Calculus II For Dummies (eBook)

Mark Zegarelli is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II Workbook For Dummies. Through online tutoring, he teaches mul-tiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.

Introduction 1

Part 1: Introduction to Integration 7

Chapter 1: An Aerial View of the Area Problem 9

Chapter 2: Forgotten but Not Gone: Review of Algebra and Pre-Calculus 27

Chapter 3: Recent Memories: Review of Calculus I 53

Part 2: From Definite to Indefinite Integrals 73

Chapter 4: Approximating Area with Riemann Sums 75

Chapter 5: There Must Be a Better Way -- Introducing the Indefinite Integral 87

Part 3: Evaluating Indefinite Integrals 103

Chapter 6: Instant Integration: Just Add Water (And C) 105

Chapter 7: Sharpening Your Integration Moves 117

Chapter 8: Here's Looking at U-Substitution 141

Part 4: Advanced Integration Techniques 153

Chapter 9: Parting Ways: Integration by Parts 155

Chapter 10: Trig Substitution: Knowing All the (Tri)Angles 173

Chapter 11: Rational Solutions: Integration with Partial Fractions 197

Part 5: Applications of Integrals 219

Chapter 12: Forging into New Areas: Solving Area Problems 221

Chapter 13: Pump Up the Volume: Using Calculus to Solve 3-D Problems 243

Chapter 14: What's So Different about Differential Equations? 265

Part 6: Infinite Series 275

Chapter 15: Following a Sequence, Winning the Series 277

Chapter 16: Where Is This Going? Testing for Convergence and Divergence 295

Chapter 17: Dressing Up Functions with the Taylor Series 319

Part 7: The Part of Tens 341

Chapter 18: Ten "Aha!" Insights in Calculus II 343

Chapter 19: Ten Tips to Take to the Test 351

Index 357