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Calculus For Dummies, 2nd Edition



Calculus For Dummies, 2nd Edition

Mark Ryan

ISBN: 978-1-119-29743-7 May 2016 384 Pages

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Slay the calculus monster with this user-friendly guide

Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be.

Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win.

  • Includes foundations in algebra, trigonometry, and pre-calculus concepts
  • Explores sequences, series, and graphing common functions
  • Instructs you how to approximate area with integration
  • Features things to remember, things to forget, and things you can't get away with

Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.

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

Bonus Chapter 1:
Finding Volume with the Matryoshka Doll Method (a.k.a. the Cylindrical Shell Method)
Bonus Chapter 2:
The Partial Fractions Technique Where the Denominator Contains Repeated Linear or Quadratic Factors
Bonus Chapter 3:
Trig Integrals Containing Sines and Cosines, Secants and Tangents, or secants and Cotangents
Bonus Chapter 4:
The Integration by Parts Method and Going in Circles
Bonus Chapter 5:
Ten Cool Calculus Tips