Calculus II For Dummies

The easy (okay, easier) way to master advanced calculus topics and theories Calculus II For Dummies will help you get through your (notoriously difficult) calc class—or pass a standardized test like the MCAT with flying colors. Calculus is required for many majors, but not everyone’s a natural at it. This friendly book breaks down tricky concepts in plain English, in a way that you can understand. Practical examples and detailed walkthroughs help you manage differentiation, integration, and everything in between. You’ll refresh your knowledge of algebra, pre-calc and Calculus I topics, then move on to the more advanced stuff, with plenty of problem-solving tips along the way. Review Algebra, Pre-Calculus, and Calculus I concepts Make sense of complicated processes and equations Get clear explanations of how to use trigonometry functions Walk through practice examples to master Calc II Use this essential resource as a supplement to your textbook or as refresher before taking a test—it’s packed with all the helpful knowledge you need to succeed in Calculus II.

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