{"product_id":"models-for-life-isbn-9781119039754","title":"Models for Life","description":"\u003cp\u003e\u003cb\u003eFeatures an authentic and engaging approach to mathematical modeling driven by real-world applications \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWith a focus on mathematical models based on real and current data, \u003ci\u003eModels for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® \u003c\/i\u003eguides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques.\u003c\/p\u003e \u003cp\u003eThe book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. \u003ci\u003eModels for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® \u003c\/i\u003ealso features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA modular organization that, after the first chapter, allows readers to explore chapters in any order\u003c\/li\u003e \u003cli\u003eNumerous practical examples and exercises that enable readers to personalize the presented models by using their own data\u003c\/li\u003e \u003cli\u003eCarefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt\u003c\/li\u003e \u003cli\u003eReferences throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study\u003c\/li\u003e \u003cli\u003eRelevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material\u003c\/li\u003e \u003cli\u003eBoth mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug’s therapeutic window\u003c\/li\u003e \u003cli\u003eA companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor’s manual with solutions to all homework problems, project ideas, and a test bank\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book is ideal for undergraduate non-mathematics majors enrolled in mathematics or quantitative reasoning courses such as introductory mathematical modeling, applications of mathematics, survey of mathematics, discrete mathematical modeling, and mathematics for liberal arts. The book is also an appropriate supplement and project source for honors and\/or independent study courses in mathematical modeling and mathematical biology.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJeffrey T. Barton, PhD,\u003c\/b\u003e is Professor of Mathematics in the Mathematics Department at Birmingham-Southern College. A member of the American Mathematical Society and Mathematical Association of America, his mathematical interests include approximation theory, analytic number theory, mathematical biology, mathematical modeling, and the history of mathematics.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Density-Independent Population Models 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Exponential Growth 1\u003c\/p\u003e \u003cp\u003e1.2 Exponential Growth with Stocking or Harvesting 22\u003c\/p\u003e \u003cp\u003e1.3 Two Fundamental Excel Techniques 32\u003c\/p\u003e \u003cp\u003e1.4 Explicit Formulas 40\u003c\/p\u003e \u003cp\u003e1.5 Equilibrium Values and Stability 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Personal Finance 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Compound Interest and Savings 60\u003c\/p\u003e \u003cp\u003e2.2 Borrowing for Major Purchases 77\u003c\/p\u003e \u003cp\u003e2.3 Credit Cards 92\u003c\/p\u003e \u003cp\u003e2.4 The Time Value of Money: Present Value 104\u003c\/p\u003e \u003cp\u003e2.5 Car Leases 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Combat Models 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Lanchester Combat Model 120\u003c\/p\u003e \u003cp\u003e3.2 Phase Plane Graphs 140\u003c\/p\u003e \u003cp\u003e3.3 The Lanchester Model with Reinforcements 146\u003c\/p\u003e \u003cp\u003e3.4 Hughes Aimed Fire Salvo Model 153\u003c\/p\u003e \u003cp\u003e3.5 Armstrong Salvo Model with Area Fire 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Spread of Infectious Diseases 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The S–I–R Model 184\u003c\/p\u003e \u003cp\u003e4.2 S–I–R with Vital Dynamics 203\u003c\/p\u003e \u003cp\u003e4.3 Determining Parameters from Real Data 216\u003c\/p\u003e \u003cp\u003e4.4 S–I–R with Vital Dynamics and Routine Vaccinations 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Density-Dependent Population Models 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Discrete Logistic Model 235\u003c\/p\u003e \u003cp\u003e5.2 Logistic Growth with Allee Effects 248\u003c\/p\u003e \u003cp\u003e5.3 Logistic Growth with Harvesting 254\u003c\/p\u003e \u003cp\u003e5.4 The Discrete Logistic Model and Chaos 263\u003c\/p\u003e \u003cp\u003e5.5 The Ricker Model 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Blood Alcohol Concentration and Pharmacokinetics 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Blood Alcohol