Applied Mathematical Modeling
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BeschreibungThe practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience. Applied Mathematical Modeling fills a gap within modeling texts, focusing on real-world 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. The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects.
InhaltsverzeichnisTHE 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
Pressestimmenscholarly 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.
Untertitel: 'Discrete Mathematics & Its App'. Sprache: Englisch.
Verlag: CRC PR INC
Erscheinungsdatum: November 1999
Seitenanzahl: 468 Seiten