Master Math

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  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2009-05-21
  • Publisher: Cengage Learning PTR
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"Master Math: Pre-Calculus and Geometry" makes the transition from algebra smooth and stress-free. This comprehensive pre-calculus book begins with the most basic fundamental principles and progresses through more advanced topics. The book covers subjects like triangles, volume, limits, derivatives, differentiation, and more in a clear, easy-to-understand manner. "Pre-Calculus and Geometry" explains the principles and operations of geometry, trigonometry, pre-calculus and introductory calculus with step-by-step procedures and solutions.

Table of Contents

Introductionp. xi
Geometryp. 1
Lines and Anglesp. 2
Polygonsp. 8
Trianglesp. 11
Quadrilaterals (Four-Sided Polygons)p. 16
Circlesp. 20
Perimeter and Area of Planar Two-Dimensional Shapesp. 26
Volume and Surface Area of Three-Dimensional Objectsp. 32
Vectorsp. 38
Trigonometryp. 41
Introductionp. 42
General Trigonometric Functionsp. 43
Addition, Subtraction, and Multiplication of Two Anglesp. 50
Oblique Trianglesp. 51
Graphs of Cosine, Sine, Tangent, Secant, Cosecant, and Cotangentp. 52
Relationship Between Trigonometric and Exponential Functionsp. 56
Hyperbolic Functionsp. 57
Sets and Functionsp. 59
Setsp. 59
Functionsp. 62
Sequences, Progressions, and Seriesp. 67
Sequencesp. 68
Arithmetic Progressionsp. 69
Geometric Progressionsp. 70
Seriesp. 71
Infinite Series: Convergence and Divergencep. 74
Tests for Convergence of Infinite Seriesp. 77
The Power Seriesp. 83
Expanding Functions into Seriesp. 84
The Binomial Expansionp. 89
Limitsp. 91
Introduction to Limitsp. 91
Limits and Continuityp. 95
Introduction to the Derivativep. 101
Definitionp. 102
Evaluating Derivativesp. 107
Differentiating Multivariable Functionsp. 109
Differentiating Polynomialsp. 110
Derivatives and Graphs of Functionsp. 110
Adding and Subtracting Derivatives of Functionsp. 113
Multiple or Repeated Derivatives of a Functionp. 114
Derivatives of Products and Powers of Functionsp. 115
Derivatives of Quotients of Functionsp. 120
The Chain Rule for Differentiating Complicated Functionsp. 122
Differentiation of Implicit vs. Explicit Functionsp. 125
Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points)p. 128
Other Rules of Differentiationp. 136
An Application of Differentiation: Curvilinear Motionp. 137
Introduction to the Integralp. 141
Definition of the Antiderivative or Indefinite Integralp. 142
Properties of the Antiderivative or Indefinite Integralp. 144
Examples of Common Indefinite Integralsp. 147
Definition and Evaluation of the Definite Integralp. 148
The Integral and the Area Under the Curve in Graphs of Functionsp. 151
Integrals and Volumep. 155
Even Functions, Odd Functions, and Symmetryp. 158
Properties of the Definite Integralp. 160
Methods for Evaluating Complex Integrals: Integration by Parts, Substitution, and Tablesp. 161
Indexp. 165
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