{"product_id":"mathematical-modeling-isbn-9781119102724","title":"Mathematical Modeling","description":"\u003cp\u003e\u003cb\u003eA logical problem-based introduction to the use of GeoGebra for mathematical modeling and problem solving within various areas of mathematics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, \u003ci\u003eMathematical Modeling: Applications with GeoGebra\u003c\/i\u003e presents a unique approach to software applications in GeoGebra and WolframAlpha. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebra can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations.\u003c\/p\u003e \u003cp\u003eEach chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, \u003ci\u003eMathematical Modeling: Applications with GeoGebra \u003c\/i\u003ealso includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eOver 400 diagrams and 300 GeoGebra examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content\u003c\/li\u003e \u003cli\u003eNumerous real-world exercises with solutions to help readers learn mathematical modeling techniques\u003c\/li\u003e \u003cli\u003eA companion website with GeoGebra constructions and screencasts\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eMathematical Modeling: Applications with GeoGebra\u003c\/i\u003eis ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eIntroduction xiii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxx\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Some Introductory Problems 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Ticket Prices, 3\u003c\/p\u003e \u003cp\u003e1.2 How Long Will the Pasture Last in a Field?, 7\u003c\/p\u003e \u003cp\u003e1.3 A Bit of Chemistry, 10\u003c\/p\u003e \u003cp\u003e1.4 Sydney Harbor Bridge, 16\u003c\/p\u003e \u003cp\u003e1.5 Perspective, 19\u003c\/p\u003e \u003cp\u003e1.6 Lake Erie’s Area, 21\u003c\/p\u003e \u003cp\u003e1.7 Zebra Crossing, 25\u003c\/p\u003e \u003cp\u003e1.8 The Security Case, 31\u003c\/p\u003e \u003cp\u003e1.9 Personal Measurements, 34\u003c\/p\u003e \u003cp\u003e1.10 Height of the Body, 34\u003c\/p\u003e \u003cp\u003e1.11 Lamp Pole, 35\u003c\/p\u003e \u003cp\u003e1.12 The Skyscraper, 35\u003c\/p\u003e \u003cp\u003e1.13 The Fence, 35\u003c\/p\u003e \u003cp\u003e1.14 The Corridor, 35\u003c\/p\u003e \u003cp\u003e1.15 Bird Feeders, 35\u003c\/p\u003e \u003cp\u003e1.16 Golf, 36\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear Models 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Are Women Faster Than Men?, 38\u003c\/p\u003e \u003cp\u003e2.2 Taxi Companies, 40\u003c\/p\u003e \u003cp\u003e2.3 Crime Development, 47\u003c\/p\u003e \u003cp\u003e2.4 The Metal Wire, 52\u003c\/p\u003e \u003cp\u003e2.5 Options Trading, 57\u003c\/p\u003e \u003cp\u003e2.6 Flying Foxes, 62\u003c\/p\u003e \u003cp\u003e2.7 Knots on a Rope, 66\u003c\/p\u003e \u003cp\u003e2.8 The Candle, 66\u003c\/p\u003e \u003cp\u003e2.9 Hooke’s Law, 66\u003c\/p\u003e \u003cp\u003e2.10 Ranking, 67\u003c\/p\u003e \u003cp\u003e2.11 Dolbear’s Law, 67\u003c\/p\u003e \u003cp\u003e2.12 Man at Office, 68\u003c\/p\u003e \u003cp\u003e2.13 A Stack of Paper, 68\u003c\/p\u003e \u003cp\u003e2.14 Milk Production in Cows, 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Nonlinear Empirical Models I 70\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Galaxy