Description
Book SynopsisThe easy (okay, easier) way to master advanced calculus topics and theories Calculus II For Dummies will help you get through your (notoriously difficult) calc classor 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 conceptsMake sense of complicated processes and equationsGet clear explanations of how to use trigonometry functionsWalk through practice examples to master Calc IIUse this essential resource as a supplement to your textbook or as refresher before taking a testit's packed with all the helpful knowledge you need to succeed in Calculus II.
Table of ContentsIntroduction 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
