Cover

Acknowledgments

Preface

How to Use This Book

Modifications for Liberal Arts and Topics Courses

I Appetizers (Before Calculus)

Precalculus

Using Parentheses with the Game of Telephone

Function Ball Toss

Mathematical Modeling Using Long-Exposure Photography

Function Composition Using Crackers and Cheese

Walking Function Transformations

Graphing Piecewise Functions with Feather Boas

Trigonometry Parameter Comparisons

II Main Courses (Calculus)

Differential Calculus

Adding Movement to Velocity Explorations with Ziplines

Creating Limit Windows with Index Cards

Extreme Values with Pipe Cleaners

Graphing Puzzles Using the First and Second Derivatives

Graphing Functions from Derivative Information Using Bendable Sticks

Spread the Word: Modeling Logistic Growth

Maximizing the Area of a Fenced in Region Using Bendable Sticks for Constraints

The Optimal Origami Box

Integral Calculus

Chewing Gum Riemann Sums

Paper Shredder Riemann Sums or Cut the Bunny

Estimating Calories in a Cookie with Riemann Sums

So Many Integration Techniques... Which to Use?

Centers of Mass of Candy Point Masses on a Plane

Volume Estimations with Fruit Cross Sections

Fun with Infinite Series

Multivariable Calculus

Physically Creating Three Dimensional Graphs

Building Functions of Two Variables with Cookies

Exploring Contours in the Physical World

Matching Photographs with Contour Lines

The Gold Mine: Tangent Plane Approximation Using Tangible Surfaces

Visualizing Second Order Partials on a Football

Partials, Gradients, and Lagrange Multipliers on a Pringles® Chip

Volume Estimation Using a Sheet Surface

Visualizing and Estimating the Mass of a Solid Using Multi-Colored Blocks

Using a Jack to Visualize the Right Hand Rule for Cross Products

Properties of Flux Using an Overhead Projector

Vector Analysis of a Pop-Up Page

III Desserts (Upper Level Courses)

Sophomore / Junior Courses

Crowdsourcing to Create Slope Fields

Who's in My Differential Equations Club?

Population Modeling Using M&M's®

Modeling of Fishing and Restocking with Pennies

Modeling a Falling Column of Water

Using Linear Algebra Definitions to Find Your Team

Picturing Prime Factorization

Traffic Jam: A Lifesize Logic Puzzle

Living De Morgan's Laws

Using Circuits to Teach Truth Tables

Determining the Validity of an Argument Using True/False Cards

Proof Rearrangements

Properties of Functions on Finite Sets Using Candy

SET® in Combinatorics/Discrete Math

Human-Powered Computing

Junior / Senior Courses

Using Candy to Represent Equivalence Relations

Finding the GCD: Euclidean Disc Toss

Symmetry and Group Theory with Plastic Triangles

Finding Groups in a (New) Color Cube Puzzle

Acting Permutations

Nametags and Derangements: A Class Permutation

Discovering Catalan Numbers Using M&M's®

Walking the Seven Bridges of Königsberg

Designing Round-Robin Tournaments Using Yarn

Constructing Disjoint Hamiltonian Cycles of Complete Graphs Using Yarn

Exploring the -N Definition of Sequence Convergence with Yarn

Exploring the - Definition of Continuity

Walking Complex Functions

Graphing Complex Functions with Feather Boas

Exploring Knots

Indexes

Concept Index

Author Index

Main Ingredient Index

Course Index

Back Cover