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by Arthur Goodman and Lewis Hirsch

Cover type: HardbackEdition: 2ND 04

Copyright: 2004

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

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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.

** Benefits: **

- A full four-color presentation provides a crisp, elegant enhancement to the text's pedagogical features, such as the Different Perspectives, Calculator Exploration, and Technology Corner boxes.
- Every new copy of this text is packaged with our suite of online, customizable technology services, giving your students dynamic, flexible online tutorial resources at their fingertips. By entering a PIN code packaged with their textbook, students gain access to text-specific tutorials with step-by-step explanations, exercises and quizzes, and vMentor--live, one-on-one help from an experienced mathematics tutor. For instructors, we offer highly customizable testing, course management, and diagnostic online resources that provide a dynamic way to power your course.
- Our student mastery system also includes the Interactive Video Skillbuilder CD-ROM. Think of it as portable office hours! Free with every copy of this text, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction.
- In addition to robust tutorial services, your students also receive anytime, anywhere access to InfoTrac College Edition. This online library offers the full text of articles from almost 4000 scholarly and popular publications, updated daily and going back as much as 22 years. Both adopters and their students receive unlimited access for four months.
- Functions and Graphs are covered in great depth in Chapters 2 and 3. Section 2.6 is devoted to the interpretation of graphs.
- Different Perspectives boxes appear wherever there is an opportunity to highlight the connection between the algebraic and graphical interpretation of the same idea.
- Applications and Mathematical Modeling are integrated throughout the text. Modeling is introduced in its own section 3.3 with a special concentration of modeling problems in chapters 3, 4, and 5. These sections provide practice in skills necessary for calculus.
- Problem Analysis is presented in a question and answer format that walks students through the process of setting up and solving problems.
- Margin Comments ask questions that help students check their understanding and provide tips to pace the reading of the material.
- Technology Corner boxes have been added to enhance the student's appreciation of the graphing calculator as a technological device and learning aid.
- The margin comments have been expanded to further encourage students to be active learners as they read the text.
- Many examples and exercises have been revised and updated to make them more current.
- The Problem Analysis approach has been applied to additional examples to allow students more opportunities to see how a mathematical problem is approached and analyzed.
- Two interim reviews have been inserted. The first contains exercises covering the material in Chapter 1 through 5, with an emphasis on those topics most critical to being successful in calculus. The second appears after Chapter 8 and consists of exercises that review the trigonometric concepts that are most frequently encountered in calculus.
- New, realistic application problems give students an idea of how the material they are learning can be applied to real situations.
- Greater integration of modeling throughout the text.
- Found in the ANNOTATED INSTRUCTOR'S EDITION, the NEW RESOURCE INTEGRATION GUIDE makes this text eminently teachable by offering a chapter-by-chapter glimpse of how the supplements support the learning system in the text, reducing the time-consuming task of choosing activities or graphing calculator exercises and directing students to valuable study aids.

1. ALGEBRA: THE FUNDAMENTALS.

The Real Numbers.

Operations with Real Numbers.

Polynomials and Rational Expressions.

Exponents and Radicals.

The Complex Numbers.

First-Degree Equations and Inequalities to One Variable.

Absolute Value Equations and Inequalities.

Quadratic Equations and Equations in Quadratic Form.

Quadratic and Rational Inequalities.

Substitution.

Chapter Summary.

Review Exercises.

Practice Test.

2. FUNCTIONS AND GRAPHS: PART I.

The Cartesian Coordinate System: Graphing Straight Lines Functions and Circles.

Slope.

Equations of a Line.

Relations and Functions.

Function Notation.

Relating Equations to Their Graphs.

Introduction to Graph Sketching: Symmetry.

Chapter Summary.

Review Exercises.

Practice Test.

3. FUNCTIONS AND GRAPHS: PART II.

Basic Graphing Principles.

More Graphing Principles: Types of Functions.

Mathematical Modeling: Extracting Functions from Real-Life Situations.

Quadratic Functions.

Operations in Functions.

Inverse Functions.

Chapter Summary.

Review Exercises.

Practice Test.

4. POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS.

Polynomial Functions.

More Polynomial Functions and Mathematical Models.

Polynomial Division, Roots of Polynomials; The Remainder and Factor Theorems.

More on Roots of Polynomial Equations; The Rational Root Theorem and Descartes's Rule of Signs.

Radical Functions.

Variation.

Chapter Summary.

Review Exercises.

Practice Test.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions.

Logarithmic Functions.

Properties of Logarithms: Logarithmic Equations.

Common and Natural Logarithms: Exponential Equations and Change of Base.

Applications.

Chapter Summary.

Review Exercises.

Practice.

6. TRIGONOMETRY.

Angle Measurement and Two Special Triangles.

The Trigonometric Functions of a General Angle.

Right Triangle Trigonometry and Applications.

The Trigonometric Functions as Functions of Real Numbers.

Chapter Summary.

Review Exercises.

Practice Test.

7. THE TRIGONOMETRIC FUNCTIONS.

The Sine and Cosine Functions and Their Graphs.

