Calculus II for Dummies

An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, with introductions to multivariable calculus, differential equations, and numerical analysis. Best of all, it includes practical exercises designed to simplify and enhance understanding of this complex subject. Introduction to integration Indefinite integrals Intermediate Integration topics Infinite series Advanced topics Practice exercises Confounded by curves? Perplexed by polynomials? This plain-English guide to Calculus II will set you straight!

Mark Zegarelli, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear — and fun — for average readers. He is the author of Logic For Dummies and Basic Math & Pre-Algebra For Dummies.

Introduction 1

Part I: Introduction to Integration 9

Chapter 1: An Aerial View of the Area Problem 11

Chapter 2: Dispelling Ghosts from the Past: A Review of Pre-Calculus and Calculus I 37

Chapter 3: From Definite to Indefinite: The Indefinite Integral 73

Part II: Indefinite Integrals 103

Chapter 4: Instant Integration: Just Add Water (And C) 105

Chapter 5: Making a Fast Switch: Variable Substitution 117

Chapter 6: Integration by Parts 135

Chapter 7: Trig Substitution: Knowing All the (Tri)Angles 151

Chapter 8: When All Else Fails: Integration with Partial Fractions 173

Part III: Intermediate Integration Topics 195

Chapter 9: Forging into New Areas: Solving Area Problems 197

Chapter 10: Pump Up the Volume: Using Calculus to Solve 3-D Problems 219

Part IV: Infinite Series 241

Chapter 11: Following a Sequence, Winning the Series 243

Chapter 12: Where Is This Going? Testing for Convergence and Divergence 261

Chapter 13: Dressing Up Functions with the Taylor Series 283

Part V: Advanced Topics 307

Chapter 14: Multivariable Calculus 309

Chapter 15: What's So Different about Differential Equations? 329

Part VI: The Part of Tens 343

Chapter 16: Ten "Aha!" Insights in Calculus II 345

Chapter 17: Ten Tips to Take to the Test 351

Index 355

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Calculus II for Dummies

Summary

Author Biography

Table of Contents

Supplemental Materials