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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: 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