9781119040026

A solutions manual to accompany An Introduction to Discrete Mathematical Modeling with Microsoft^® Office Excel^®

With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft^® Office Excel^® guides readers in the solution of relevant, practical problems by introducing both mathematical and 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 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. Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft^® Office Excel^®also features:

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

Jeffrey T. Barton, PhD, 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.

Preface vii

About the Companion Website ix

1 Density Independent Population Models 1

1.1 Exponential Growth, 1

1.2 Exponential Growth with Stocking or Harvesting, 8

1.3 Two Fundamental Excel Techniques, 13

1.4 Explicit Formulas, 18

1.5 Equilibrium Values and Stability, 24

2 Personal Finance 31

2.1 Compound Interest and Savings, 31

2.2 Borrowing for Major Purchases, 43

2.3 Credit Cards, 48

2.4 The Time Value of Money: Present Value, 50

2.5 Car Leases, 54

3 Combat Models 57

3.1 Lanchester Combat Model, 57

3.2 Phase Plane Graphs, 63

3.3 The Lanchester Model with Reinforcements, 64

3.4 Hughes Aimed Fire Salvo Model, 69

3.5 Armstrong Salvo Model with Area Fire, 72

4 The Spread of Infectious Diseases 79

4.1 The S-I-R Model, 79

4.2 S-I-R with Vital Dynamics, 84

4.3 Determining Parameters from Real Data, 88

4.4 S-I-R with Vital Dynamics and Routine Vaccinations, 91

5 Density Dependent Population Models 95

5.1 The Discrete Logistic Model, 95

5.2 Logistic Growth with Allee Effects, 97

5.3 Logistic Growth with Harvesting, 100

5.5 The Ricker Model, 102

6 Blood Alcohol Concentration and Pharmacokinetics 107

6.1 Blood Alcohol Concentration (BAC), 107

6.2 The Widmark Model, 110

6.3 The Wagner Model, 114

6.4 Alcohol Consumption Patterns, 118

6.5 More General Drug Elimination, 122

6.6 The Volume of Distribution, 125

6.7 Common Drugs, 126

7 Ranking Methods 131

7.1 Introduction to Markov Models, 131

7.2 Ranking Sports Teams, 139

7.3 Google PageRank, 147

8 Body Weight and Body Composition 153

8.1 Constant Calorie Expenditure, 153

8.2 Variable Calorie Expenditure, 154

8.3 Health Metrics, 159

8.4 Body Composition, 163

8.5 The Body Composition Model for Body Weight, 166

8.6 Points-based Systems: The Weight Watchers™ Model, 170

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Solutions Manual to Accompany Models for Life An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel

Solutions Manual to Accompany Models for Life An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel

1119040027

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Table of Contents

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