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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:
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
Anonymous
Posted November 8, 2007
This is the best book on learning basic algebra. It is thorough yet concise. The information is presented very clearly. The author has obviously tried to explain the concepts so that they `make sense¿ to students - and their parents. I use the book to explain algebra to my students. Like the other Master Math books by Ross, the topics flow logically and build in difficulty. What a breath of fresh air after the often confusing text books students are given in school. This book is helpful for students struggling with algebra and the parents who are tutoring them. This book is also extremely useful for older students who did not adequately learn algebra, yet find they need to know it later. Topics can easily be looked up and reviewed or learned. I highy recommend this book!
5 out of 7 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Log-IC
Posted October 10, 2009
Splendid clarity and progression.
A cherry on top of this fine sundae,
maybe a single page of exponential,
radical,and complex properties for
a quick reference,( but that's nitpicking).
3 out of 5 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted November 20, 2007
This is the best book out there on learning trigonometry. I especially appreciate the visually-oriented focus. Each concept is described in all its forms, such as sine. Do you know each of the different ways sine can be described? Like the other Master Math books by Ross, the topics flow logically and are in context with what precedes and follows. It is thorough yet concise, and packed full of everything you, as tutor, or your kids need to know. The real world and fun applications are wonderful! The information is explained clearly and in a way that makes sense, so that a given concept is explained in such a way you understand what is being discussed rather than just memorizing formulas. What a breath of fresh air after the often confusing text books I was and my children are given in school. I really feel I can explain trigonometry to young people using this book! if I were going back to school, and taking math or science, this book would be in my backpack.
3 out of 5 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted November 21, 2012
i am not sure if i am missing something but on page 14 the book says x times $1.00 per glass will equal 20. then shows this equation
X + ($1.00 per glass)=$20.00
1 out of 1 people found this review helpful.
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Posted February 12, 2012
This book is terrible. There are many books that are better. I found websites more helpful.
1 out of 3 people found this review helpful.
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Overview
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 ...