Master Math: Pre-Calculus: Pre-Calculus

by Debra Anne Ross

Overview

From the Author

Introduction to Master Math: Pre-Calculus and Geometry: Pre-Calculus and Geometry is the third book in the Master Math series. The first and second books are entitled Basic Math and Pre-Algebra and Algebra, and the fourth book is entitled Calculus. The Master Math series presents the general principles of mathematics from grade school through college including arithmetic, algebra, geometry, trigonometry, pre-calculus and introductory calculus. Pre-Calculus and Geometry is a comprehensive pre-calculus book that explains the subject matter in a way that makes sense to the reader. It begins with the most basic principles and progresses through more advanced topics. Pre-Calculus and Geometry explains the principles and operations of geometry, trigonometry, pre-calculus and introductory calculus, provides step-by-step procedures and solutions, and presents examples and applications. Pre-Calculus and Geometry is a comprehensive reference book for high school and college students that explains and clarifies principles of pre-calculus and calculus they are learning in school. The information provided in each book and in the series as a whole is progressive in difficulty and builds on itself, which allows the reader to gain perspective on the connected nature of mathematics. The skills required to understand every topic presented are explained in an earlier chapter or book within the series. Each of the first three books contains a complete table of contents, a comprehensive index, and the tables of con-tents of the other two books in the series so that specific subjects, principles and formulas can be easily found. The books are written in a simple style that facilitates understanding and easy referencing of sought-after principles, definitions and explanations. Pre-Calculus and Geometry and the Master Math series are not replacements for textbooks but rather reference books providing explanations and perspective. The Master Math series would have been in-valuable to me during my entire education from grade school through graduate school. There is no other source that provides the breadth and depth of the Master Math series in a single book or series. Finally, mathematics is a language-the universal language. A person struggling with mathematics should approach it in the same fashion he or she would approach learning any other language. If someone moves to a foreign country, he or she does not expect to know the language automatically. It takes practice and contact with a language in order to master it. After a short time in the foreign country he or she would not say, 'I do not know this language well yet. I must not have an aptitude for it.' Yet many people have this attitude toward mathematics. If time is spent learning and practicing the principles, mathematics will be-come familiar and understandable. Don't give up.

Debra Ross, the author, February 16, 1999 Note to the reader:
There are three misprints in books from the first printing:

1. The definition of Pi on page 23. Pi is equivalent to the circumference divided by the diameter of a circle (not the radius of a circle).
2. The equation for the volume of a pyramid on page 40. The equation should read: Volume of a pyramid = (1/3)(area of base)(height) = (1/3)(area of base)(d) The (1/3) was left out.
3. The third line on page 79 should read ...'then r^m -> 0'.

Product Details

ISBN-13:	9781435455146
Publisher:	Course Technology PTR
Publication date:	01/05/2009
Series:	Master Math
Sold by:	CENGAGE LEARNING
Format:	eBook
File size:	3 MB

About the Author

Debra Anne Ross has a double BA in Chemistry and Biology from the University of California, Santa Cruz, and and MS in Chemical Engineering from Stanford University. Debra's career encompasses biology, chemistry, biochemistry, engineering, biosensors, pharmaceutical drug discovery, and intellectual property. She is the author of the popular Master Math books, The 3:00 PM Secret: Live Slim and Strong Live Your Dreams, The 3:00 PM Secret: Ten Day Dream Diet (2009), and Arrows Through Time: A Time Travel Tale of Adventure, Courage, and Faith (2009).

Table of Contents

Introduction xi

Chapter 1 Geometry 1

1.1 Lines and Angles 2

1.2 Polygons 8

1.3 Triangles 11

1.4 Quadrilaterals (Four-Sided Polygons) 16

1.5 Circles 20

1.6 Perimeter and Area of Planar Two-Dimensional Shapes 26

1.7 Volume and Surface Area of Three-Dimensional Objects 32

1.8 Vectors 38

Chapter 2 Trigonometry 41

2.1 Introduction 42

2.2 General Trigonometric Functions 43

2.3 Addition, Subtraction, and Multiplication of Two Angles 50

2.4 Oblique Triangles 51

2.5 Graphs of Cosine, Sine, Tangent, Secant, Cosecant, and Cotangent 52

2.6 Relationship Between Trigonometric and Exponential Functions 56

2.7 Hyperbolic Functions 57

Chapter 3 Sets and Functions 59

3.1 Sets 59

3.2 Functions 62

Chapter 4 Sequences, Progressions, and Series 67

4.1 Sequences 68

4.2 Arithmetic Progressions 69

4.3 Geometric Progressions 70

4.4 Series 71

4.5 Infinite Series: Convergence and Divergence 74

4.6 Tests for Convergence of Infinite Series 77

4.7 The Power Series 83

4.8 Expanding Functions into Series 84

4.9 The Binomial Expansion 89

Chapter 5 Limits 91

5.1 Introduction to Limits 91

5.2 Limits and Continuity 95

Chapter 6 Introduction to the Derivative 101

6.1 Definition 102

6.2 Evaluating Derivatives 107

6.3 Differentiating Multivariable Functions 109

6.4 Differentiating Polynomials 110

6.5 Derivatives and Graphs of Functions 110

6.6 Adding and Subtracting Derivatives of Functions 113

6.7 Multiple or Repeated Derivatives of a Function 114

6.8 Derivatives of Products and Powers of Functions 115

6.9 Derivatives of Quotients of Functions 120

6.10 The Chain Rule for Differentiating Complicated Functions 122

6.11 Differentiationof Implicit vs. Explicit Functions 125

6.12 Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points) 128

6.13 Other Rules of Differentiation 136

6.14 An Application of Differentiation: Curvilinear Motion 137

Chapter 7 Introduction to the Integral 141

7.1 Definition of the Antiderivative or Indefinite Integral 142

7.2 Properties of the Antiderivative or Indefinite Integral 144

7.3 Examples of Common Indefinite Integrals 147

7.4 Definition and Evaluation of the Definite Integral 148

7.5 The Integral and the Area Under the Curve in Graphs of Functions 151

7.6 Integrals and Volume 155

7.7 Even Functions, Odd Functions, and Symmetry 158

7.8 Properties of the Definite Integral 160

7.9 Methods for Evaluating Complex Integrals: Integration by Parts, Substitution, and Tables 161

Index 165