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Produktbild: Calculus Essentials For Dummies
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Calculus Essentials For Dummies 2nd Edition

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

14.06.2019

Verlag

Wiley

Seitenzahl

192

Maße (L/B/H)

21,2/13,7/1,2 cm

Gewicht

242 g

Sprache

Englisch

ISBN

978-1-119-59120-7

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

14.06.2019

Verlag

Wiley

Seitenzahl

192

Maße (L/B/H)

21,2/13,7/1,2 cm

Gewicht

242 g

Sprache

Englisch

ISBN

978-1-119-59120-7

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Calculus Essentials For Dummies

  • Introduction 1

    About This Book 1

    Conventions Used in This Book 2

    Foolish Assumptions 2

    Icons Used in This Book 3

    Where to Go from Here 3

    Chapter 1: Calculus: No Big Deal 5

    So What is Calculus Already? 5

    Real-World Examples of Calculus 7

    Differentiation 8

    Integration 9

    Why Calculus Works 11

    Limits: Math microscopes 11

    What happens when you zoom in 12

    Chapter 2: Limits and Continuity 15

    Taking it to the Limit 15

    Three functions with one limit 15

    One-sided limits 17

    Limits and vertical asymptotes 18

    Limits and horizontal asymptotes 18

    Instantaneous speed 19

    Limits and Continuity 21

    The hole exception 22

    Chapter 3: Evaluating Limits 25

    Easy Limits 25

    Limits to memorize 25

    Plug-and-chug limits 26

    "Real" Limit Problems 26

    Factoring 27

    Conjugate multiplication 27

    Miscellaneous algebra 28

    Limits at Infinity 29

    Horizontal asymptotes 30

    Solving limits at infinity 31

    Chapter 4: Differentiation Orientation 33

    The Derivative: It's Just Slope 34

    The slope of a line 35

    The derivative of a line 36

    The Derivative: It's Just a Rate 36

    Calculus on the playground 36

    The rate-slope connection 38

    The Derivative of a Curve 39

    The Difference Quotient 40

    Average and Instantaneous Rate 46

    Three Cases Where the Derivative Does Not Exist 47

    Chapter 5: Differentiation Rules 49

    Basic Differentiation Rules 49

    The constant rule 49

    The power rule 49

    The constant multiple rule 50

    The sum and difference rules 51

    Differentiating trig functions 52

    Exponential and logarithmic functions 52

    Derivative Rules for Experts 53

    The product and quotient rules 53

    The chain rule 54

    Differentiating Implicitly 59

    Chapter 6: Differentiation and the Shape of Curves 61

    A Calculus Road Trip 61

    Local Extrema 63

    Finding the critical numbers 63

    The First Derivative Test 65

    The Second Derivative Test 66

    Finding Absolute Extrema on a Closed Interval 69

    Finding Absolute Extrema over a Function's Entire Domain 71

    Concavity and Inflection Points 73

    Graphs of Derivatives 75

    The Mean Value Theorem 78

    Chapter 7: Differentiation Problems 81

    Optimization Problems 81

    The maximum area of a corral 81

    Position, Velocity, and Acceleration 83

    Velocity versus speed 84

    Maximum and minimum height 86

    Velocity and displacement 87

    Speed and distance travelled 88

    Acceleration 89

    Tying it all together 90

    Related Rates 91

    A calculus crossroads 91

    Filling up a trough 94

    Linear Approximation 97

    Chapter 8: Introduction to Integration 101

    Integration: Just Fancy Addition 101

    Finding the Area under a Curve 103

    Dealing with negative area 105

    Approximating Area 105

    Approximating area with left sums 105

    Approximating area with right sums 108

    Approximating area with midpoint sums 110

    Summation Notation 112

    Summing up the basics 112

    Writing Riemann sums with sigma notation 113

    Finding Exact Area with the Definite Integral 116

    Chapter 9: Integration: Backwards Differentiation 119

    Antidifferentiation: Reverse Differentiation 119

    The Annoying Area Function 121

    The Fundamental Theorem 124

    Fundamental Theorem: Take Two 126

    Antiderivatives: Basic Techniques 128

    Reverse rules 128

    Guess and check 130

    Substitution 132

    Chapter 10: Integration for Experts 137

    Integration by Parts 137

    Picking your u 139

    Tricky Trig Integrals 141

    Sines and cosines 141

    Secants and tangents 144

    Cosecants and cotangents 147

    Trigonometric Substitution 147

    Case 1: Tangents 148

    Case 2: Sines 150

    Case 3: Secants 151

    Partial Fractions 152

    Case 1: The denominator contains only linear factors 152

    Case 2: The denominator contains unfactorable quadratic factors 153

    Case 3: The denominator contains repeated factors 155

    Equating coefficients 155

    Chapter 11: Using the Integral to Solve Problems 157

    The Mean Value Theorem for Integrals and Average Value 158

    The Area between Two Curves 160

    Volumes of Weird Solids 162

    The meat-slicer method 162

    The disk method 163

    The washer method 165

    The matryoshka doll method 166

    Arc Length 168

    Improper Integrals 171

    Improper integrals with vertical asymptotes 171

    Improper integrals with infinite limits of integration 173

    Chapter 12: Eight Things to Remember 175

    a2- b2 = (a - b)(a + b) 175

    0/5 = 0 But 5/0 is Undefined 175

    SohCahToa 175

    Trig Values to Know 176

    sin2¿ + cos2¿ = 1 176

    The Product Rule 176

    The Quotient Rule 176

    Your Sunglasses 176

    Index 177