The 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.
The 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.
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-Dispers
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-Dispers
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