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Calculus the easy way
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Author
Publisher
Barron's Educational Series
Publication Date
Varies, see individual formats and editions
Language
English
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ISBN
9780764129209
9780812091410
9780812091410
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Table of Contents
From the Book - Regular Print - Fourth edition.
Chapter 1 Slope of the Tangent Line 1 --
Graph of the Train's Position 2 --
Function Machines 3 --
Slope of a Line 6 --
Slope of a Secant Line 7 --
Slope of a Tangent Line 8 --
Tangent Slope for y = x[superscript 2] 10 --
Worksheet: Slope of a Secant Line 11 --
Chapter 2 Calculating Derivatives 13 --
Definition of Derivative 14 --
Derivative of a Constant Function 15 --
Derivative of a Straight-Line Function 17 --
Derivative of y = cx[superscript 2] 18 --
Derivative of a Sum 21 --
Derivative of y = x[superscript 3] 22 --
Derivative of y = x[superscript n] 23 --
Worksheet: Derivatives of Polynomials 26 --
Chapter 3 Drawing Curves with Derivatives 31 --
Horizontal Tangents 32 --
Derivative of the Derivative 35 --
Professor's Bug and the Meaning of the Second Derivative 36 --
Concave-up and Concave-down Curves 37 --
Spilled Water 38 --
Local Maximum Points 39 --
Worksheet: Maximum and Minimum Points 40 --
Points of Inflection 41 --
Worksheet: Local Maximum and Minimum Points 42 --
Chapter 4 Derivatives of Complicated Functions 49 --
Multiplied Functions 51 --
Product Rule 55 --
Embedded Functions 55 --
Chain Rule 58 --
Fractional Exponents 58 --
Implicit Functions 59 --
Power Rule 61 --
Worksheet: The Product Rule 61 --
Chapter 5 Derivatives of Trigonometric Functions 66 --
Gremlin's Horrible Oscillating Chicken-Scaring Machine 67 --
Trigonometeris' Sine Function 68 --
Derivative of the Sine Function 73 --
Derivative of the Cosine Function 74 --
Derivatives of Other Trigonometric Functions 75 --
Worksheet: Derivatives of Trigonometric Functions 76 --
Chapter 6 Optimum Values and Related Rates 79 --
Differentiation and the Get-Rich-Quick Scheme 80 --
Optimum-size Box 81 --
Carmorra Magazine and the Optimum Subscription Price 82 --
Birthday Party Balloon 85 --
National Park Beach Lifeguard and the Racing Shadow 86 --
Chapter 7 Integral: A Backward Derivative 91 --
Recordis' Exhaustion and the Story of Rutherford 91 --
Differentiating Backwards 92 --
Antiderivative or the Integral 93 --
Discovering the Indefiniteness of an Indefinite Integral 93 --
Using an Initial Condition to Track Down Rutherford 94 --
Differentials 96 --
Integral Sign 96 --
Sum Rule for Integrals 98 --
Multiplication Rule for Integrals 99 --
Perfect Integral Rule 100 --
Power Rule for Integrals 101 --
Worksheet: Integrals of Polynomials 102 --
Worksheet: Integration by Substitution 104 --
Chapter 8 Finding Areas with Integrals 108 --
Recordis' Pools and the Magic Crystal Water Rate Increase 108 --
Summation Notation 110 --
Curve's Area Defined as a Limit 112 --
Gremlin's Terrible Fire-and-Water Threat 112 --
Mysterious Function A(x) 113 --
Derivative of A(x) 114 --
Fundamental Theorem of Integral Calculus 115 --
Discovering the Definiteness of Definite Integrals 116 --
Worksheet: Definite Integrals 117 --
Chapter 9 Natural Logarithms 122 --
Unfortunate Accident with Some Beads 123 --
Power Rule Breakdown: n = -1 124 --
Mysterious Function L(a) 125 --
Some Properties of L(a) 126 --
Substitution Method for Evaluating Definite Integrals 128 --
Remembering Logarithms 128 --
Derivative of the Logarithm Function 129 --
Fundamental Number e 130 --
Worksheet: Derivatives and Integrals with Logarithms 132 --
