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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.
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
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