Master Math

by Ross, Debra Anne

• ISBN13: 9781598639810
• ISBN10: 1598639811
• Format: Paperback
• Copyright: 2009-05-21
• Publisher: Cengage Learning PTR

Summary

"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

Introduction	p. xi
Geometry	p. 1
Lines and Angles	p. 2
Polygons	p. 8
Triangles	p. 11
Quadrilaterals (Four-Sided Polygons)	p. 16
Circles	p. 20
Perimeter and Area of Planar Two-Dimensional Shapes	p. 26
Volume and Surface Area of Three-Dimensional Objects	p. 32
Vectors	p. 38
Trigonometry	p. 41
Introduction	p. 42
General Trigonometric Functions	p. 43
Addition, Subtraction, and Multiplication of Two Angles	p. 50
Oblique Triangles	p. 51
Graphs of Cosine, Sine, Tangent, Secant, Cosecant, and Cotangent	p. 52
Relationship Between Trigonometric and Exponential Functions	p. 56
Hyperbolic Functions	p. 57
Sets and Functions	p. 59
Sets	p. 59
Functions	p. 62
Sequences, Progressions, and Series	p. 67
Sequences	p. 68
Arithmetic Progressions	p. 69
Geometric Progressions	p. 70
Series	p. 71
Infinite Series: Convergence and Divergence	p. 74
Tests for Convergence of Infinite Series	p. 77
The Power Series	p. 83
Expanding Functions into Series	p. 84
The Binomial Expansion	p. 89
Limits	p. 91
Introduction to Limits	p. 91
Limits and Continuity	p. 95
Introduction to the Derivative	p. 101
Definition	p. 102
Evaluating Derivatives	p. 107
Differentiating Multivariable Functions	p. 109
Differentiating Polynomials	p. 110
Derivatives and Graphs of Functions	p. 110
Adding and Subtracting Derivatives of Functions	p. 113
Multiple or Repeated Derivatives of a Function	p. 114
Derivatives of Products and Powers of Functions	p. 115
Derivatives of Quotients of Functions	p. 120
The Chain Rule for Differentiating Complicated Functions	p. 122
Differentiation of Implicit vs. Explicit Functions	p. 125
Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points)	p. 128
Other Rules of Differentiation	p. 136
An Application of Differentiation: Curvilinear Motion	p. 137
Introduction to the Integral	p. 141
Definition of the Antiderivative or Indefinite Integral	p. 142
Properties of the Antiderivative or Indefinite Integral	p. 144
Examples of Common Indefinite Integrals	p. 147
Definition and Evaluation of the Definite Integral	p. 148
The Integral and the Area Under the Curve in Graphs of Functions	p. 151
Integrals and Volume	p. 155
Even Functions, Odd Functions, and Symmetry	p. 158
Properties of the Definite Integral	p. 160
Methods for Evaluating Complex Integrals: Integration by Parts, Substitution, and Tables	p. 161
Index	p. 165
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