Models for life : an introduction to discrete mathematical modeling with Microsoft Office Excel /: an introduction to discrete mathematical modeling with Microsoft Office Excel. (2016)

• Record Type: Book
• Further Information: Note: Jeffrey T. Barton.
• Authors: Barton, Jeffrey T, 1970-
• Contents: Preface 9 Acknowledgments 11 Dedication 12 Chapter 1 Density Independent Population Models 12 1.1 Exponential Growth 12 1.1.1 Modeling Yellowstone Grizzlies 13 E.1 Introduction to Excel 16 E.2 Absolute Addressing 19 E.3 Multiple Formulas 20 1.1.2 Counting Yellowstone Grizzlies 21 1.1.3 California Condors 21 1.1.4 Section Exercises 23 1.2 Exponential Growth with Stocking or Harvesting 25 1.2.1 Stocking Mississippi Sandhill Cranes 25 1.2.2 Harvesting White-tailed Deer in the Northeast 27 1.2.3 Section Exercises 30 1.3 Two Fundamental Excel Techniques 31 E.4 Graphing in Excel 31 E.5 Goal Seek 33 1.3.1 Section Exercises 34 1.4 Explicit Formulas 36 1.4.1 Explicit Formula for Exponential Growth 36 1.4.2 The Geometric Series Formula 38 1.4.3 Explicit Formula for Harvesting and Stocking 39 1.4.4 Applying New Tools to Old Problems 41 1.4.5 Section Exercises 43 1.5 Equilibrium Values and Stability 45 1.5.1 Equilibrium Values 45 1.5.2 Stability 47 E.6 Working with Multiple Columns 47 1.5.3 Section Exercises 48 List of Figure Captions 49 Chapter 2 Personal Finance 51 2.1 Compound Interest and Savings 51 E.7 Improving Spreadsheet Readability 55 2.1.1 Saving for a Car 56 2.1.2 Saving for Retirement 58 2.1.3 Section Exercises 60 2.2 Borrowing for Major Purchases 63 2.2.1 Car Loans 63 2.2.2 Home Mortgages 66 2.2.3 Amortization Schedules 67 2.2.4 Points 69 2.2.5 Section Exercises 71 2.3 Credit Cards 72 2.3.1 The Schumer Box 73 2.3.2 The Credit CARD Act 75 2.3.3 Calculating Finance Charges 76 E.8 The SUM Command and Working with Dates 78 E.9 The AVG and COUNT Commands 79 E.10 The MAX Command 80 2.3.4 Section Exercises 80 2.4 The Time Value of Money – Present Value 81 2.4.1 Present Value of Regular Payments 81 2.4.2 Present Value of Irregular Payments 83 2.4.3 Lottery Payouts 84 2.4.4 Section Exercises 85 2.5 Car Leases 86 2.5.1 Lease Takeovers 88 2.5.2 Section Exercises 90 List of Figure Captions 90 Chapter 3 Combat Models 91 3.1 Lanchester Combat Model 91 E.11 IF Statements. 94 3.1.1 The Fractional Exchange Ratio and Fighting Strength 94 3.1.2 Lanchester’s Square Law 98 3.1.3 Strategic Implications and the Battle of Trafalgar 99 3.1.4 Equilibrium Points 102 3.1.5 Section Exercises 103 3.2 Phase Plane Graphs 104 E.12 Phase Plane Graphs 105 E.13 Phase Planes with Multiple Trajectories 105 3.2.1 Section Exercises 107 3.3 The Lanchester Model with Reinforcements 107 3.3.1 Equilibrium Points and Global Behavior 108 3.3.2 The Battle of Iwo Jima 109 3.3.3 Section Exercises 110 3.4 Hughes Aimed Fire Salvo Model 111 E.14 Nested IF Statements 112 3.4.1 The Fractional Exchange Ratio and Fighting Strength 113 3.4.2 Quality versus Quantity: Assessing Warship Attributes 113 3.4.3 Equilibrium Points 115 3.4.4 Overkill and Stalemates 116 3.4.5 Phase Plane Diagram and Combat Implications 119 3.4.6 Section Exercises 120 3.5 Armstrong Salvo Model with Area Fire 121 3.5.1 The Fractional Exchange Ratio and Fighting Strength 124 3.5.2 Stealth versus Open Combat 125 3.5.3 Equilibrium Points 125 3.5.4 Overkill and Stalemates 126 3.5.5 Phase Plane Diagram and Combat Implications 128 3.5.6 Section Exercises 129 List of Figure Captions 129 Chapter 4 The Spread of Infectious Diseases 131 4.1 The