Precalculus - 1st Edition - ISBN: 9780124178946, 9781483265070

Precalculus

1st Edition

Functions & Graphs

Authors: Bernard Kolman Arnold Shapiro
eBook ISBN: 9781483265070
Imprint: Academic Press
Published Date: 1st January 1984
Page Count: 637
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Description

Precalculus: Functions & Graphs provides a complete and self-contained presentation of the basic mathematical techniques and ideas required for the successful completion of a calculus course.

The book emphasizes the learning and understanding of the concept of a function, using function notation, and being able to sketch graphs of functions with ease. The text employs a number of pedagogic devices that have been proven effective in teaching college mathematics. The mathematical concepts are presented in a style that is informal, supportive, and "user-friendly". Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appr

This textbook is intended for college students.

Table of Contents


Preface

Acknowledgments

To the Student

Chapter 1 The Foundations of Algebra

1.1 The Real Number System

1.2 Polynomials and Factoring

1.3 Exponents, Radicals, and Complex Numbers

1.4 Linear Equations and Linear Inequalities in One Unknown

1.5 Absolute Value in Equations and Inequalities

1.6 Second-Degree Inequalities

Chapter 2 Functions and Graphs

2.1 The Rectangular Coordinate System

2.2 Functions and Function Notation

2.3 Graphs of Functions

2.4 Aids in Graphing

2.5 Linear Functions

2.6 Quadratic Equations

2.7 Quadratic Functions

2.8 Combining Functions; Inverse Functions

Chapter 3 Roots of Polynomials

3.1 Synthetic Division; The Remainder and Factor Theorems

3.2 Graphs of Polynomial Functions

3.3 The Rational Root Theorem and the Depressed Equation

3.4 Rational Functions and Their Graphs

3.5 Partial Fractions

Chapter 4 Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Fundamental Properties of Logarithms

4.4 Computing with Logarithms (Optional)

4.5 Exponential and Logarithmic Equations

Chapter 5 Trigonometry: The Circular Functions

5.0 Review of Geometry

5.1 The Wrapping Function

5.2 The Sine, Cosine, and Tangent Functions

5.3 Graphs of Sine, Cosine, and Tangent

5.4 Values of Sine, Cosine, and Tangent

5.5 Graphs: Amplitude, Period, and Phase Shift

5.6 Secant, Cosecant, and Cotangent

5.7 The Inverse Trigonometric Functions

Chapter 6 Angles and Triangles

6.1 Angles and Their Measurement

6.2 Trigonometric Functions of Angles

6.3 Right Triangle Trigonometry

6.4 Law of Cosines

6.5 Law of Sines

Chapter 7 Analytic Trigonometry

7.1 Trigonometric Identities

7.2 The Addition Formulas

7.3 Double- and Half-Angle Formulas

7.4 The Product-Sum Formulas

7.5 Trigonometric Equations

Chapter 8 Complex Numbers and the Fundamental Theorem of Algebra

8.1 Complex Numbers and Their Properties

8.2 Trigonometry and Complex Numbers

8.3 The Fundamental Theorem of Algebra

8.4 Descartes's Rule of Signs

Chapter 9 Analytic Geometry: The Conic Sections

9.1 Analytic Geometry

9.2 The Circle

9.3 The Parabola

9.4 The Ellipse

9.5 The Hyperbola

9.6 Translation of Axes

9.7 Rotation of Axes

9.8 Polar Coordinates

9.9 Parametric Equations

Chapter 10 Systems of Equations and Inequalities

10.1 Systems of Equations

10.2 Systems of Linear Inequalities

10.3 Linear Programming (Optional)

10.4 Systems of Linear Equations in Three Unknowns

10.5 Matrices and Linear Systems

10.6 Matrix Operations and Applications (Optional)

10.7 Inverses of Matrices (Optional)

10.8 Determinants and Cramer's Rule

Chapter 11 Sequences and Series

11.1 Sequences and Sigma Notation

11.2 Arithmetic Sequences

11.3 Geometric Sequences

11.4 Mathematical Induction

11.5 The Binomial Theorem

Appendix A. Applications

Appendix B. Limits: A Preview of Calculus

Tables Appendix

Answers to Odd-Numbered Exercises and to Review Exercises and Progress Tests

Solutions to Selected Review Exercises

Index

Details

No. of pages:
637
Language:
English
Copyright:
© Academic Press 1984
Published:
Imprint:
Academic Press
eBook ISBN:
9781483265070

About the Author

Bernard Kolman

Affiliations and Expertise

Drexel University

Arnold Shapiro