Table of Contents

Introduction 1

Part 1: An Overview of Calculus 5

Chapter 1: What Is Calculus? 7

Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration — plus Infinite Series 13

Chapter 3: Why Calculus Works 21

Part 2: Warming Up with Calculus Prerequisites 27

Chapter 4: Pre-Algebra and Algebra Review 29

Chapter 5: Funky Functions and Their Groovy Graphs 43

Chapter 6: The Trig Tango 61

Part 3: Limits 73

Chapter 7: Limits and Continuity 75

Chapter 8: Evaluating Limits 89

Part 4: Differentiation 105

Chapter 9: Differentiation Orientation 107

Chapter 10: Differentiation Rules — Yeah, Man, It Rules 127

Chapter 11: Differentiation and the Shape of Curves 147

Chapter 12: Your Problems Are Solved: Differentiation to the Rescue! 171

Chapter 13: More Differentiation Problems: Going Off on a Tangent 193

Part 5: Integration and Infinite Series 207

Chapter 14: Intro to Integration and Approximating Area 209

Chapter 15: Integration: It’s Backwards Differentiation 233

Chapter 16: Integration Techniques for Experts 263

Chapter 17: Forget Dr Phil: Use the Integral to Solve Problems 285

Chapter 18: Taming the Infinite with Improper Integrals 303

Chapter 19: Infinite Series 315

Part 6: The Part of Tens 339

Chapter 20: Ten Things to Remember 341

Chapter 21: Ten Things to Forget 345

Chapter 22: Ten Things You Can’t Get Away With 349

Index 353

About the Author

Mark Ryan is the founder and owner of The Math Center, a math and test prep tutoring center in Winnetka, Illinois. He is the author of Calculus Workbook For Dummies, Calculus Essentials For Dummies, and three books on geometry in the For Dummies series. Ryan has taught junior high and high school math since 1989. He lives in Evanston, Illinois.