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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.
Klappentext
WITH ONLINE PRACTICE
Review key math concepts The easy way to conquer calculus Calculus is tough no doubt about it. But now you can leave your fear at the door! Inside, you'll find problems involving trigonometric, logarithmic, and exponential functions, as well as limits, continuity, differentiation, integration, and infinite series. Plus, you'll get more than 500 practice problems inside and online, with detailed solutions that will help you master the math that is critical for scoring your highest in calculus. Inside
Zusammenfassung
The easy way to conquer calculus
Calculus is hardno doubt about itand 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.
Inhalt
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 Trigonometri...