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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