Make calculus more manageable with simplified instruction and tons of practice

Calculus All-in-One For Dummies pairs no-nonsense explanations of calculus content with practical examples and practice problems, so you can untangle the difficult concepts and improve your score in any calculus class. Plus, this book comes with access to chapter quizzes online. Dummies makes differentiation, integration, and everything in between more manageable, so you can crush calculus with confidence. Review the foundational basics, then dive into calc lessons that track your class. This book takes you through a full year of high-school calculus or a first semester of college calculus, only explained more clearly.

• Work through easy-to-understand lessons on everything in a typical calc class
• Get the score you want and need on standardized tests like AP Calculus
• Access online chapter quizzes for additional practice
• Untangle tricky problems and discover clever ways to solve them

With clear definitions, concise explanations, and plenty of helpful information on everything from limits and vectors to integration and curve-sketching, Calculus All-in-One For Dummies is the must-have resource for students who want to review for exams or just need extra help understanding the concepts from class.

Mark Ryan has more than three decades’ experience as a calculus teacher and tutor. He has a gift for mathematics and a gift for explaining it in plain English. He tutors students in all junior high and high school math courses as well as math test prep, and he’s the founder of The Math Center on Chicago’s North Shore. Ryan is the author of Calculus For Dummies, Calculus Essentials For Dummies, Geometry For Dummies, and several other math books.

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