Calculus the Easy Way

Name: Calculus the Easy Way
Price: 3.46 USD
Availability: InStock
ISBN: 9780764129209

ISBN-10: 0764129201

ISBN-13: 9780764129209

Edition: 4th 2006

Authors: Douglas A. Downing

List price: $14.99

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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…

Book details

List price: $14.99
Edition: 4th
Copyright year: 2006
Publisher: Kaplan Publishing
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

List of Symbols	p. viii
Introduction	p. ix
The Slope of the Tangent Line	p. 1
The Graph of the Train's Position	p. 2
Function Machines	p. 3
Slope of a Line	p. 6
Slope of a Secant Line	p. 7
Slope of a Tangent Line	p. 8
Tangent Slope for y = x[superscript 2]	p. 10
Worksheet: Slope of a Secant Line	p. 11
Exercises	p. 11
Calculating Derivatives	p. 13
Definition of Derivative	p. 14
Derivative of a Constant Function	p. 15
Derivative of a Straight-Line Function	p. 17
Derivative of y = cx[superscript 2]	p. 18
Derivative of a Sum	p. 21
Derivative of y = x[superscript 3]	p. 22
Derivative of y = x[superscript n]	p. 23
Worksheet: Derivatives of Polynomials	p. 26
Exercises	p. 28
Drawing Curves with Derivatives	p. 31
Horizontal Tangents	p. 32
The Derivative of the Derivative	p. 35
The Professor's Bug and the Meaning of the Second Derivative	p. 36
Concave-up and Concave-down Curves	p. 37
The Spilled Water	p. 38
Local Maximum Points	p. 39
Worksheet: Maximum and Minimum Points	p. 40
Points of Inflection	p. 41
Worksheet: Local Maximum and Minimum Points	p. 42
Exercises	p. 47
Derivatives of Complicated Functions	p. 49
Multiplied Functions	p. 51
The Product Rule	p. 55
Embedded Functions	p. 55
The Chain Rule	p. 58
Fractional Exponents	p. 58
Implicit Functions	p. 59
The Power Rule	p. 61
Worksheet: The Product Rule	p. 61
Exercises	p. 64
Derivatives of Trigonometric Functions	p. 66
The Gremlin's Horrible Oscillating Chicken-Scaring Machine	p. 67
Trigonometeris' Sine Function	p. 68
The Derivative of the Sine Function	p. 73
The Derivative of the Cosine Function	p. 74
Derivatives of Other Trigonometric Functions	p. 75
Worksheet: Derivatives of Trigonometric Functions	p. 76
Exercises	p. 77
Optimum Values and Related Rates	p. 79
Differentiation and the Get-Rich-Quick Scheme	p. 80
The Optimum-size Box	p. 81
Carmorra Magazine and the Optimum Subscription Price	p. 82
The Birthday Party Balloon	p. 85
The National Park Beach Lifeguard and the Racing Shadow	p. 86
Exercises	p. 88
The Integral: A Backward Derivative	p. 91
Recordis' Exhaustion and the Story of Rutherford	p. 91
Differentiating Backwards	p. 92
The Antiderivative or the Integral	p. 93
Discovering the Indefiniteness of an Indefinite Integral	p. 93
Using an Initial Condition to Track Down Rutherford	p. 94
Differentials	p. 96
The Integral Sign	p. 96
Sum Rule for Integrals	p. 98
Multiplication Rule for Integrals	p. 99
Perfect Integral Rule	p. 100
Power Rule for Integrals	p. 101
Worksheet: Integrals of Polynomials	p. 102
Worksheet: Integration by Substitution	p. 104
Exercises	p. 105
Finding Areas with Integrals	p. 108
Recordis' Pools and the Magic Crystal Water Rate Increase	p. 108
Summation Notation	p. 110
The Curve's Area Defined as a Limit	p. 112
The Gremlin's Terrible Fire-and-Water Threat	p. 112
The Mysterious Function A(x)	p. 113
The Derivative of A(x)	p. 114
Fundamental Theorem of Integral Calculus	p. 115
Discovering the Definiteness of Definite Integrals	p. 116
Worksheet: Definite Integrals	p. 117
Exercises	p. 119
Natural Logarithms	p. 122
The Unfortunate Accident with Some Beads	p. 123
The Power Rule Breakdown: n = -1	p. 124
The Mysterious Function L(a)	p. 125
Some Properties of L(a)	p. 126
Substitution Method for Evaluating Definite Integrals	p. 128
Remembering Logarithms	p. 128
The Derivative of the Logarithm Function	p. 129
The Fundamental Number e	p. 130
Worksheet: Derivatives and Integrals with Logarithms	p. 132
Exercises	p. 135
