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