This text presents a wide variety of common types of models found in other mathematical modeling texts, as well as some new types. However, the models are presented in a very unique format. A typical section begins with a general description of the scenario being modeled. The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.
| Preface |
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1 What is Mathematical Modeling? |
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1 | (10) |
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1 | (1) |
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2 | (1) |
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3 | (3) |
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6 | (5) |
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2 Proportionality and Geometric Similarity |
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11 | (56) |
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11 | (1) |
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12 | (10) |
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2.3 Modeling with Proportionality |
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22 | (6) |
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2.4 Fitting Straight Lines Analytically |
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28 | (9) |
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37 | (8) |
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45 | (13) |
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2.7 Coefficient of Determination |
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58 | (9) |
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67 | (50) |
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3.1 Linear Algebra Basics |
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67 | (14) |
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3.2 Modeling with Systems of Equations |
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81 | (8) |
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89 | (9) |
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98 | (10) |
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108 | (9) |
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4 Discrete Dynamical Systems |
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117 | (32) |
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117 | (1) |
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4.2 Long-Term Behavior and Equilibria |
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118 | (8) |
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4.3 Discrete Logistic Equation |
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126 | (6) |
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4.4 A Linear Predator-Prey Model |
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132 | (5) |
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4.5 A Nonlinear Predator-Prey Model |
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137 | (4) |
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141 | (8) |
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149 | (50) |
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149 | (2) |
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151 | (8) |
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159 | (6) |
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5.4 Systems of Differential Equations |
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165 | (7) |
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5.5 Quadratic Population Model |
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172 | (8) |
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180 | (5) |
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5.7 Lanchester Combat Models |
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185 | (5) |
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190 | (9) |
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199 | (52) |
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199 | (1) |
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200 | (9) |
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6.3 Three Famous Problems |
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209 | (7) |
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216 | (3) |
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6.5 Random Number Generators |
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219 | (5) |
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6.6 Modeling Random Variables |
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224 | (10) |
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6.7 A Theoretical Queuing Model |
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234 | (5) |
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239 | (4) |
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243 | (8) |
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251 | (46) |
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251 | (1) |
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252 | (7) |
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7.3 The Transportation Problem |
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259 | (10) |
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7.4 The Assignment Problem and Binary Constraints |
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269 | (11) |
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7.5 Solving Linear Programs |
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280 | (5) |
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285 | (5) |
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290 | (7) |
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297 | (50) |
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297 | (3) |
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300 | (6) |
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8.3 The Golden Section Method |
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306 | (5) |
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8.4 The One-Dimensional Gradient Method |
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311 | (5) |
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8.5 Two-Dimensional Gradient Method |
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316 | (8) |
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324 | (7) |
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331 | (7) |
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8.8 The Traveling Salesman Problem |
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338 | (9) |
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347 | (10) |
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347 | (1) |
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A.2 Entering Text, Data, and Formulas |
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348 | (3) |
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A.2.1 Understanding Cell References |
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349 | (1) |
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350 | (1) |
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A.3 Creating Charts and Graphs |
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351 | (4) |
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A.3.1 Adding Data to a Chart |
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352 | (2) |
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354 | (1) |
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355 | (1) |
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356 | (1) |
| Index |
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357 | |
Brian Albright grew up in Colby, KS; received undergraduate degrees in mathematics and secondary education from Emporia State University, Emporia, KS; and received a D.Sc. in systems science and mathematics from Washington University in St. Louis. In early 2004 he worked as a civilian transportation analyst at the United States Transportation Command. Since 2004 he has taught all levels of undergraduate mathematics at Concordia University, Seward, NE. He has published two textbooks, Mathematical Modeling with Exceland Essentials of Mathematical Statistics; has written two articles for The College Mathematics Journal; and has written ancillary material for several textbooks.
