Efnisyfirlit

• Cover
• Introduction
  • About This Book
  • Foolish Assumptions
  • Icons Used in This Book
  • Beyond the Book
  • Where to Go from Here
• Part 1: An Overview of Calculus
  • Chapter 1: What Is Calculus?
    • What Calculus Is Not
    • So What Is Calculus, Already?
    • Real-World Examples of Calculus
  • Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration — plus Infinite Series
    • Defining Differentiation
    • Investigating Integration
    • Sorting Out Infinite Series
  • Chapter 3: Why Calculus Works
    • The Limit Concept: A Mathematical Microscope
    • What Happens When You Zoom In
    • Two Caveats; or, Precision, Preschmidgen
• Part 2: Warming Up with Calculus Prerequisites
  • Chapter 4: Pre-Algebra and Algebra Review
    • Fine-Tuning Your Fractions
    • Absolute Value — Absolutely Easy
    • Empowering Your Powers
    • Rooting for Roots
    • Logarithms — This Is Not an Event at a Lumberjack Competition
    • Factoring Schmactoring — When Am I Ever Going to Need It?
    • Solving Quadratic Equations
  • Chapter 5: Funky Functions and Their Groovy Graphs
    • What Is a Function?
    • What Does a Function Look Like?
    • Common Functions and Their Graphs
    • Inverse Functions
    • Shifts, Reflections, Stretches, and Shrinks
  • Chapter 6: The Trig Tango
    • Studying Trig at Camp SohCahToa
    • Two Special Right Triangles
    • Circling the Enemy with the Unit Circle
    • Graphing Sine, Cosine, and Tangent
    • Inverse Trig Functions
    • Identifying with Trig Identities
• Part 3: Limits
  • Chapter 7: Limits and Continuity
    • Take It to the Limit — NOT
    • Linking Limits and Continuity
    • The 33333 Limit Mnemonic
  • Chapter 8: Evaluating Limits
    • Easy Limits
    • The “Real Deal” Limit Problems
    • Evaluating Limits at Infinity
• Part 4: Differentiation
  • Chapter 9: Differentiation Orientation
    • Differentiating: It’s Just Finding the Slope
    • The Derivative: It’s Just a Rate
    • The Derivative of a Curve
    • The Difference Quotient
    • Average Rate and Instantaneous Rate
    • To Be or Not to Be? Three Cases Where the Derivative Does Not Exist
  • Chapter 10: Differentiation Rules — Yeah, Man, It Rules
    • Basic Differentiation Rules
    • Differentiation Rules for Experts — Oh, Yeah, I’m a Calculus Wonk
    • Differentiating Implicitly
    • Getting into the Rhythm with Logarithmic Differentiation
    • Differentiating Inverse Functions
    • Scaling the Heights of Higher Order Derivatives
  • Chapter 11: Differentiation and the Shape of Curves
    • Taking a Calculus Road Trip
    • Finding Local Extrema — My Ma, She’s Like, Totally Extreme
    • Finding Absolute Extrema on a Closed Interval
    • Finding Absolute Extrema over a Function’s Entire Domain
    • Locating Concavity and Inflection Points
    • Looking at Graphs of Derivatives Till They Derive You Crazy
    • The Mean Value Theorem — GRRRRR
  • Chapter 12: Your Problems Are Solved: Differentiation to the Rescue!
    • Getting the Most (or Least) Out of Life: Optimization Problems
    • Yo-Yo a Go-Go: Position, Velocity, and Acceleration
    • Related Rates — They Rate, Relatively
  • Chapter 13: More Differentiation Problems: Going Off on a Tangent
    • Tangents and Normals: Joined at the Hip
    • Straight Shooting with Linear Approximations
    • Business and Economics Problems
• Part 5: Integration and Infinite Series
  • Chapter 14: Intro to Integration and Approximating Area
    • Integration: Just Fancy Addition
    • Finding the Area Under a Curve
    • Approximating Area
    • Getting Fancy with Summation Notation
    • Finding Exact Area with the Definite Integral
    • Approximating Area with the Trapezoid Rule and Simpson’s Rule
  • Chapter 15: Integration: It’s Backwards Differentiation
    • Antidifferentiation
    • Vocabulary, Voshmabulary: What Difference Does It Make?
    • The Annoying Area Function
    • The Power and the Glory of the Fundamental Theorem of Calculus
    • The Fundamental Theorem of Calculus: Take Two
    • Finding Antiderivatives: Three Basic Techniques
    • Finding Area with Substitution Problems
  • Chapter 16: Integration Techniques for Experts
    • Integration by Parts: Divide and Conquer
    • Tricky Trig Integrals
    • Your Worst Nightmare: Trigonometric Substitution
    • The As, Bs, and Cxs of Partial Fractions
  • Chapter 17: Forget Dr. Phil: Use the Integral to Solve Problems
    • The Mean Value Theorem for Integrals and Average Value
    • The Area between Two Curves — Double the Fun
    • Finding the Volumes of Weird Solids
    • The Washer Method
    • Analyzing Arc Length
    • Surfaces of Revolution — Pass the Bottle ’Round
  • Chapter 18: Taming the Infinite with Improper Integrals
    • L’Hôpital’s Rule: Calculus for the Sick
    • Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!
  • Chapter 19: Infinite Series
    • Sequences and Series: What They’re All About
    • Convergence or Divergence? That Is the Question
    • Alternating Series
    • Keeping All the Tests Straight
• Part 6: The Part of Tens
  • Chapter 20: Ten Things to Remember
  • Chapter 21: Ten Things to Forget
  • Chapter 22: Ten Things You Can’t Get Away With
    • Give Two Answers on Exam Questions
    • Write Illegibly on Exams
    • Don’t Show Your Work on Exams
    • Don’t Do All of the Exam Problems
    • Blame Your Study Partner for Low Grade
    • Tell Your Teacher You Need an “A” in Calculus to Impress Your Significant Other
    • Claim Early-Morning Exams Are Unfair Because You’re Not a “Morning Person”
    • Protest the Whole Idea of Grades
    • Pull the Fire Alarm During an Exam
    • Use This Book as an Excuse
• About the Author
• Connect with Dummies
• End User License Agreement

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