Rotation, 71\u003c\/p\u003e \u003cp\u003e3.2 Olympic Pole Vaulting, 73\u003c\/p\u003e \u003cp\u003e3.3 Kepler’s Third Law, 79\u003c\/p\u003e \u003cp\u003e3.4 Density, 83\u003c\/p\u003e \u003cp\u003e3.5 Yeast, 87\u003c\/p\u003e \u003cp\u003e3.6 Cooling I, 88\u003c\/p\u003e \u003cp\u003e3.7 Modeling the Population of Ireland, 93\u003c\/p\u003e \u003cp\u003e3.8 The Rule of 72, 96\u003c\/p\u003e \u003cp\u003e3.9 The Fish Farm I, 100\u003c\/p\u003e \u003cp\u003e3.10 New Orleans Temperatures, 104\u003c\/p\u003e \u003cp\u003e3.11 The Record Mile, 107\u003c\/p\u003e \u003cp\u003e3.12 The Rocket, 107\u003c\/p\u003e \u003cp\u003e3.13 Stopping Distances, 107\u003c\/p\u003e \u003cp\u003e3.14 A Bottle with Holes, 108\u003c\/p\u003e \u003cp\u003e3.15 The Pendulum, 108\u003c\/p\u003e \u003cp\u003e3.16 Radio Range, 108\u003c\/p\u003e \u003cp\u003e3.17 Running 400 Meters, 108\u003c\/p\u003e \u003cp\u003e3.18 Blue Whale, 109\u003c\/p\u003e \u003cp\u003e3.19 Used Cars, 109\u003c\/p\u003e \u003cp\u003e3.20 Texts, 110\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Nonlinear Empirical Models II 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Cooling II, 112\u003c\/p\u003e \u003cp\u003e4.2 Body Surface Area, 116\u003c\/p\u003e \u003cp\u003e4.3 Warm]Blooded Animals, 120\u003c\/p\u003e \u003cp\u003e4.4 Control of Insect Pests, 123\u003c\/p\u003e \u003cp\u003e4.5 Selling Magazines for Christmas, 125\u003c\/p\u003e \u003cp\u003e4.6 Tumor, 136\u003c\/p\u003e \u003cp\u003e4.7 Free Fall, 141\u003c\/p\u003e \u003cp\u003e4.8 Concentration, 145\u003c\/p\u003e \u003cp\u003e4.9 Air Current, 150\u003c\/p\u003e \u003cp\u003e4.10 Tides, 153\u003c\/p\u003e \u003cp\u003e4.11 Fitness, 156\u003c\/p\u003e \u003cp\u003e4.12 Life Expectancy versus Average Income, 157\u003c\/p\u003e \u003cp\u003e4.13 Stockholm Center, 157\u003c\/p\u003e \u003cp\u003e4.14 Workforce, 157\u003c\/p\u003e \u003cp\u003e4.15 Population of Sweden, 158\u003c\/p\u003e \u003cp\u003e4.16 Who Killed the Lion?, 158\u003c\/p\u003e \u003cp\u003e4.17 AIDS in United States, 159\u003c\/p\u003e \u003cp\u003e4.18 Thermal Comfort, 159\u003c\/p\u003e \u003cp\u003e4.19 Watts and Lumen, 159\u003c\/p\u003e \u003cp\u003e4.20 The Beaufort Scale, 160\u003c\/p\u003e \u003cp\u003e4.21 The von Bertalanffy Growth Equation, 161\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Modeling with Calculus 162\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Fish Farm II, 163\u003c\/p\u003e \u003cp\u003e5.2 Titration, 169\u003c\/p\u003e \u003cp\u003e5.3 The Bowl, 176\u003c\/p\u003e \u003cp\u003e5.4 The Aircraft Wing, 180\u003c\/p\u003e \u003cp\u003e5.5 The Gateway Arch in St. Louis, 182\u003c\/p\u003e \u003cp\u003e5.6 Volume of a Pear, 187\u003c\/p\u003e \u003cp\u003e5.7 Storm Flood, 190\u003c\/p\u003e \u003cp\u003e5.8 Exercise, 193\u003c\/p\u003e \u003cp\u003e5.9 Bicycle Reflectors, 202\u003c\/p\u003e \u003cp\u003e5.10 Cardiac Output, 206\u003c\/p\u003e \u003cp\u003e5.11 Medication, 210\u003c\/p\u003e \u003cp\u003e5.12 New Song on Spotify, 215\u003c\/p\u003e \u003cp\u003e5.13 Temperature Change, 221\u003c\/p\u003e \u003cp\u003e5.14 Tar, 224\u003c\/p\u003e \u003cp\u003e5.15 Bicycle Reflectors Revisited, 229\u003c\/p\u003e \u003cp\u003e5.16 Gas Pressure, 229\u003c\/p\u003e \u003cp\u003e5.17 Airborne