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• 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