Applied Mathematical Modeling

Applied Mathematical Modeling : A Multidisciplinary Approach

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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.
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Product details

  • Hardback | 472 pages
  • 153.4 x 246.9 x 29.5mm | 771.12g
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 41 Tables, black and white
  • 1584880481
  • 9781584880486

Table of 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 Vigenere 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
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Review quote

scholarly and thought provokingThe book is described as 'a handbook of in-depth case studies' and in this it undersells itselfover 600 pages of delighta nice mixture of mathematical rigour and scientific analoques and intuitionthe mathematical techniques are treated with just the right level of common-sense rigour that I associate with the best applied mathematics teachersthe 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 seenhundreds of worked examples and exercises. The Special Topics chapter is superbThere are countless references, and the book is literally a gold-mine.
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