Calculus II For Dummies
by Zegarelli, MarkEdition: 3rd
Format: Paperback
Pub. Date: 2023-04-18
Publisher(s): For Dummies
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Summary
Calculus II For Dummies, 3e helps students gain a greater understanding of the fundamentals of Calculus II. The book covers intermediate calculus topics such as substitution, integration techniques and when to use them, approximate integration, and improper integrals. Inside, students will find explanations and practical examples that mirror today's teaching methods, fresh examples, and relevant cultural vernacular and references. Whether students use the book as a supplement to their textbook or a refresher before taking a standardized test such as the MCAT, Calculus II For Dummies, 3e is packed with all the helpful knowledge they need to succeed in this difficult subject.
Author Biography
Mark Zegarelli is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II Workbook For Dummies. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.
Table of Contents
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
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