and Projects

References

MATHEMATICAL MODELS IN CLASSICAL CRYPTOLOGY

Introduction

Some Terminology of Cryptology

Simple Substitution Systems

The Vigenére Cipher and One-Time Pads

The Basic Hill System and Variations

Exercises and Projects

References

MATHEMATICAL METHODS IN PUBLIC-KEY CRYPTOLOGY

Introduction

Cryptosystems Based on Integer Factorization

Cryptosystems Based on Discrete Logarithms

Digital Signatures

Exercises and Projects

References

NONLINEAR TRANSVERSE VIBRATIONS IN AN ELASTIC MEDIUM

Introduction

A String Embedded in an Elastic Medium

An Approximation Technique

Base Equation Solution of Ricatti Equation

Exercises and Projects

References

SIMULATING NETWORKS WITH TIME-VARYING ARRIVALS

Introduction

The Registration Problem

Generating Random Numbers

Statistical Tools

Arrival Processes

Queueing Models

Exercises and Projects

References

MATHEMATICAL MODELING OF UNSATURATED POROUS MEDIA FLOW AND TRANSPORT

Introduction

Governing Equations

Constant-Coefficient Convection-Dispersion

Coupling the Equations

Summary and Suggestions for Further Study

Exercises and Projects

References

INVENTORY REPLENISHMENT POLICIES AND PRODUCTION STRATEGIES

Introduction

Piston Production and the Multinomial Model

Sleeve Inventory Safety Stocks

Comparison of Three Reordering Policies

Variable Piston Production Quantities

The Supplier's Production Problem

Target Selection for Multinomial Distributions

The Supplier's Cost Function

Target Selection Using Normal Distributions

Conclusion

Exercises and Projects

References

MODELING NONLINEAR PHENOMENA BY DYNAMICAL SYSTEMS

Introduction

Simple Pendulum

Periodically Forced Pendulum

Exercises and Projects

References

MODULATED POISSON PROCESS MODELS FOR BURSTY TRAFFIC BEHAVIOR

Introduction

Workstation Utilization Problem

Constructing a Modulated Poisson Process

Simulation Techniques

Analysis Techniques

Exercises and Projects

References

GRAPH-THEORETIC ANALYSIS OF FINITE MARKOV CHAINS

Introduction

State Classification

Periodicity

Conclusion

Exercises and Projects

References

SOME ERROR-CORRECTING CODES AND THEIR APPLICATIONS

Introduction

Background Coding Theory

Computer Memories and Hamming Codes

Photographs in Space and Reed-Muller Codes

Compact Discs and Reed-Solomon Codes

Conclusion

Exercises and Projects

References

BROADCASTING AND GOSSIPING IN COMMUNICATION NETWORKS

Introduction

Standard Gossiping and Broadcasting

Examples of Communication

Results from Selected Gossiping Problems

Conclusion

Exercises and Projects

References

MODELING THE IMPACT OF ENVIRONMENTAL REGULATIONS ON HYDROELECTRIC REVENUES

Introduction

Preliminaries

Model Formulation

Model Development

Case Study

Exercises and Projects

References

VERTICAL STABILIZATION OF A ROCKET ON A MOVABLE PLATFORM

Introduction

Mathematical Model

State-Space Control Theory

The KNvD Algorithm

Exercises and Problems

References

DISTINGUISHED SOLUTIONS OF A FORCED OSCILLATOR

Introduction

Linear Model with Modified External Forcing

Nonlinear Oscillator Periodically Forced by Impulses

A Suspension Bridge Model

Model Extension to Two Spatial Dimensions

Exercises and Projects

References

MATHEMATICAL MODELING AND COMPUTER SIMULATION OF A POLYMERIZATION PROCESS

Introduction

Formulating a Mathematical Model

Computational Approach

Conclusion

Exercises and Problems

References

THE CLEMSON GRADUATE PROGRAM

Introduction

Historical Background

Transformation of a Department

The Clemson Program

Communication Skills

Program Governance

Measures of Success

Conclusion

References

Name: Applied Mathematical Modeling: A Multidisciplinary Approach (Hardback) – CRC Press 
Description: Edited by Douglas R. Shier, K.T. WalleniusSeries Editor: Kenneth H. RosenContributors: William F. Lucas, Marc Artzrouni. The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often...
Categories: Applied Mathematics, Mathematical Modeling