Calculus Workbook For Dummies - Mark Ryan

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The easy way to conquer calculus Calculus is hard no doubt about it and students often need help understanding or retaining the key concepts covered in class. Calculus Workbook For Dummies serves up the concept review and practice problems with an easy-to-follow, practical approach. Plus, you ll get

Résumé :

Introduction 1

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 2

Beyond the Book 3

Where to Go from Here 3

Part 1: Pre-Calculus Review 5

Chapter 1: Getting Down to Basics: Algebra and Geometry 7

Fraction Frustration 7

Misc. Algebra: You Know, Like Miss South Carolina 9

Geometry: When Am I Ever Going to Need It? 11

Solutions for This Easy, Elementary Stuff 16

Chapter 2: Funky Functions and Tricky Trig 25

Figuring Out Your Functions 25

Trigonometric Calisthenics 29

Solutions to Functions and Trigonometry 33

Part 2: Limits and Continuity 41

Chapter 3: A Graph Is Worth a Thousand Words: Limits and Continuity 43

Digesting the Definitions: Limit and Continuity 44

Taking a Closer Look: Limit and Continuity Graphs 46

Solutions for Limits and Continuity 50

Chapter 4: Nitty-Gritty Limit Problems 53

Solving Limits with Algebra 54

Pulling Out Your Calculator: Useful Cheating 59

Making Yourself a Limit Sandwich 61

Into the Great Beyond: Limits at Infinity 63

Solutions for Problems with Limits 67

Part 3: Differentiation 77

Chapter 5: Getting the Big Picture: Differentiation Basics 79

The Derivative: A Fancy Calculus Word for Slope and Rate 79

The Handy-Dandy Difference Quotient 81

Solutions for Differentiation Basics 84

Chapter 6: Rules, Rules, Rules: The Differentiation Handbook 89

Rules for Beginners 89

Giving It Up for the Product and Quotient Rules 92

Linking Up with the Chain Rule 94

What to Do with Y's: Implicit Differentiation 98

Getting High on Calculus: Higher Order Derivatives 101

Solutions for Differentiation Problems 103

Chapter 7: Analyzing Those Shapely Curves with the Derivative 117

The First Derivative Test and Local Extrema 117

The Second Derivative Test and Local Extrema 120

Finding Mount Everest: Absolute Extrema 122

Smiles and Frowns: Concavity and Inflection Points 126

The Mean Value Theorem: Go Ahead, Make My Day 129

Solutions for Derivatives and Shapes of Curves 131

Chapter 8: Using Differentiation to Solve Practical Problems 147

Optimization Problems: From Soup to Nuts 147

Problematic Relationships: Related Rates 150

A Day at the Races: Position, Velocity, and Acceleration 153

Solutions to Differentiation Problem Solving 157

Chapter 9: Even More Practical Applications of Differentiation 173

Make Sure You Know Your Lines: Tangents and Normals 173

Looking Smart with Linear Approximation 177

Calculus in the Real World: Business and Economics 179

Solutions to Differentiation Problem Solving 183

Part 4: Integration and Infinite Series 191

Chapter 10: Getting into Integration 193

Adding Up the Area of Rectangles: Kid Stuff 193

Sigma Notation and Riemann Sums: Geek Stuff 196

Close Isn't Good Enough: The Definite Integral and Exact Area 200

Finding Area with the Trapezoid Rule and Simpson's Rule 202

Solutions to Getting into Integration 205

Chapter 11: Integration: Reverse Differentiation 213

The Absolutely Atrocious and Annoying Area Function 213

Sound the Trumpets: The Fundamental Theorem of Calculus 216

Finding Antiderivatives: The Guess-and-Check Method 219

The Substitution Method: Pulling the Switcheroo 221

Solutions to Reverse Differentiation Problems 225

Chapter 12: Integration Rules for Calculus Connoisseurs 229...

Biographie:

Mark Ryan has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses as well as standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics....

Sommaire:

The easy way to conquer calculus

Calculus is hard-no doubt about it-and students often need help understanding or retaining the key concepts covered in class. Calculus Workbook For Dummies serves up the concept review and practice problems with an easy-to-follow, practical approach. Plus, you'll get free access to a quiz for every chapter online.

With a wide variety of problems on everything covered in calculus class, you'll find multiple examples of limits, vectors, continuity, differentiation, integration, curve-sketching, conic sections, natural logarithms, and infinite series.?Plus, you'll get hundreds of practice opportunities with detailed solutions that will help you master the math that is critical for scoring your highest in calculus.

• Review key concepts
• Take hundreds of practice problems
• Get access to free chapter quizzes online
• Use as a classroom supplement or with a tutor

Get ready to quickly and easily increase your confidence and improve your skills in calculus.?