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    Calculus Workbook For Dummies

    4.0 3

    by Mark Ryan

    Paperback

    $19.99
    $19.99

    Temporarily Out of Stock Online

    Customer Reviews

    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.

    Table of Contents

    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

    Integration by Parts: Here’s How u du It 229

    Transfiguring Trigonometric Integrals 233

    Trigonometric Substitution: It’s Your Lucky Day! 235

    Partaking of Partial Fractions 237

    Solutions for Integration Rules 241

    Chapter 13: Who Needs Freud? Using the Integral to Solve Your Problems 255

    Finding a Function’s Average Value 255

    Finding the Area between Curves 256

    Volumes of Weird Solids: No, You’re Never Going to Need This 258

    Arc Length and Surfaces of Revolution 265

    Solutions to Integration Application Problems 268

    Chapter 14: Infinite (Sort of) Integrals 277

    Getting Your Hopes Up with L’Hôpital’s Rule 278

    Disciplining Those Improper Integrals 280

    Solutions to Infinite (Sort of) Integrals 283

    Chapter 15: Infinite Series: Welcome to the Outer Limits 287

    The Nifty nth Term Test 287

    Testing Three Basic Series 289

    Apples and Oranges . . . and Guavas: Three Comparison Tests 291

    Ratiocinating the Two “R” Tests 295

    He Loves Me, He Loves Me Not: Alternating Series 297

    Solutions to Infinite Series 299

    Part 5: The Part of Tens 309

    Chapter 16: Ten Things about Limits, Continuity, and Infinite Series 311

    The 33333 Mnemonic 311

    First 3 over the “l”: 3 parts to the definition of a limit 312

    Fifth 3 over the “l”: 3 cases where a limit fails to exist 312

    Second 3 over the “i”: 3 parts to the definition of continuity 312

    Fourth 3 over the “i”: 3 cases where continuity fails to exist 312

    Third 3 over the “m”: 3 cases where a derivative fails to exist 313

    The 13231 Mnemonic 313

    First 1: The nth term test of divergence 313

    Second 1: The nth term test of convergence for alternating series 313

    First 3: The three tests with names 313

    Second 3: The three comparison tests 314

    The 2 in the middle: The two R tests 314

    Chapter 17: Ten Things You Better Remember about Differentiation 315

    The Difference Quotient 315

    The First Derivative Is a Rate 315

    The First Derivative Is a Slope 316

    Extrema, Sign Changes, and the First Derivative 316

    The Second Derivative and Concavity 316

    Inflection Points and Sign Changes in the Second Derivative 316

    The Product Rule 317

    The Quotient Rule 317

    Linear Approximation 317

    “PSST,” Here’s a Good Way to Remember the Derivatives of Trig Functions 317

    Index 319

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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 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.

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