S-I-R Model 132 4.1.1 The Eyam Plague 137 E.15 Date Format and Plotting Data Points 138 4.1.2 The Basic Reproductive Rate 139 4.1.3 Threshold Theorem 140 4.1.4 Vaccination Programs and Herd Immunity 142 4.1.5 Equilibrium Points 144 4.1.6 Section Exercises 144 4.2 S-I-R with Vital Dynamics 146 4.2.1 The Basic Reproductive Rate 148 4.2.2 The Waiting Time Principle 148 4.2.3 Threshold Theorems 151 4.2.4 Herd Immunity 152 4.2.5 Equilibrium Points 153 4.2.6 Section Exercises 157 4.3 Determining Parameters from Real Data 157 4.3.1 Determining R0 at the Onset of an Epidemic 157 4.3.2 Determining R0 from Serosurveys 160 4.3.3 Ebola Virus Disease 162 4.3.4 Section Exercises 164 4.4 S-I-R with Vital Dynamics and Routine Vaccinations 165 4.4.1 The Basic Reproductive Rate 166 4.4.2 Equilibrium Points 166 4.4.3 Life Expectancy and Average Age at Infection: a Complication for Vaccination Programs 168 4.4.4 Rubella and CRS in The Gambia 170 4.4.5 Section Exercises 171 List of Figure Captions 172 Chapter 5 Density Dependent Population Models 172 5.1 The Discrete Logistic Model 172 5.1.1 Antarctic Baleen Whales 174 5.1.2 Equilibrium Values 175 5.1.3 Cobweb Diagrams 177 E.16 Graphing Functions 178 5.1.4 Section Exercises 180 5.2 Logistic Growth with Allee Effects 180 5.2.1 Equilibrium Analysis 182 5.2.2 Section Exercises 183 5.3 Logistic Growth with Harvesting 184 5.3.1 Constant Take Harvesting 184 5.3.2 Equilibrium Analysis 185 5.3.3 Maximum Sustainable Yield for Constant Take 187 5.3.4 Constant Effort Harvesting 188 5.3.5 Equilibrium Analysis 189 5.3.6 Maximum Sustainable Yield for Constant Effort 189 5.3.7 Section Exercises 190 5.4 The Discrete Logistic Model and Chaos 191 5.5 The Ricker Model 192 E.17 Exponential and Logarithmic Functions 194 5.5.1 Equilibrium Analysis 194 5.5.2 Exercises 195 List of Figure Captions 196 Chapter 6 Blood Alcohol Concentration and Pharmacokinetics 197 6.1 Blood Alcohol Concentration (BAC) 197 E.18 Data Validation 199 6.1.1 Section Exercises 200 6.2 Widmark Model 201 6.2.1 Section Exercises 202 6.3 Wagner Model 203 6.3.1 Equilibrium Analysis 205 6.3.2 Determining and from Data 205 6.3.3 Section Exercises 206 6.4 Alcohol Consumption Patterns 207 6.4.1 Equilibrium Analysis and Maintaining a Buzz 208 E.19 Setting the Error Tolerance for Goal Seek 210 6.4.2 Turning Off Drinking 211 6.4.3 Section Exercises 213 6.5 More General Drug Elimination 213 6.5.1 Drug Half-life 214 E.20 Exponents 215 6.5.2 Variations on Half-life 216 6.5.3 Absorption 216 6.5.4 The Dosing Function 218 6.5.5 Modular Arithmetic 219 E.21 The MOD Command 220 6.5.6 Dissolution 221 6.5.7 Turning Off the Dosing Function 222 6.5.8 The Therapeutic Window 223 6.5.9 Section Exercises 224 6.6 The Volume of Distribution 224 6.6.1 Section Exercises 226 6.7 Common Drugs 226 6.7.1 Ibuprofen 226 6.7.2 Caffeine 227 6.7.3 Exercises 229 List of Figure Captions 230 Chapter 7 Ranking Methods 231 7.1 Introduction to Markov Models 231 7.1.1 Truck Rentals 232 7.1.2 Existence of a Positive Stable Distribution 234 7.1.3 Equilibrium Distributions 235 7.1.4 Interpreting Markov Flow Diagrams 238 7.1.5 Section Exe
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 511.80285554; Mathematical models -- Data processing; Electronic spreadsheets -- Computer programs
• Languages: English
• ISBNs: 9781119039761; 9781119039815; 9781119039891; 9781119039952
• Related ISBNs: 9781119039754
• Notes: Note: Description based on CIP data; item not viewed.
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