Efnisyfirlit

• Cover
• Introduction
  • About This Book
  • Foolish Assumptions
  • Icons Used in This Book
  • Beyond the Book
  • Where to Go from Here
• Part 1: Pre-Calculus Review
  • Chapter 1: Getting Down to Basics: Algebra and Geometry
    • Fraction Frustration
    • Misc. Algebra: You Know, Like Miss South Carolina
    • Geometry: When Am I Ever Going to Need It?
    • Solutions for This Easy, Elementary Stuff
  • Chapter 2: Funky Functions and Tricky Trig
    • Figuring Out Your Functions
    • Trigonometric Calisthenics
    • Solutions to Functions and Trigonometry
• Part 2: Limits and Continuity
  • Chapter 3: A Graph Is Worth a Thousand Words: Limits and Continuity
    • Digesting the Definitions: Limit and Continuity
    • Taking a Closer Look: Limit and Continuity Graphs
    • Solutions for Limits and Continuity
  • Chapter 4: Nitty-Gritty Limit Problems
    • Solving Limits with Algebra
    • Pulling Out Your Calculator: Useful “Cheating”
    • Making Yourself a Limit Sandwich
    • Into the Great Beyond: Limits at Infinity
    • Solutions for Problems with Limits
• Part 3: Differentiation
  • Chapter 5: Getting the Big Picture: Differentiation Basics
    • The Derivative: A Fancy Calculus Word for Slope and Rate
    • The Handy-Dandy Difference Quotient
    • Solutions for Differentiation Basics
  • Chapter 6: Rules, Rules, Rules: The Differentiation Handbook
    • Rules for Beginners
    • Giving It Up for the Product and Quotient Rules
    • Linking Up with the Chain Rule
    • What to Do with Y’s: Implicit Differentiation
    • Getting High on Calculus: Higher Order Derivatives
    • Solutions for Differentiation Problems
  • Chapter 7: Analy zing Those Shapely Curves with the Derivative
    • The First Derivative Test and Local Extrema
    • The Second Derivative Test and Local Extrema
    • Finding Mount Everest: Absolute Extrema
    • Smiles and Frowns: Concavity and Inflection Points
    • The Mean Value Theorem: Go Ahead, Make My Day
    • Solutions for Derivatives and Shapes of Curves
  • Chapter 8: Using Differentiation to Solve Practical Problems
    • Optimization Problems: From Soup to Nuts
    • Problematic Relationships: Related Rates
    • A Day at the Races: Position, Velocity, and Acceleration
    • Solutions to Differentiation Problem Solving
  • Chapter 9: Even More Practical Applications of Differentiation
    • Make Sure You Know Your Lines: Tangents and Normals
    • Looking Smart with Linear Approximation
    • Calculus in the Real World: Business and Economics
    • Solutions to Differentiation Problem Solving
• Part 4: Integration and Infinite Series
  • Chapter 10: Getting into Integration
    • Adding Up the Area of Rectangles: Kid Stuff
    • Sigma Notation and Riemann Sums: Geek Stuff
    • Close Isn’t Good Enough: The Definite Integral and Exact Area
    • Finding Area with the Trapezoid Rule and Simpson’s Rule
    • Solutions to Getting into Integration
  • Chapter 11: Integration: Reverse Differentiation
    • The Absolutely Atrocious and Annoying Area Function
    • Sound the Trumpets: The Fundamental Theorem of Calculus
    • Finding Antiderivatives: The Guess-and-Check Method
    • The Substitution Method: Pulling the Switcheroo
    • Solutions to Reverse Differentiation Problems
  • Chapter 12: Integration Rules for Calculus Connoisseurs
    • Integration by Parts: Here’s How u du It
    • Transfiguring Trigonometric Integrals
    • Trigonometric Substitution: It’s Your Lucky Day!
    • Partaking of Partial Fractions
    • Solutions for Integration Rules
  • Chapter 13: Who Needs Freud? Using the Integral to Solve Your Problems
    • Finding a Function’s Average Value
    • Finding the Area between Curves
    • Volumes of Weird Solids: No, You’re Never Going to Need This
    • Arc Length and Surfaces of Revolution
    • Solutions to Integration Application Problems
  • Chapter 14: Infinite (Sort of) Integrals
    • Getting Your Hopes Up with L’Hôpital’s Rule
    • Disciplining Those Improper Integrals
    • Solutions to Infinite (Sort of) Integrals
  • Chapter 15: Infinite Series: Welcome to the Outer Limits
    • The Nifty nth Term Test
    • Testing Three Basic Series
    • Apples and Oranges … and Guavas: Three Comparison Tests
    • Ratiocinating the Two “R” Tests
    • He Loves Me, He Loves Me Not: Alternating Series
    • Solutions to Infinite Series
• Part 5: The Part of Tens
  • Chapter 16: Ten Things about Limits, Continuity, and Infinite Series
    • The 33333 Mnemonic
    • The 13231 Mnemonic
  • Chapter 17: Ten Things You Better Remember about Differentiation
    • The Difference Quotient
    • The First Derivative Is a Rate
    • The First Derivative Is a Slope
    • Extrema, Sign Changes, and the First Derivative
    • The Second Derivative and Concavity
    • Inflection Points and Sign Changes in the Second Derivative
    • The Product Rule
    • The Quotient Rule
    • Linear Approximation
    • “PSST,” Here’s a Good Way to Remember the Derivatives of Trig Functions
• About the Author
• Connect with Dummies
• Index
• End User License Agreement

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