Acknowledgments |
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ix | |
Preface |
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xi | |
How to Use This Book |
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xv | |
Modifications for Liberal Arts and Topics Courses |
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xvi | |
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I Appetizers (Before Calculus) |
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1 | (38) |
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3 | (36) |
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1.1 Using Parentheses with the Game of Telephone |
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5 | (5) |
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10 | (4) |
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1.3 Mathematical Modeling Using Long-Exposure Photography |
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14 | (4) |
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1.4 Function Composition Using Crackers and Cheese |
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18 | (4) |
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1.5 Walking Function Transformations |
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22 | (5) |
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1.6 Graphing Piecewise Functions with Feather Boas |
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27 | (4) |
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1.7 Trigonometry Parameter Comparisons |
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31 | (8) |
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II Main Courses (Calculus) |
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39 | (122) |
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41 | (34) |
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2.1 Adding Movement to Velocity Explorations with Ziplines |
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43 | (5) |
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2.2 Creating Limit Windows with Index Cards |
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48 | (3) |
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2.3 Extreme Values with Pipe Cleaners |
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51 | (3) |
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2.4 Graphing Puzzles Using the First and Second Derivatives |
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54 | (4) |
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2.5 Graphing Functions from Derivative Information Using Bendable Sticks |
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58 | (4) |
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2.6 Spread the Word: Modeling Logistic Growth |
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62 | (5) |
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2.7 Maximizing the Area of a Fenced in Region Using Bendable Sticks for Constraints |
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67 | (3) |
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2.8 The Optimal Origami Box |
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70 | (5) |
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75 | (34) |
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3.1 Chewing Gum Riemann Sums |
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77 | (4) |
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3.2 Paper Shredder Riemann Sums or Cut the Bunny |
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81 | (4) |
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3.3 Estimating Calories in a Cookie with Riemann Sums |
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85 | (4) |
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3.4 So Many Integration Techniques Which to Use? |
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89 | (4) |
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3.5 Centers of Mass of Candy Point Masses on a Plane |
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93 | (4) |
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3.6 Volume Estimations with Fruit Cross Sections |
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97 | (4) |
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3.7 Fun with Infinite Series |
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101 | (8) |
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109 | (52) |
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4.1 Physically Creating Three Dimensional Graphs |
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110 | (5) |
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4.2 Building Functions of Two Variables with Cookies |
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115 | (5) |
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4.3 Exploring Contours in the Physical World |
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120 | (4) |
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4.4 Matching Photographs with Contour Lines |
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124 | (4) |
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4.5 The Gold Mine: Tangent Plane Approximation Using Tangible Surfaces |
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128 | (4) |
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4.6 Visualizing Second Order Partials on a Football |
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132 | (4) |
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4.7 Partials, Gradients, and Lagrange Multipliers on a Pringles® Chip |
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136 | (4) |
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4.8 Volume Estimation Using a Sheet Surface |
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140 | (3) |
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4.9 Visualizing and Estimating the Mass of a Solid Using Multi-Colored Blocks |
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143 | (5) |
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4.10 Using a Jack to Visualize the Right Hand Rule for Cross Products |
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148 | (3) |
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4.11 Properties of Flux Using an Overhead Projector |
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151 | (4) |
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4.12 Vector Analysis of a Pop-Up Page |
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155 | (6) |
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III Desserts (Upper Level Courses) |
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161 | (136) |
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5 Sophomore / Junior Courses |
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163 | (66) |
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5.1 Crowdsourcing to Create Slope Fields |
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165 | (4) |
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5.2 Who's in My Differential Equations Club? |
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169 | (4) |
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5.3 Population Modeling Using M&M's® |
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173 | (5) |
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5.4 Modeling of Fishing and Restocking with Pennies |
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178 | (5) |
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5.5 Modeling a Falling Column of Water |
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183 | (4) |
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5.6 Using Linear Algebra Definitions to Find Your Team |
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187 | (3) |
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5.7 Picturing Prime Factorization |
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190 | (4) |
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5.8 Traffic Jam: A Lifesize Logic Puzzle |
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194 | (4) |
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5.9 Living De Morgan's Laws |
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198 | (4) |
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5.10 Using Circuits to Teach Truth Tables |
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202 | (5) |
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5.11 Determining the Validity of an Argument Using True/False Cards |
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207 | (4) |
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5.12 Proof Rearrangements |
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211 | (4) |
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5.13 Properties of Functions on Finite Sets Using Candy |
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215 | (4) |
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5.14 SET® in Combinatorics/Discrete Math |
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219 | (5) |
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5.15 Human-Powered Computing |
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224 | (5) |
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6 Junior / Senior Courses |
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229 | (68) |
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6.1 Using Candy to Represent Equivalence Relations |
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231 | (4) |
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6.2 Finding the GCD: Euclidean Disc Toss |
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235 | (5) |
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6.3 Symmetry and Group Theory with Plastic Triangles |
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240 | (5) |
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6.4 Finding Groups in a (New) Color Cube Puzzle |
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245 | (5) |
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250 | (4) |
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6.6 Nametags and Derangements: A Class Permutation |
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254 | (4) |
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6.7 Discovering Catalan Numbers Using M&M's® |
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258 | (4) |
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6.8 Walking the Seven Bridges of Konigsberg |
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262 | (4) |
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6.9 Designing Round-Robin Tournaments Using Yarn |
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266 | (6) |
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6.10 Constructing Disjoint Hamiltonian Cycles of Complete Graphs Using Yarn |
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272 | (5) |
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6.11 Exploring the e-N Definition of Sequence Convergence with Yarn |
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277 | (4) |
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6.12 Exploring the e-6 Definition of Continuity |
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281 | (4) |
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6.13 Walking Complex Functions |
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285 | (4) |
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6.14 Graphing Complex Functions with Feather Boas |
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289 | (4) |
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293 | (4) |
Indexes |
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297 | (1) |
Concept Index |
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297 | (2) |
Author Index |
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299 | (2) |
Main Ingredient Index |
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301 | (2) |
Course Index |
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303 | |