Chapter 10 Exponential Functions and Integration by Parts 137 --
Graph of the Logarithm Function 138 --
Pal's Stumble and the Inverse Function 138 --
Exponential Function and the Professor's Amazing Income 139 --
Indestructible Function e[superscript x] 141 --
Differentiation of Exponential Functions 142 --
Method of Logarithmic Implicit Differentiation 142 --
Integral of the Logarithm Function 144 --
Method of Integration by Parts 146 --
Worksheet: Integration by Parts 148 --
Chapter 11 Integration by Trigonometric Substitution 153 --
Elliptical Rose Garden 153 --
Ellipse Area Integral 154 --
Trying a Trigonometric Substitution 155 --
Area of the Ellipse 158 --
Method of Trigonometric Substitution 158 --
Derivatives of Inverse Trigonometric Functions 160 --
Worksheet: Integration by Trigonometric Substitution 163 --
Chapter 12 Integration by Partial Fractions 167 --
Red-and-Yellow Fireworks Problem 169 --
Integral of the Secant Function 174 --
Worksheet: Partial Fractions 175 --
Partial Fractions with Quadratic Denominators 179 --
Method of Partial Fractions 185 --
Chapter 13 Finding Volumes with Integrals 190 --
Pancake Method of Approximating Volume 192 --
Amazing Resemblance Between the Continuous Sum and the Definite Integral 193 --
Volume of the Paraboloid 194 --
Finding Volumes with Cylindrical Shells 197 --
Worksheet: Volume 199 --
Chapter 14 Arc Lengths, Surface Areas, and the Center of Mass 205 --
Straight-line Approximation for a Curve 206 --
Integral for Arc Lengths 208 --
Frustum Method of Finding Surface Areas 213 --
Center of Mass of the Concert Hall Stage 215 --
Chapter 15 Introduction to Differential Equations 221 --
Oscillating Ride and the Ordinary Differential Equation 222 --
Linear Differential Equations 224 --
Force of Friction and the Damped Sine Wave 231 --
Solution Method for Second-order Linear Homogeneous Constant-Coefficient Differential Equations 233 --
Driving Force and the Nonhomogeneous Equation 234 --
Resonance and the Infinite Amplitude Ride 240 --
Chapter 16 Partial Derivatives and Vectors 243 --
Two-variable Magazine Subscription Problem 243 --
Partial Derivatives 245 --
Dome 246 --
Graphs of Functions of Two Variables 247 --
Gradient Vector 248 --
Sleigh Ride and the Falling Basket Ride 250 --
Work, Kinetic Energy, and Potential Energy 251 --
Describing Motion: The Position Vector as a Function of Time 252 --
Derivative of a Vector: Velocity 254 --
Dot Product of Two Vectors 255 --
Circular Motion 256 --
Force Vector as the Gradient of the Potential Energy Function 256 --
Chain Rule for Vector Functions 257 --
Potential Energy for Gravity 258 --
Chapter 17 Numerical Methods, Taylor Series, and Limits 268 --
Problem Closet Break-in and the Gremlin's Secret Plan 268 --
Intractable Elliptic Integral 272 --
Height of the Children and the Area Under the Bell-shaped Normal Curve 272 --
Approximating the Area with Rectangles 273 --
Numerical Integration 278 --
Approximating a Function with an Infinite Series of Derivatives 281 --
Taylor Series 283 --
Visualizing Differential Equations with Slope Fields 284 --
Ups and Downs of the Space Probe 285 --
Euler's Method for Finding Numerical Solutions to Differential Equations 287 --
Formal Definition of Limit 288 --
Continuous Curves 289 --
L'Hopital's Rule for Finding Otherwise Unobtainable Limits 291 --
Chapter 18 Comprehensive Test of Calculus Problems 296 --
Return of the Gremlin 296 --
Chapter 19 Stanislavsky Guide to Calculus 322 --
Appendix 1 Answers to Worksheets and Exercises 326 --
Appendix 2 Summary of Trigonometric Formulas 391 --
Appendix 3 Brief Table of Integrals 396.
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