Attacks, 229\u003c\/p\u003e \u003cp\u003e5.18 Railroad Tracks, 230\u003c\/p\u003e \u003cp\u003e5.19 Cobb–Douglas Production Functions, 230\u003c\/p\u003e \u003cp\u003e5.20 Future Carbon Dioxide Emissions, 231\u003c\/p\u003e \u003cp\u003e5.21 Overtaking, 232\u003c\/p\u003e \u003cp\u003e5.22 Population Dynamics of India, 232\u003c\/p\u003e \u003cp\u003e5.23 Drag Racing, 232\u003c\/p\u003e \u003cp\u003e5.24 Super Eggs, 233\u003c\/p\u003e \u003cp\u003e5.25 Measuring Sticks, 234\u003c\/p\u003e \u003cp\u003e5.26 The Lecture Hall, 234\u003c\/p\u003e \u003cp\u003e5.27 Progressive Braking Distances, 234\u003c\/p\u003e \u003cp\u003e5.28 Cylinder in a Cone, 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Using Differential Equations 236\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Cooling III, 237\u003c\/p\u003e \u003cp\u003e6.2 Moose Hunting, 241\u003c\/p\u003e \u003cp\u003e6.3 The Water Container, 247\u003c\/p\u003e \u003cp\u003e6.4 Skydiving, 250\u003c\/p\u003e \u003cp\u003e6.5 Flu Epidemics, 256\u003c\/p\u003e \u003cp\u003e6.6 USA’s Population, 263\u003c\/p\u003e \u003cp\u003e6.7 Predators and Prey, 274\u003c\/p\u003e \u003cp\u003e6.8 Smoke, 285\u003c\/p\u003e \u003cp\u003e6.9 Alcohol Consumption, 289\u003c\/p\u003e \u003cp\u003e6.10 Who Killed the Mathematics Teacher, 292\u003c\/p\u003e \u003cp\u003e6.11 River Clams, 297\u003c\/p\u003e \u003cp\u003e6.12 Contamination, 297\u003c\/p\u003e \u003cp\u003e6.13 Damped Oscillation, 297\u003c\/p\u003e \u003cp\u003e6.14 The Potassium–Argon Method, 298\u003c\/p\u003e \u003cp\u003e6.15 Barium, Lanthanum, and Cerium, 298\u003c\/p\u003e \u003cp\u003e6.16 Iodine, 298\u003c\/p\u003e \u003cp\u003e6.17 Endemic Epidemics, 299\u003c\/p\u003e \u003cp\u003e6.18 War, 299\u003c\/p\u003e \u003cp\u003e6.19 Farmers, Bandits, and Rulers, 299\u003c\/p\u003e \u003cp\u003e6.20 Epidemics Without Immunity, 300\u003c\/p\u003e \u003cp\u003e6.21 Zombie Apocalypse I, 300\u003c\/p\u003e \u003cp\u003e6.22 Zombie Apocalypse II, 300\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Geometrical Models 301\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Looping Pen, 302\u003c\/p\u003e \u003cp\u003e7.2 Comparing Areas, 304\u003c\/p\u003e \u003cp\u003e7.3 Crossing Lines, 307\u003c\/p\u003e \u003cp\u003e7.4 Points in a Triangle, 310\u003c\/p\u003e \u003cp\u003e7.5 Trisected Area, 316\u003c\/p\u003e \u003cp\u003e7.6 Spirograph, 320\u003c\/p\u003e \u003cp\u003e7.7 Connected LP Players, 326\u003c\/p\u003e \u003cp\u003e7.8 Folding Paper, 332\u003c\/p\u003e \u003cp\u003e7.9 The Locomotive, 336\u003c\/p\u003e \u003cp\u003e7.10 Maximum Volume, 340\u003c\/p\u003e \u003cp\u003e7.11 Pascal’s Snail or Limaçon, 340\u003c\/p\u003e \u003cp\u003e7.12 Equilateral Triangle Dissection, 341\u003c\/p\u003e \u003cp\u003e7.13 Dividing the Sides of a Triangle, 341\u003c\/p\u003e \u003cp\u003e7.14 The Pedal Triangle, 342\u003c\/p\u003e \u003cp\u003e7.15 The Infinity Diagram, 343\u003c\/p\u003e \u003cp\u003e7.16 Dissecting a Circular Segment, 344\u003c\/p\u003e \u003cp\u003e7.17 Neuberg Cubic Art, 344\u003c\/p\u003e \u003cp\u003e7.18 Phase Plots for Triangles, 345\u003c\/p\u003e \u003cp\u003e7.19 The Joukowski Airfoil, 347\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Discrete Models 348\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Cabinetmaker, 