Concentration 273\u003c\/p\u003e \u003cp\u003e6.2 The Widmark Model 280\u003c\/p\u003e \u003cp\u003e6.3 The Wagner Model 283\u003c\/p\u003e \u003cp\u003e6.4 Alcohol Consumption Patterns 289\u003c\/p\u003e \u003cp\u003e6.5 More General Drug Elimination 301\u003c\/p\u003e \u003cp\u003e6.6 The Volume of Distribution 319\u003c\/p\u003e \u003cp\u003e6.7 Common Drugs 321\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Ranking Methods 329\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction to Markov Models 329\u003c\/p\u003e \u003cp\u003e7.2 Ranking Sports Teams 342\u003c\/p\u003e \u003cp\u003e7.3 Google PageRank 361\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Body Weight and Body Composition 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Constant Calorie Expenditure 382\u003c\/p\u003e \u003cp\u003e8.2 Variable Calorie Expenditure 385\u003c\/p\u003e \u003cp\u003e8.3 Health Metrics 394\u003c\/p\u003e \u003cp\u003e8.4 Body Composition 397\u003c\/p\u003e \u003cp\u003e8.5 The Body Composition Model for Body Weight 406\u003c\/p\u003e \u003cp\u003e8.6 Points-based Systems: The Weight Watchers Model 419\u003c\/p\u003e \u003cp\u003eAppendix A: The Geometric Series Formula 431\u003c\/p\u003e \u003cp\u003eAppendix B: Lanchester’s Square Law and the Fractional Exchange Ratio 433\u003c\/p\u003e \u003cp\u003eAppendix C: Derivation of the FER = 1 Line for the Hughes Salvo Model 439\u003c\/p\u003e \u003cp\u003eAppendix D: The Waiting Time Principle 441\u003c\/p\u003e \u003cp\u003eAppendix E: Creating Cobweb Diagrams in Excel 445\u003c\/p\u003e \u003cp\u003eAppendix F: Proportion of Total Credit Distributed Does Not Exceed 1 449\u003c\/p\u003e \u003cp\u003eBibliography 451\u003c\/p\u003e \u003cp\u003eIndex 459\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eJeffrey T. Barton, PhD,\u003c\/b\u003e is Professor of Mathematics in the Mathematics Department at Birmingham-Southern College. A member of the American Mathematical Society and Mathematical Association of America, his mathematical interests include approximation theory, analytic number theory, mathematical biology, mathematical modeling, and the history of mathematics.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eFEATURES AN AUTHENTIC AND ENGAGING APPROACH TO MATHEMATICAL MODELING DRIVEN BY REAL-WORLD APPLICATIONS\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003eWith a focus on mathematical models based on real and current data, \u003ci\u003eModels for Life: An Introduction to Discrete Mathematical Modeling with Microsoft\u003csup\u003e®\u003c\/sup\u003e Office\u003c\/i\u003e \u003ci\u003eExcel\u003csup\u003e®\u003c\/sup\u003e\u003c\/i\u003e guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques.  \u003c\/p\u003e\u003cp\u003eThe book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. \u003ci\u003eModels for Life: An Introduction to Discrete Mathematical Modeling with Microsoft\u003csup\u003e®\u003c\/sup\u003e Office Excel\u003csup\u003e®\u003c\/sup\u003e\u003c\/i\u003e also features: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eA modular organization that, after the first chapter, allows readers to explore chapters in any order\u003c\/li\u003e \u003cli\u003eNumerous practical examples and exercises that enable readers to personalize the presented models by using their own data\u003c\/li\u003e \u003cli\u003eCarefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt\u003c\/li\u003e \u003cli\u003eReferences throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study\u003c\/li\u003e \u003cli\u003eRelevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material\u003c\/li\u003e \u003cli\u003eBoth mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug's therapeutic window\u003c\/li\u003e \u003cli\u003eA companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor's manual with solutions to all homework problems, project ideas, and a test bank\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book is ideal for undergraduate non-mathematics majors enrolled in mathematics or quantitative reasoning courses such as introductory mathematical modeling, applications of mathematics, survey of mathematics, discrete mathematical modeling, and mathematics for liberal arts. The book is also an appropriate supplement and project source for honors and\/or independent study courses in mathematical modeling and mathematical biology.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989639217381,"sku":"NP9781119039754","price":106.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119039754.jpg?v=1761784914","url":"https:\/\/k12savings.com\/products\/models-for-life-isbn-9781119039754","provider":"K12savings","version":"1.0","type":"link"}