Calculus II For Dummies

An easy–to–understand primer on advanced calculus topics Confounded by curves? Perplexed by polynomials? This plain–English guide to Calculus II will set you straight! Calculus II For Dummies offers expert instruction, advice, and tips to help students get a handle on intermediate calculus topics. Best of all, it includes example problems and explanations that enhance your understanding of this complex subject. Calculus II 101 — get an easy–to–follow introduction to the definite integral, the Reimann sum equation, and the indefinite integral Strike that, reverse it — discover everything you need to know about reversing the differential process to solve a limited set of indefinite integrals using anti–differentiation Go big with trig — find out how to use a whole host of trig functions to integrate powers of sines and cosines, and then tangents and secants, and finally cotangents and cosecants Conquer the Mount Everest of Math — move on to intermediate integration, infinite series, and the math you can expect in higher–level Calculus courses Open the book and find: A need–to–know refresher on Pre–Calculus and Calculus I The "Aha!" insights in Calculus II Useful test–taking tips The 4–1–1 on area problems Plain–English explanations of integrals Everything you need to know about the infinite series Help on solving area problems How to use calculus to solve 3–D problems Learn to: Make sense of advanced calculus topics Get ahead of the curve with easy–to–understand explanations of complicated subject matter Score high in your Calculus II class

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

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 .