Page 8 - Calculus Demystified

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CONTENTS

Preface xi

CHAPTER 1 Basics 1

1.0 Introductory Remarks 1
1.1 Number Systems 1
1.2 Coordinates in One Dimension 3
1.3 Coordinates in Two Dimensions 5
1.4 The Slope of a Line in the Plane 8
1.5 The Equation of a Line 13
1.6 Loci in the Plane 15
1.7 Trigonometry 19
1.8 Sets and Functions 30
1.8.1 Examples of Functions of a Real Variable 31
1.8.2 Graphs of Functions 33
1.8.3 Plotting the Graph of a Function 35
1.8.4 Composition of Functions 40
1.8.5 The Inverse of a Function 42
1.9 A Few Words About Logarithms and Exponentials 49

CHAPTER 2 Foundations of Calculus 57

2.1 Limits 57
2.1.1 One-Sided Limits 60
2.2 Properties of Limits 61
2.3 Continuity 64
2.4 The Derivative 66
2.5 Rules for Calculating Derivatives 71
2.5.1 The Derivative of an Inverse 76
2.6 The Derivative as a Rate of Change 76

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