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An Introduction to Mathematical Modeling / Edward A. Bender

Public ISBD Titre : An Introduction to Mathematical Modeling Type de document : texte imprimé Auteurs : Edward A. Bender, Auteur Editeur : Mineola, New York : Dover Publications Inc. Année de publication : 2003 Importance : 256 p. Présentation : couv. ill. en coul., ill. Format : 21,5 cm. ISBN/ISSN/EAN : 978-0-486-41180-4 Langues : Anglais (eng) Catégories : AUTOMATISME Index. décimale : 25-06 Identification et simulation des processus Résumé : Employing a practical, learn by doing approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields -- including science, engineering, and operations research -- to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications. Note de contenu : Table of Contents CHAPTER 1 - WHAT IS MODELING PART 1 - ELEMENTARY METHODS CHAPTER 2 - ARGUMENTS FROM SCALE CHAPTER 3 - GRAPHICAL METHODS CHAPTER 4 - BASIC OPTIMIZATION 4.1. OPTIMIZATION BY DIFFERENTIATION 4.2. GRAPHICAL METHODS CHAPTER 5 - BASIC PROBABILITY 5.1. ANALYTICAL MODELS 5.2. MONTE CARLO SIMULATION CHAPTER 6 - POTPOURRI Desert Lizards and Radiant Energy Are Fair Election Procedures Possible? Impaired Carbon Dioxide Elimination PART 2 - MORE ADVANCED METHODS CHAPTER 7 - APPROACHES TO DIFFERENTIAL EQUATIONS CHAPTER 8 - QUANTITATIVE DIFFERENTIAL EQUATIONS 8.1. ANALYTICAL METHODS 8.2. NUMERICAL METHODS CHAPTER 9 - LOCAL STABILITY THEORY CHAPTER 10 - STOCHASTIC MODELS Radioactive Decay Optimal Facility Location Distribution of Particle Sizes PROBLEMS APPENDIX SOME PROBABILISTIC BACKGROUND REFERENCES A GUIDE TO MODEL TOPICS INDEX An Introduction to Mathematical Modeling [texte imprimé] / Edward A. Bender, Auteur . - Mineola, New York : Dover Publications Inc., 2003 . - 256 p. : couv. ill. en coul., ill. ; 21,5 cm. ISBN : 978-0-486-41180-4 Langues : Anglais (eng) Catégories : AUTOMATISME Index. décimale : 25-06 Identification et simulation des processus Résumé : Employing a practical, learn by doing approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields -- including science, engineering, and operations research -- to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications. Note de contenu : Table of Contents CHAPTER 1 - WHAT IS MODELING PART 1 - ELEMENTARY METHODS CHAPTER 2 - ARGUMENTS FROM SCALE CHAPTER 3 - GRAPHICAL METHODS CHAPTER 4 - BASIC OPTIMIZATION 4.1. OPTIMIZATION BY DIFFERENTIATION 4.2. GRAPHICAL METHODS CHAPTER 5 - BASIC PROBABILITY 5.1. ANALYTICAL MODELS 5.2. MONTE CARLO SIMULATION CHAPTER 6 - POTPOURRI Desert Lizards and Radiant Energy Are Fair Election Procedures Possible? Impaired Carbon Dioxide Elimination PART 2 - MORE ADVANCED METHODS CHAPTER 7 - APPROACHES TO DIFFERENTIAL EQUATIONS CHAPTER 8 - QUANTITATIVE DIFFERENTIAL EQUATIONS 8.1. ANALYTICAL METHODS 8.2. NUMERICAL METHODS CHAPTER 9 - LOCAL STABILITY THEORY CHAPTER 10 - STOCHASTIC MODELS Radioactive Decay Optimal Facility Location Distribution of Particle Sizes PROBLEMS APPENDIX SOME PROBABILISTIC BACKGROUND REFERENCES A GUIDE TO MODEL TOPICS INDEX

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