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| Introduction | |
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| About This Book | |
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| Conventions Used in This Book | |
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| Foolish Assumptions | |
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| Icons Used in This Book | |
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| Where to Go from Here | |
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| Calculus: No Big Deal | |
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| So What Is Calculus Already? | |
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| Real-World Examples of Calculus | |
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| Differentiation | |
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| Integration | |
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| Why Calculus Works | |
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| Limits: Math microscopes | |
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| What happens when you zoom in | |
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| Limits and Continuity | |
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| Taking It to the Limit | |
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| Three functions with one limit | |
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| One-sided limits | |
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| Limits and vertical asymptotes | |
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| Limits and horizontal asymptotes | |
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| Instantaneous speed | |
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| Limits and Continuity | |
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| The hole exception | |
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| Evaluating Limits | |
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| Easy Limits | |
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| Limits to memorize | |
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| Plug-and-chug limits | |
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| "Real" Limit Problems | |
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| Factoring | |
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| Conjugate multiplication | |
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| Miscellaneous algebra | |
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| Limits at Infinity | |
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| Horizontal asymptotes | |
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| Solving limits at infinity | |
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| Differentiation Orientation | |
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| The Derivative: It's Just Slope | |
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| The slope of a line | |
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| The derivative of a line | |
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| The Derivative: It's Just a Rate | |
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| Calculus on the playground | |
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| The rate-slope connection | |
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| The Derivative of a Curve | |
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| The Difference Quotient | |
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| Average and Instantaneous Rate | |
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| Three Cases Where the Derivative Does Not Exist | |
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| Differentiation Rules | |
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| Basic Differentiation Rules | |
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| The constant rule | |
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| The power rule | |
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| The constant multiple rule | |
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| The sum and difference rules | |
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| Differentiating trig functions | |
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| Exponential and logarithmic functions | |
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| Derivative Rules for Experts | |
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| The product and quotient rules | |
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| The chain rule | |
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| Differentiating Implicitly | |
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| Differentiation and the Shape of Curves | |
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| A Calculus Road Trip | |
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| Local Extrema | |
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| Finding the critical numbers | |
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| The First Derivative Test | |
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| The Second Derivative Test | |
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| Finding Absolute Extrema on a Closed Interval | |
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| Finding Absolute Extrema over a Function's Entire Domain | |
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| Concavity and Inflection Points | |
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| Graphs of Derivatives | |
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| The Mean Value Theorem | |
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| Differentiation Problems | |
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| Optimization Problems | |
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| The maximum area of a corral | |
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| Position, Velocity, and Acceleration | |
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| Velocity versus speed | |
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| Maximum and minimum height | |
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| Velocity and displacement | |
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| Speed and distance traveled | |
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| Acceleration | |
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| Tying it all together | |
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| Related Rates | |
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| A calculus crossroads | |
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| Filling up a trough | |
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| Linear Approximation | |
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| Introduction to Integration | |
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| Integration: Just Fancy Addition | |
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| Finding the Area under a Curve | |
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| Dealing with negative area | |
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| Approximating Area | |
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| Approximating area with left sums | |
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| Approximating area with right sums | |
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| Approximating area with midpoint sums | |
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| Summation Notation | |
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| Summing up the basics | |
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| Writing Riemann sums with sigma notation | |
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| Finding Exact Area with the Definite Integral | |
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| Integration: Backwards Differentiation | |
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| Antidifferentiation: Reverse Differentiation | |
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| The Annoying Area Function | |
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| The Fundamental Theorem | |
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| Fundamental Theorem: Take Two | |
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| Antiderivatives: Basic Techniques | |
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| Reverse rules | |
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| Guess and check | |
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| Substitution | |
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| Integration for Experts | |
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| Integration by Parts | |
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| Picking your u | |
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| Tricky Trig Integrals | |
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| Sines and cosines | |
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| Secants and tangents | |
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| Cosecants and cotangents | |
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| Trigonometric Substitution | |
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| Tangents | |
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| Sines | |
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| Secants | |
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| Partial Fractions | |
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| The denominator contains only linear factors | |
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| The denominator contains unfactorable quadratic factors | |
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| The denominator contains repeated factors | |
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| Equating coefficients | |
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| Using the Integral to Solve Problems | |
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| The Mean Value Theorem for Integrals and Average Value | |
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| The Area between Two Curves | |
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| Volumes of Weird Solids | |
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| The meat-slicer method | |
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| The disk method | |
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| The washer method | |
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| The matryoshka doll method | |
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| Arc Length | |
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| Improper Integrals | |
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| Improper integrals with vertical asymptotes | |
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| Improper integrals with infinite limits of integration | |
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| Eight Things to Remember | |
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| a<sup>2</sup> - b<sup>2</sup> = (a - b)(a + b) | |
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| 0/5 = 0 But 5/0 Is Undefined | |
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| SohCahToa | |
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| Trig Values to Know | |
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| sin<sup>2</sup> � + cos<sup>2</sup> � = 1 | |
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| The Product Rule | |
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| The Quotient Rule | |
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| Your Sunglasses | |
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| Index | |