Calculus II For Dummies, 3rd Edition

Table of contents

1. Cover
2. Title Page
3. Copyright
4. Introduction
   1. About This Book
   2. Conventions Used in This Book
   3. What You're Not to Read
   4. Foolish Assumptions
   5. Icons Used in This Book
   6. Beyond the Book
   7. Where to Go from Here
5. Part 1: Introduction to Integration
   1. Chapter 1: An Aerial View of the Area Problem
      1. Checking Out the Area
      2. Slicing Things Up
      3. Defining the Indefinite
      4. Solving Problems with Integration
      5. Differential Equations
      6. Understanding Infinite Series
   2. Chapter 2: Forgotten but Not Gone: Review of Algebra and Pre-Calculus
      1. Quick Review of Pre-Algebra and Algebra
      2. Review of Pre-Calculus
   3. Chapter 3: Recent Memories: Review of Calculus I
      1. Knowing Your Limits
      2. Hitting the Slopes with Derivatives
      3. Understanding Differentiation
      4. Finding Limits Using L’Hôpital’s Rule
6. Part 2: From Definite to Indefinite Integrals
   1. Chapter 4: Approximating Area with Riemann Sums
      1. Three Ways to Approximate Area with Rectangles
      2. Two More Ways to Approximate Area
      3. Building the Riemann Sum Formula
   2. Chapter 5: There Must Be a Better Way — Introducing the Indefinite Integral
      1. FTC2: The Saga Begins
      2. Your New Best Friend: The Indefinite Integral
      3. FTC1: The Journey Continues
7. Part 3: Evaluating Indefinite Integrals
   1. Chapter 6: Instant Integration: Just Add Water (And C)
      1. Evaluating Basic Integrals
      2. Evaluating More Difficult Integrals
      3. Understanding Integrability
   2. Chapter 7: Sharpening Your Integration Moves
      1. Integrating Rational and Radical Functions
      2. Using Algebra to Integrate Using the Power Rule
      3. Integrating Trig Functions
      4. Integrating Compositions of Functions with Linear Inputs
   3. Chapter 8: Here’s Looking at U-Substitution
      1. Knowing How to Use U-Substitution
      2. Recognizing When to Use U-Substitution
      3. Using Substitution to Evaluate Definite Integrals
8. Part 4: Advanced Integration Techniques
   1. Chapter 9: Parting Ways: Integration by Parts
      1. Introducing Integration by Parts
      2. Integrating by Parts with the DI-agonal Method
   2. Chapter 10: Trig Substitution: Knowing All the (Tri)Angles
      1. Integrating the Six Trig Functions
      2. Integrating Powers of Sines and Cosines
      3. Integrating Powers of Tangents and Secants
      4. Integrating Powers of Cotangents and Cosecants
      5. Integrating Weird Combinations of Trig Functions
      6. Using Trig Substitution
   3. Chapter 11: Rational Solutions: Integration with Partial Fractions
      1. Strange but True: Understanding Partial Fractions
      2. Solving Integrals by Using Partial Fractions
      3. Beyond the Four Cases: Knowing How to Set Up Any Partial Fraction
      4. Integrating Improper Rationals
9. Part 5: Applications of Integrals
   1. Chapter 12: Forging into New Areas: Solving Area Problems
      1. Breaking Us in Two
      2. Improper Integrals
      3. Finding the Unsigned Area of Shaded Regions on the xy-Graph
      4. The Mean Value Theorem for Integrals
      5. Calculating Arc Length
   2. Chapter 13: Pump Up the Volume: Using Calculus to Solve 3-D Problems
      1. Slicing Your Way to Success
      2. Turning a Problem on Its Side
      3. Two Revolutionary Problems
      4. Finding the Space Between
      5. Playing the Shell Game
      6. Knowing When and How to Solve 3-D Problems
   3. Chapter 14: What’s So Different about Differential Equations?
      1. Basics of Differential Equations
      2. Solving Differential Equations
10. Part 6: Infinite Series
    1. Chapter 15: Following a Sequence, Winning the Series
       1. Introducing Infinite Sequences
       2. Introducing Infinite Series
       3. Getting Comfy with Sigma Notation
       4. Connecting a Series with Its Two Related Sequences
       5. Recognizing Geometric Series and p-Series
    2. Chapter 16: Where Is This Going? Testing for Convergence and Divergence
       1. Starting at the Beginning
       2. Using the nth-Term Test for Divergence
       3. Let Me Count the Ways
       4. Choosing Comparison Tests
       5. Two-Way Tests for Convergence and Divergence
       6. Looking at Alternating Series
    3. Chapter 17: Dressing Up Functions with the Taylor Series
       1. Elementary Functions
       2. Power Series: Polynomials on Steroids
       3. Expressing Functions as Series
       4. Introducing the Maclaurin Series
       5. Introducing the Taylor Series
       6. Understanding Why the Taylor Series Works
11. Part 7: The Part of Tens
    1. Chapter 18: Ten “Aha!” Insights in Calculus II
       1. Integrating Means Finding the Area
       2. When You Integrate, Area Means Signed Area
       3. Integrating Is Just Fancy Addition
       4. Integration Uses Infinitely Many Infinitely Thin Slices
       5. Integration Contains a Slack Factor
       6. A Definite Integral Evaluates to a Number
       7. An Indefinite Integral Evaluates to a Function
       8. Integration Is Inverse Differentiation
       9. Every Infinite Series Has Two Related Sequences
       10. Every Infinite Series Either Converges or Diverges
    2. Chapter 19: Ten Tips to Take to the Test
       1. Breathe
       2. Start by Doing a Memory Dump as You Read through the Exam
       3. Solve the Easiest Problem First
       4. Don’t Forget to Write dx and + C
       5. Take the Easy Way Out Whenever Possible
       6. If You Get Stuck, Scribble
       7. If You Really Get Stuck, Move On
       8. Check Your Answers
       9. If an Answer Doesn’t Make Sense, Acknowledge It
       10. Repeat the Mantra, “I’m Doing My Best,” and Then Do Your Best
12. Index
13. About the Author
14. Advertisement Page
15. Connect with Dummies
16. End User License Agreement