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These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their text addresses three critical issues in teaching precalculus: poor student preparation, the need for thoughtful integration of the graphing calculator, and poor student study skills. Their texts have a strong reputation built on mathematically sound presentation, excellent applications, and on challenging students to develop algebraic, graphical, and verbal mathematical skills. Goodman and Hirsch help students go beyond the mechanics of mathematics to developing a coherent strategy to solving problems.

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Book details

List price: $318.95 Edition: 2nd Copyright year: 2004 Publisher: Brooks/Cole Publication date: 10/17/2003 Binding: Hardcover Pages: 975 Size: 8.50" wide x 9.75" long x 1.50" tall Weight: 4.4 Language: English

AuthorTable of Contents

Dr. Arthur Goodman (Ph.D., Yeshiva University) currently teaches in the mathematics department at Queens College of the City University of New York. Dr. Goodman takes great pride in the mathematical accuracy and in depth explanation in all of his textbooks.

Lewis Hirsch (Ph.D., Pennsylvania State University) currently teaches in the mathematics department at Rutgers University. Dr. Hirsch teaches both developmental mathematics and higher level courses such as college algebra and pre-calculus. His experiences in the classroom make him committed to properly preparing students in lower-level courses so they can succeed in for credit courses, and this is reflected in the way he writes his textbooks.

Preface

Algebra: The Fundamentals

The Real Numbers

Different Perspectives: Inequalities

Operations with Real Numbers

Polynomials and Rational Expressions

Exponents and Radicals

The Complex Numbers

First-Degree Equations and Inequalities in One Variable

Absolute Value Equations and Inequalities

Different Perspectives: Absolute Value Equations and Inequalities

Quadratic Equations and Equations in Quadratic Form

Quadratic and Rational Inequalities

Substitution

Review Exercises

Practice Test

Functions and Graphs: Part I

The Cartesian Coordinate System: Graphing Straight Lines and Circles

Different Perspectives: The Graph of an Equation

Different Perspectives: Intercepts

Slope

Equations of a Line

Technology Corner

Relations and Functions

Different Perspectives: Representing Relations

Different Perspectives: Functions

Function Notation

Different Perspectives: Function Notation

Relating Functions to Their Graphs

Different Perspectives: Solving f(x) = k

Different Perspectives: The Zeros of a Function

Different Perspectives: Solving Inequalities

Introduction to Graph Sketching: Symmetry

Different Perspectives: Symmetry

Summary

Review Exercises

Practice Test

Functions and Graphs: Part II

Basic Graphing Principles

Different Perspectives: The Vertical Shift Principle

Different Perspectives: The Horizontal Shift Principle

Technology Corner

More Graphing Principles: Types of Functions

Extracting Functions from Real-Life Situations

Quadratic Functions

Operations on Functions

Technology Corner

Inverse Functions

Different Perspectives: One-to-One Functions

Summary

Review Exercises

Practice Test

Polynomial, Rational, and Radical Functions

Polynomial Functions

Different Perspectives: End Behavior

More on Polynomial Functions and Mathematical Models

Polynomial Division, Roots of Polynomial Equations: The Remainder and Factor Theorems

Roots of Polynomial Equations (continued): The Rational Root Theorem and Descartes' Rule of Signs

Rational Functions

Radical Functions

Variation

Summary

Review Exercises

Practice Test

Exponential and Logarithmic Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithms; Logarithmic Equations

Common and Natural Logarithms; Exponential Equations and Change of Base

Applications

Summary

Review Exercises

Practice Test

Interim Review 1 (Chapters 1-5)

Trigonometry

Angle Measurement and Two Special Triangles

Technology Corner

The Trigonometric Functions

Right-Triangle Trigonometry and Applications

The Trigonometric Functions as Functions of Real Numbers

Summary

Review Exercises

Practice Test

The Trigonometric Functions

The Sine and Cosine Functions and Their Graphs

The Tangent, Secant, Cosecant, and Cotangent Functions

Basic Identities

Trigonometric Equations

Different Perspectives: Trigonometric Equations

The Inverse Trigonometric Functions

Summary

Review Exercises

Practice Test

More Trigonometry and Its Applications

The Addition Formulas

The Double-Angle and Half-Angle Formulas

The Law of Sines and the Law of Cosines

Vectors

The Trigonometric Form of Complex Numbers and DeMoivre's Theorem

Polar Coordinates

Summary

Review Exercises

Practice Test

Interim Review 2 (Chapters 6-8)

Systems of Linear Equations and Inequalities

2 x 2 Linear Systems: Elimination and Substitution

3 x 3 Linear Systems: Elimination and Gaussian Elimination

Solving Linear Systems Using Augmented Matrices

The Algebra of Matrices

Solving Linear Systems Using Matrix Inverses

Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems

Properties of Determinants

Systems of Linear Inequalities

An Introduction to Linear Programming: Geometric Solutions

Summary

Review Exercises

Practice Test

Conic Sections and Nonlinear Systems

Conic Sections: Circles

The Parabola

The Ellipse

Different Perspectives: Eccentricity

The Hyperbola

Identifying Conic Sections: Degenerate Forms

Translations and Rotations of Coordinate Axes

Nonlinear Systems of Equations and Inequalities

Summary

Review Exercises

Practice Test

Sequences, Series, and Related Topics

Sequences

Series and Sigma Notation

Arithmetic Sequences and Series

Geometric Sequences and Series

Mathematical Induction

Permutations and Combinations

The Binomial Theorem

Summary

Review Exercises

Practice Test

Using Technology to Model Data

Answers to Selected Exercises

Index of Applications

Index

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