Exponential Functions and Integration by Parts	p. 137
The Graph of the Logarithm Function	p. 138
Pal's Stumble and the Inverse Function	p. 138
The Exponential Function and the Professor's Amazing Income	p. 139
The Indestructible Function e[superscript x]	p. 141
Differentiation of Exponential Functions	p. 142
The Method of Logarithmic Implicit Differentiation	p. 142
The Integral of the Logarithm Function	p. 144
The Method of Integration by Parts	p. 146
Worksheet: Integration by Parts	p. 148
Exercises	p. 151
Integration by Trigonometric Substitution	p. 153
The Elliptical Rose Garden	p. 153
The Ellipse Area Integral	p. 154
Trying a Trigonometric Substitution	p. 155
The Area of the Ellipse	p. 158
The Method of Trigonometric Substitution	p. 158
Derivatives of Inverse Trigonometric Functions	p. 160
Worksheet: Integration by Trigonometric Substitution	p. 163
Exercises	p. 164
Integration by Partial Fractions	p. 167
The Red-and-Yellow Fireworks Problem	p. 169
The Integral of the Secant Function	p. 174
Worksheet: Partial Fractions	p. 175
Partial Fractions with Quadratic Denominators	p. 179
The Method of Partial Fractions	p. 185
Exercises	p. 185
Finding Volumes with Integrals	p. 190
The Pancake Method of Approximating Volume	p. 192
The Amazing Resemblance Between the Continuous Sum and the Definite Integral	p. 193
The Volume of the Paraboloid	p. 194
Finding Volumes with Cylindrical Shells	p. 197
Worksheet: Volume	p. 199
Exercises	p. 203
Arc Lengths, Surface Areas, and the Center of Mass	p. 205
The Straight-line Approximation for a Curve	p. 206
The Integral for Arc Lengths	p. 208
The Frustum Method of Finding Surface Areas	p. 213
The Center of Mass of the Concert Hall Stage	p. 215
Exercises	p. 219
Introduction to Differential Equations	p. 221
The Oscillating Ride and the Ordinary Differential Equation	p. 222
Linear Differential Equations	p. 224
The Force of Friction and the Damped Sine Wave	p. 231
Solution Method for Second-order Linear Homogeneous Constant-Coefficient Differential Equations	p. 233
The Driving Force and the Nonhomogeneous Equation	p. 234
Resonance and the Infinite Amplitude Ride	p. 240
Exercises	p. 241
Partial Derivatives and Vectors	p. 243
The Two-variable Magazine Subscription Problem	p. 243
Partial Derivatives	p. 245
The Dome	p. 246
Graphs of Functions of Two Variables	p. 247
The Gradient Vector	p. 248
The Sleigh Ride and the Falling Basket Ride	p. 250
Work, Kinetic Energy, and Potential Energy	p. 251
Describing Motion: The Position Vector as a Function of Time	p. 252
The Derivative of a Vector: Velocity	p. 254
The Dot Product of Two Vectors	p. 255
Circular Motion	p. 256
The Force Vector as the Gradient of the Potential Energy Function	p. 256
The Chain Rule for Vector Functions	p. 257
The Potential Energy for Gravity	p. 258
Exercises	p. 262
Numerical Methods, Taylor Series, and Limits	p. 268
The Problem Closet Break-in and the Gremlin's Secret Plan	p. 268
The Intractable Elliptic Integral	p. 272
The Height of the Children and the Area Under the Bell-shaped Normal Curve	p. 272
Approximating the Area with Rectangles	p. 273
Numerical Integration	p. 278
Approximating a Function with an Infinite Series of Derivatives	p. 281
Taylor Series	p. 283
Visualizing Differential Equations with Slope Fields	p. 284
The Ups and Downs of the Space Probe	p. 285
Euler's Method for Finding Numerical Solutions to Differential Equations	p. 287
The Formal Definition of Limit	p. 288
Continuous Curves	p. 289
L'Hopital's Rule for Finding Otherwise Unobtainable Limits	p. 291
Exercises	p. 293
Comprehensive Test of Calculus Problems	p. 296
The Return of the Gremlin	p. 296
The 45 Problems	p. 297
The Solutions	p. 301
Stanislavsky Guide to Calculus	p. 322
Answers to Worksheets and Exercises	p. 326
Summary of Trigonometric Formulas	p. 391
Brief Table of Integrals	p. 396
Glossary	p. 401
Index	p. 402
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