Calculus the Easy Way

ISBN-10: 0764129201
ISBN-13: 9780764129209
Edition: 4th 2006
List price: $14.99
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Description: This ingenious, user-friendly introduction to calculus recounts adventures that take place in the mythical land of Carmorra. As the story's narrator meets Carmorra's citizens, they confront a series of practical problems, and their method of working  More...

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Book details

List price: $14.99
Edition: 4th
Copyright year: 2006
Publisher: Barron's Educational Series, Incorporated
Publication date: 1/1/2006
Binding: Paperback
Pages: 416
Size: 8.00" wide x 11.00" long x 1.25" tall
Weight: 1.936
Language: English

This ingenious, user-friendly introduction to calculus recounts adventures that take place in the mythical land of Carmorra. As the story's narrator meets Carmorra's citizens, they confront a series of practical problems, and their method of working out solutions employs calculus. As readers follow their adventures, they are introduced to calculating derivatives; finding maximum and minimum points with derivatives; determining derivatives of trigonometric functions; discovering and using integrals; working with logarithms, exponential functions, vectors, and Taylor series; using differential equations; and much more. This introduction to calculus presents exercises at the end of each chapter and gives their answers at the back of the book. Step-by-step worksheets with answers are included in the chapters. Computers are used for numerical integration and other tasks. The book also includes graphs, charts, and whimsical line illustrations. Barron'sEasy Waybooks introduce a variety of academic and practical subjects to students and general readers in clear, understandable language. Ideal as self-teaching manuals for readers interested in learning a new career-related skill, these books have also found widespread classroom use as supplementary texts and brush-up test-preparation guides. Subject heads and key phrases that need to be learned are set in a second color.

