Pre-Calculus and Geometry - D. Ross (1996) WW

8/20/2019 Pre-Calculus and Geometry - D. Ross (1996) WW

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Master Math:

Pre-Calculus and Geometry

ByDebra Ross


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Copyright © 1996 by Debra Anne Ross

All rights reserved under the Pan-American and International Copyright Conventions.This book may not be reproduced, in whole or in part, in any form or by any means

electronic or mechanical, including photocopying, recording, or by any information

storage and retrieval system now known or hereafter invented, without written

permission from the publisher, The Career Press.

MASTER MATH: PRE-CALCULUS AND GEOMETRYISBN 1-56414-218-3

Cover design by The Visual GroupPrinted in the U.S.A. by Book-mart Press

Library of Congress Cataloging-in-Publication Data

Ross, Debra Anne, 1958-

Master math: pre-calculus and geometry / by Debra Anne Ross. p. cm.

Includes index.ISBN 1-56414-218-3 (pbk.)

1. Geometry. 2. Trigonometry. I. Title.

QA445.R585 1996515'.1--dc20 96-22994

CIP


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Acknowledgments

I am indebted to Dr. Melanie McNeil, Professor of Chemical Engineering at San JoseState University, for reviewing this text for accuracy.


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Table of Contents

Introduction 1

Chapter 1Geometry 3

1.1. Lines and Angles 4

1.2. Polygons 10

1.3. Triangles 13

1.4. Quadrilaterals (Four Sided Polygons)

18

1.5. Circles 22

1.6. Perimeter and Area of Planar Two-Dimensional Shapes

29


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1.7. Volume and Surface Area of Three-Dimensional Objects

34

1.8. Vectors 40

Chapter 2

Trigonometry 43

2.1. Introduction 43

2.2. General Trigonometric Functions

44

2.3. Addition, Subtraction and Multiplication of Two Angles

52

2.4. Oblique Triangles

53

2.5. Graphs of Cosine, Sine, Tangent, Secant, Cosecant and

Cotangent 54

2.6. Relationship Between Trigonometric and Exponential

Functions 58


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2.7. Hyperbolic Functions 60

Chapter 3

Sets and Functions 62

3.1. Sets 62

3.2. Functions 65

Chapter 4

Sequences, Progressions and Series

70

4.1. Sequences 70

4.2. Arithmetic Progressions

71

4.3. Geometric Progressions

73

4.4. Series 74


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4.5. Infinite Series: Convergence and Divergence

77

4.6. Tests for Convergence of Infinite Series 80

4.7. The Power Series 86

4.8. Expanding Functions into Series

88

4.9. The Binomial Expansion

92

Chapter 5Limits 94

5.1. Introduction to Limits 94

5.2. Limits and Continuity 98

Chapter 6

Introduction to the Derivative104

6.1. Definition 105


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6.2. Evaluating Derivatives 110

6.3. Differentiating Multivariable Functions

113

6.4. Differentiating Polynomials

114

6.5. Derivatives and Graphs of Functions

114

6.6. Adding and Subtracting Derivatives of Functions

118

6.7. Multiple or Repeated Derivatives of a Function

119

6.8. Derivatives of Products and powers of Functions

120

6.9. Derivatives of quotients of Functions

125

6.10. The Chain Rule for Differentiating Complicated Functions

128

6.11. Differentiation of Implicit vs. Explicit Functions

131


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6.12. Using Derivatives to Determine the Shape of the Graph of a

Function (Minimum and Maximum Points) 134

6.13. Other rules of Differentiation

142

6.14. An Application of Differentiation: Curvilinear Motion

143

Chapter 7Introduction to the Integral 146

7.1. Definition of the Antiderivative or Indefinite Integral

147

7.2. Properties of the Antiderivative or Indefinite Integral

150

7.3. Examples of Common Indefinite Integrals

152

7.4. Definition and Evaluation of the Definite Integral

153

7.5. The Integral and the Area under the Curve in Graphs of

Functions 156


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7.6. Integrals and Volume 160

7.7. Even functions, Odd Functions and Symmetry

162

7.8. Properties of the Definite Integral

164

7.9. Methods for Evaluating Complex Integrals; Integration byParts, Substitution and Tables 165


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Pre-Calculus and Geometry - D. Ross (1996) WW