349\u003c\/p\u003e \u003cp\u003e8.2 Weather, 358\u003c\/p\u003e \u003cp\u003e8.3 Squirrels, 362\u003c\/p\u003e \u003cp\u003e8.4 Chlorine, 365\u003c\/p\u003e \u003cp\u003e8.5 The Deer Farm, 369\u003c\/p\u003e \u003cp\u003e8.6 Analyzing a Number Sequence, 373\u003c\/p\u003e \u003cp\u003e8.7 Inner Areas in a Square, 376\u003c\/p\u003e \u003cp\u003e8.8 Inner Areas in a Triangle, 382\u003c\/p\u003e \u003cp\u003e8.9 A Climate Model Based on Albedo, 387\u003c\/p\u003e \u003cp\u003e8.10 Traffic Jam, 392\u003c\/p\u003e \u003cp\u003e8.11 Wildfire, 399\u003c\/p\u003e \u003cp\u003e8.12 A Modern Carpenter, 408\u003c\/p\u003e \u003cp\u003e8.13 Conway’s Game of Life, 409\u003c\/p\u003e \u003cp\u003e8.14 Matrix Taxis, 409\u003c\/p\u003e \u003cp\u003e8.15 The Car Park, 409\u003c\/p\u003e \u003cp\u003e8.16 Selecting a Collage, 410\u003c\/p\u003e \u003cp\u003e8.17 Apportionment, 410\u003c\/p\u003e \u003cp\u003e8.18 Steiner Trees for Regular Polygons, 410\u003c\/p\u003e \u003cp\u003e8.19 Hugs and High Fives, 411\u003c\/p\u003e \u003cp\u003e8.20 Pythagorean Triples, 411\u003c\/p\u003e \u003cp\u003e8.21 Credits, 412\u003c\/p\u003e \u003cp\u003e8.22 The Piano, 413\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Modeling in the Classroom 415\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Teacher Creating Diagrams, 416\u003c\/p\u003e \u003cp\u003e9.2 Student’s Lab Reports, 416\u003c\/p\u003e \u003cp\u003e9.3 Making Screencast Instructions, 417\u003c\/p\u003e \u003cp\u003e9.4 Demonstrations, 417\u003c\/p\u003e \u003cp\u003e9.5 Students Investigating Constructions, 418\u003c\/p\u003e \u003cp\u003e9.6 Working in Groups, 418\u003c\/p\u003e \u003cp\u003e9.7 Students Constructing Models, 419\u003c\/p\u003e \u003cp\u003e9.8 Broader Assignments, 420\u003c\/p\u003e \u003cp\u003e9.9 The Same or Different Assignments, 421\u003c\/p\u003e \u003cp\u003e9.10 Previous Assignments, 421\u003c\/p\u003e \u003cp\u003e9.11 The Consultancy Bureau, 422\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Assessing Modeling 425\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 To Evaluate Mathematical Modeling Assignments, 426\u003c\/p\u003e \u003cp\u003e10.2 Concretizing Grading Criteria, 426\u003c\/p\u003e \u003cp\u003e10.3 Evaluating Students’ Work, 431\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Assessing Models 434\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Relative Error, 435\u003c\/p\u003e \u003cp\u003e11.2 Correlation, 435\u003c\/p\u003e \u003cp\u003e11.3 Sum of Squared Errors, 436\u003c\/p\u003e \u003cp\u003e11.4 Simple Linear Regression, 436\u003c\/p\u003e \u003cp\u003e11.5 Multiple Regression Analysis, 438\u003c\/p\u003e \u003cp\u003e11.6 Nonlinear Regression, 438\u003c\/p\u003e \u003cp\u003e11.7 Confidence Intervals, 439\u003c\/p\u003e \u003cp\u003e11.8 2D Confidence Interval Tools, 441\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Interpreting Models 443\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Mathematical Representations, 443\u003c\/p\u003e \u003cp\u003e12.2 Graphical Representations, 444\u003c\/p\u003e \u003cp\u003e12.3 A Sample Model Interpreted, 445\u003c\/p\u003e \u003cp\u003e12.4 Creating the Model, 446\u003c\/p\u003e \u003cp\u003eAppendix A: Introduction to GeoGebra 448\u003c\/p\u003e \u003cp\u003eAppendix