Models for Life : An Introduction to Real-World Mathematical Modeling with Excel® by Jeffrey T. Barton download book FB2, EPUB, DJV
9781119039754 English 1119039754 Features an authentic and engaging approach to mathematical modeling driven by real-world applications With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Excel® guides readers in the solution of relevant, practical problems by introducing both mathematical and Microsoft Office® Excel techniques. The 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 and 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 such areas as military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Excel alsofeatures: A modular organization that, after the first chapter, allows readers to explore chapters in any order Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt References 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 Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug's therapeutic window A 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 The 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., This book presents an applications-driven approach as well as a rich, hands-on mathematical experience for students. In addition, the book features a step-by-step introduction to the creation and analysis of mathematical models using Microsoft Office Excel. Part I introduces the reader to discrete dynamical systems, which are mathematical models that relate a quantity at one point in time to a previous point. The reader is taken step-by-step through the process, language, and notation required to construct such models along with how to implement them in Excel. Part II introduces students to more complex, multi-compartment models. Examples include age-structured population models, interacting species models, and infectious disease models. New mathematical and graphical techniques are presented including stable population distributions, phase diagrams and nullclines. Students also learn some new Excel techniques in constructing phase diagrams and dealing with multiple dependent variables. Part III focuses on applications of our modeling techniques to models of health related topics. Predicting body weight, body composition, and blood alcohol concentration are some of the applications that will engage students with their relevance and currency. Part IV discusses tochastic models, i.e. those that incorporate some randomness are an important class of models. In this part, students modify some existing models to include random effects. For example, a random chance of natural disasters is presented, and students are introduced to the first stochastic disease model, the Reed-Frost model. Topical coverage includes: Density Independent Population Models; Analytic Tools for Discrete Dynamical Systems; Density Dependent Population Models; The Discrete Logistic Model; Personal Finance; Population Interaction Models; The Spread of Infectious Diseases; Body Weight; Pharmacokinetics of Alcohol and Other Drugs; and Incorporating Random Effects - Stochastic Models.
9781119039754 English 1119039754 Features an authentic and engaging approach to mathematical modeling driven by real-world applications With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Excel® guides readers in the solution of relevant, practical problems by introducing both mathematical and Microsoft Office® Excel techniques. The 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 and 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 such areas as military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Excel alsofeatures: A modular organization that, after the first chapter, allows readers to explore chapters in any order Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt References 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 Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug's therapeutic window A 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 The 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., This book presents an applications-driven approach as well as a rich, hands-on mathematical experience for students. In addition, the book features a step-by-step introduction to the creation and analysis of mathematical models using Microsoft Office Excel. Part I introduces the reader to discrete dynamical systems, which are mathematical models that relate a quantity at one point in time to a previous point. The reader is taken step-by-step through the process, language, and notation required to construct such models along with how to implement them in Excel. Part II introduces students to more complex, multi-compartment models. Examples include age-structured population models, interacting species models, and infectious disease models. New mathematical and graphical techniques are presented including stable population distributions, phase diagrams and nullclines. Students also learn some new Excel techniques in constructing phase diagrams and dealing with multiple dependent variables. Part III focuses on applications of our modeling techniques to models of health related topics. Predicting body weight, body composition, and blood alcohol concentration are some of the applications that will engage students with their relevance and currency. Part IV discusses tochastic models, i.e. those that incorporate some randomness are an important class of models. In this part, students modify some existing models to include random effects. For example, a random chance of natural disasters is presented, and students are introduced to the first stochastic disease model, the Reed-Frost model. Topical coverage includes: Density Independent Population Models; Analytic Tools for Discrete Dynamical Systems; Density Dependent Population Models; The Discrete Logistic Model; Personal Finance; Population Interaction Models; The Spread of Infectious Diseases; Body Weight; Pharmacokinetics of Alcohol and Other Drugs; and Incorporating Random Effects - Stochastic Models.