List of Symbolsp. viii
Introductionp. ix
The Slope of the Tangent Linep. 1
The Graph of the Train's Positionp. 2
Function Machinesp. 3
Slope of a Linep. 6
Slope of a Secant Linep. 7
Slope of a Tangent Linep. 8
Tangent Slope for y = x[superscript 2]p. 10
Worksheet: Slope of a Secant Linep. 11
Exercisesp. 11
Calculating Derivativesp. 13
Definition of Derivativep. 14
Derivative of a Constant Functionp. 15
Derivative of a Straight-Line Functionp. 17
Derivative of y = cx[superscript 2]p. 18
Derivative of a Sump. 21
Derivative of y = x[superscript 3]p. 22
Derivative of y = x[superscript n]p. 23
Worksheet: Derivatives of Polynomialsp. 26
Exercisesp. 28
Drawing Curves with Derivativesp. 31
Horizontal Tangentsp. 32
The Derivative of the Derivativep. 35
The Professor's Bug and the Meaning of the Second Derivativep. 36
Concave-up and Concave-down Curvesp. 37
The Spilled Waterp. 38
Local Maximum Pointsp. 39
Worksheet: Maximum and Minimum Pointsp. 40
Points of Inflectionp. 41
Worksheet: Local Maximum and Minimum Pointsp. 42
Exercisesp. 47
Derivatives of Complicated Functionsp. 49
Multiplied Functionsp. 51
The Product Rulep. 55
Embedded Functionsp. 55
The Chain Rulep. 58
Fractional Exponentsp. 58
Implicit Functionsp. 59
The Power Rulep. 61
Worksheet: The Product Rulep. 61
Exercisesp. 64
Derivatives of Trigonometric Functionsp. 66
The Gremlin's Horrible Oscillating Chicken-Scaring Machinep. 67
Trigonometeris' Sine Functionp. 68
The Derivative of the Sine Functionp. 73
The Derivative of the Cosine Functionp. 74
Derivatives of Other Trigonometric Functionsp. 75
Worksheet: Derivatives of Trigonometric Functionsp. 76
Exercisesp. 77
Optimum Values and Related Ratesp. 79
Differentiation and the Get-Rich-Quick Schemep. 80
The Optimum-size Boxp. 81
Carmorra Magazine and the Optimum Subscription Pricep. 82
The Birthday Party Balloonp. 85
The National Park Beach Lifeguard and the Racing Shadowp. 86
Exercisesp. 88
The Integral: A Backward Derivativep. 91
Recordis' Exhaustion and the Story of Rutherfordp. 91
Differentiating Backwardsp. 92
The Antiderivative or the Integralp. 93
Discovering the Indefiniteness of an Indefinite Integralp. 93
Using an Initial Condition to Track Down Rutherfordp. 94
Differentialsp. 96
The Integral Signp. 96
Sum Rule for Integralsp. 98
Multiplication Rule for Integralsp. 99
Perfect Integral Rulep. 100
Power Rule for Integralsp. 101
Worksheet: Integrals of Polynomialsp. 102
Worksheet: Integration by Substitutionp. 104
Exercisesp. 105
Finding Areas with Integralsp. 108
Recordis' Pools and the Magic Crystal Water Rate Increasep. 108
Summation Notationp. 110
The Curve's Area Defined as a Limitp. 112
The Gremlin's Terrible Fire-and-Water Threatp. 112
The Mysterious Function A(x)p. 113
The Derivative of A(x)p. 114
Fundamental Theorem of Integral Calculusp. 115
Discovering the Definiteness of Definite Integralsp. 116
Worksheet: Definite Integralsp. 117
Exercisesp. 119
Natural Logarithmsp. 122
The Unfortunate Accident with Some Beadsp. 123
The Power Rule Breakdown: n = -1p. 124
The Mysterious Function L(a)p. 125
Some Properties of L(a)p. 126
Substitution Method for Evaluating Definite Integralsp. 128
Remembering Logarithmsp. 128
The Derivative of the Logarithm Functionp. 129
The Fundamental Number ep. 130
Worksheet: Derivatives and Integrals with Logarithmsp. 132
Exercisesp. 135
Exponential Functions and Integration by Partsp. 137
The Graph of the Logarithm Functionp. 138
Pal's Stumble and the Inverse Functionp. 138
The Exponential Function and the Professor's Amazing Incomep. 139
The Indestructible Function e[superscript x]p. 141
Differentiation of Exponential Functionsp. 142
The Method of Logarithmic Implicit Differentiationp. 142
The Integral of the Logarithm Functionp. 144
The Method of Integration by Partsp. 146
Worksheet: Integration by Partsp. 148
Exercisesp. 151
Integration by Trigonometric Substitutionp. 153
The Elliptical Rose Gardenp. 153
The Ellipse Area Integralp. 154
Trying a Trigonometric Substitutionp. 155
The Area of the Ellipsep. 158
The Method of Trigonometric Substitutionp. 158
Derivatives of Inverse Trigonometric Functionsp. 160
Worksheet: Integration by Trigonometric Substitutionp. 163
Exercisesp. 164
Integration by Partial Fractionsp. 167
The Red-and-Yellow Fireworks Problemp. 169
The Integral of the Secant Functionp. 174
Worksheet: Partial Fractionsp. 175
Partial Fractions with Quadratic Denominatorsp. 179
The Method of Partial Fractionsp. 185
Exercisesp. 185
Finding Volumes with Integralsp. 190
The Pancake Method of Approximating Volumep. 192
The Amazing Resemblance Between the Continuous Sum and the Definite Integralp. 193
The Volume of the Paraboloidp. 194
Finding Volumes with Cylindrical Shellsp. 197
Worksheet: Volumep. 199
Exercisesp. 203
Arc Lengths, Surface Areas, and the Center of Massp. 205
The Straight-line Approximation for a Curvep. 206
The Integral for Arc Lengthsp. 208
The Frustum Method of Finding Surface Areasp. 213
The Center of Mass of the Concert Hall Stagep. 215
Exercisesp. 219
Introduction to Differential Equationsp. 221
The Oscillating Ride and the Ordinary Differential Equationp. 222
Linear Differential Equationsp. 224
The Force of Friction and the Damped Sine Wavep. 231
Solution Method for Second-order Linear Homogeneous Constant-Coefficient Differential Equationsp. 233
The Driving Force and the Nonhomogeneous Equationp. 234
Resonance and the Infinite Amplitude Ridep. 240
Exercisesp. 241
Partial Derivatives and Vectorsp. 243
The Two-variable Magazine Subscription Problemp. 243
Partial Derivativesp. 245
The Domep. 246
Graphs of Functions of Two Variablesp. 247
The Gradient Vectorp. 248
The Sleigh Ride and the Falling Basket Ridep. 250
Work, Kinetic Energy, and Potential Energyp. 251
Describing Motion: The Position Vector as a Function of Timep. 252
The Derivative of a Vector: Velocityp. 254
The Dot Product of Two Vectorsp. 255
Circular Motionp. 256
The Force Vector as the Gradient of the Potential Energy Functionp. 256
The Chain Rule for Vector Functionsp. 257
The Potential Energy for Gravityp. 258
Exercisesp. 262
Numerical Methods, Taylor Series, and Limitsp. 268
The Problem Closet Break-in and the Gremlin's Secret Planp. 268
The Intractable Elliptic Integralp. 272
The Height of the Children and the Area Under the Bell-shaped Normal Curvep. 272
Approximating the Area with Rectanglesp. 273
Numerical Integrationp. 278
Approximating a Function with an Infinite Series of Derivativesp. 281
Taylor Seriesp. 283
Visualizing Differential Equations with Slope Fieldsp. 284
The Ups and Downs of the Space Probep. 285
Euler's Method for Finding Numerical Solutions to Differential Equationsp. 287
The Formal Definition of Limitp. 288
Continuous Curvesp. 289
L'Hopital's Rule for Finding Otherwise Unobtainable Limitsp. 291
Exercisesp. 293
Comprehensive Test of Calculus Problemsp. 296
The Return of the Gremlinp. 296
The 45 Problemsp. 297
The Solutionsp. 301
Stanislavsky Guide to Calculusp. 322
Answers to Worksheets and Exercisesp. 326
Summary of Trigonometric Formulasp. 391
Brief Table of Integralsp. 396
Glossaryp. 401
Indexp. 402
Table of Contents provided by Ingram. All Rights Reserved.

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