Table of Contents
Introduction 1
Unit 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
Unit 2: Warming Up with Calculus Prerequisites 25
Chapter 4: Pre-Algebra, Algebra, and Geometry Review 27
Chapter 5: Funky Functions and Their Groovy Graphs 67
Chapter 6: The Trig Tango 95
Unit 3: Limits 117
Chapter 7: Limits and Continuity 119
Chapter 8: Evaluating Limits 141
Unit 4: Differentiation 181
Chapter 9: Differentiation Orientation 183
Chapter 10: Differentiation Rules — Yeah, Man, It Rules 215
Chapter 11: Differentiation and the Shape of Curves 259
Chapter 12: Your Problems Are Solved: Differentiation to the Rescue! 321
Chapter 13: More Differentiation Problems: Going Off on a Tangent 367
Unit 5: Integration and Infinite Series 397
Chapter 14: Intro to Integration and Approximating Area 399
Chapter 15: Integration: It’s Backwards Differentiation 439
Chapter 16: Integration Techniques for Experts 479
Chapter 17: Who Needs Freud? Using the Integral to Solve Your Problems 521
Chapter 18: Taming the Infinite with Improper Integrals 557
Chapter 19: Infinite Series: Welcome to the Outer Limits 581
Index 623