B: Function Library 485\u003c\/p\u003e \u003cp\u003eInteger Properties 509\u003c\/p\u003e \u003cp\u003eIndex 523\u003c\/p\u003e \u003cp\u003eIndex of Problems by Name 535\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJonas Hall \u003c\/b\u003eis Head of Mathematics at Rodengymnasiet in Norrtälje, Sweden, where he teaches mathematics and physics. His research interests include problem solving, the aesthetics of mathematics, and teaching with technology. He is a multiple finalist in Kappa, which is a competition for mathematics teachers in Sweden offered by the University of Stockholm.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eThomas Lingefjärd, PhD\u003c\/b\u003e, is Associate Professor of Mathematics Education in the Department of Education at the University of Gothenburg. The author of more than 25 articles and 10 chapter contributions, Dr. Lingefjärd's research interests include mathematical modeling and advanced mathematical thinking.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA logical problem-based introduction to the use of GeoGebraTM for mathematical modeling and problem solving within various areas of mathematics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, \u003ci\u003eMathematical Modeling: Applications with GeoGebraTM\u003c\/i\u003e presents a unique approach to software applications in GeoGebraTM and WolframAlpha®. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebraTM can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations.\u003c\/p\u003e \u003cp\u003eEach chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, \u003ci\u003eMathematical Modeling: Applications with GeoGebraTM \u003c\/i\u003ealso includes:\u003c\/p\u003e \u003cp\u003e• Over 400 diagrams and 300 GeoGebraTM examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content\u003c\/p\u003e \u003cp\u003e• Numerous real-world exercises with solutions to help readers learn mathematical modeling techniques\u003c\/p\u003e \u003cp\u003e• A companion website with GeoGebraTM constructions and screencasts\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematical Modeling: Applications with GeoGebraTM \u003c\/i\u003eis ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJonas Hall \u003c\/b\u003eis Head of Mathematics at Rodengymnasiet in Norrtälje, Sweden, where he teaches mathematics and physics. His research interests include problem solving, the aesthetics of mathematics, and teaching with technology. He is a multiple finalist in Kappa, which is a competition for mathematics teachers in Sweden offered by the University of Stockholm.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eThomas Lingefjärd, PhD\u003c\/b\u003e, is Associate Professor of Mathematics Education in the Department of Education at the University of Gothenburg. The author of more than 25 articles and 10 chapter contributions, Dr. Lingefjärd’s research interests include mathematical modeling and advanced mathematical thinking.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989587050725,"sku":"NP9781119102724","price":106.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119102724.jpg?v=1761784706","url":"https:\/\/k12savings.com\/products\/mathematical-modeling-isbn-9781119102724","provider":"K12savings","version":"1.0","type":"link"}