The Tangent, Secant, Cosecant, and Contangent Functions and Their Graphs.

Basic Identities.

Trigonometric Equations.

The Inverse Trigonometric Functions.

Chapter Summary.

Review Exercises.

Practice Test.

8. 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.

Chapter Summary.

Review Exercises.

Practice Test.

9. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.

Elimination and Substitution: 2 X 2 Linear Systems.

Elimination and Gaussian Elimination: 3 X 3 Linear Systems.

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.

Chapter Summary. Review Exercises.

Practice Test.

10. CONIC SECTIONS.

Conic Sections: Circles.

The Parabola. The Ellipse.

The Hyperbola.

Identifying Conic Sections: Degenerate Forms.

Translations and Rotations of Coordinate Axes.

Nonlinear Systems of Equations and Inequalities.

Chapter Summary.

Review Exercises.

Practice Test.

11. SEQUENCE, 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.

Chapter Summary.

Review Exercises.

Practice Test.

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Summary

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.

** Benefits: **

- A full four-color presentation provides a crisp, elegant enhancement to the text's pedagogical features, such as the Different Perspectives, Calculator Exploration, and Technology Corner boxes.
- Every new copy of this text is packaged with our suite of online, customizable technology services, giving your students dynamic, flexible online tutorial resources at their fingertips. By entering a PIN code packaged with their textbook, students gain access to text-specific tutorials with step-by-step explanations, exercises and quizzes, and vMentor--live, one-on-one help from an experienced mathematics tutor. For instructors, we offer highly customizable testing, course management, and diagnostic online resources that provide a dynamic way to power your course.
- Our student mastery system also includes the Interactive Video Skillbuilder CD-ROM. Think of it as portable office hours! Free with every copy of this text, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction.
- In addition to robust tutorial services, your students also receive anytime, anywhere access to InfoTrac College Edition. This online library offers the full text of articles from almost 4000 scholarly and popular publications, updated daily and going back as much as 22 years. Both adopters and their students receive unlimited access for four months.
- Functions and Graphs are covered in great depth in Chapters 2 and 3. Section 2.6 is devoted to the interpretation of graphs.
- Different Perspectives boxes appear wherever there is an opportunity to highlight the connection between the algebraic and graphical interpretation of the same idea.
- Applications and Mathematical Modeling are integrated throughout the text. Modeling is introduced in its own section 3.3 with a special concentration of modeling problems in chapters 3, 4, and 5. These sections provide practice in skills necessary for calculus.
- Problem Analysis is presented in a question and answer format that walks students through the process of setting up and solving problems.
- Margin Comments ask questions that help students check their understanding and provide tips to pace the reading of the material.
- Technology Corner boxes have been added to enhance the student's appreciation of the graphing calculator as a technological device and learning aid.
- The margin comments have been expanded to further encourage students to be active learners as they read the text.
- Many examples and exercises have been revised and updated to make them more current.
- The Problem Analysis approach has been applied to additional examples to allow students more opportunities to see how a mathematical problem is approached and analyzed.
- Two interim reviews have been inserted. The first contains exercises covering the material in Chapter 1 through 5, with an emphasis on those topics most critical to being successful in calculus. The second appears after Chapter 8 and consists of exercises that review the trigonometric concepts that are most frequently encountered in calculus.
- New, realistic application problems give students an idea of how the material they are learning can be applied to real situations.
- Greater integration of modeling throughout the text.
- Found in the ANNOTATED INSTRUCTOR'S EDITION, the NEW RESOURCE INTEGRATION GUIDE makes this text eminently teachable by offering a chapter-by-chapter glimpse of how the supplements support the learning system in the text, reducing the time-consuming task of choosing activities or graphing calculator exercises and directing students to valuable study aids.

Table of Contents

1. ALGEBRA: THE FUNDAMENTALS.

The Real Numbers.

Operations with Real Numbers.

Polynomials and Rational Expressions.

Exponents and Radicals.

The Complex Numbers.

First-Degree Equations and Inequalities to One Variable.

Absolute Value Equations and Inequalities.

Quadratic Equations and Equations in Quadratic Form.

Quadratic and Rational Inequalities.

Substitution.

Chapter Summary.

Review Exercises.

Practice Test.

2. FUNCTIONS AND GRAPHS: PART I.

The Cartesian Coordinate System: Graphing Straight Lines Functions and Circles.

Slope.

Equations of a Line.

Relations and Functions.

Function Notation.

Relating Equations to Their Graphs.

Introduction to Graph Sketching: Symmetry.

Chapter Summary.

Review Exercises.

Practice Test.

3. FUNCTIONS AND GRAPHS: PART II.

Basic Graphing Principles.

More Graphing Principles: Types of Functions.

Mathematical Modeling: Extracting Functions from Real-Life Situations.

Quadratic Functions.

Operations in Functions.

Inverse Functions.

Chapter Summary.

Review Exercises.

Practice Test.

4. POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS.

Polynomial Functions.

More Polynomial Functions and Mathematical Models.

Polynomial Division, Roots of Polynomials; The Remainder and Factor Theorems.

More on Roots of Polynomial Equations; The Rational Root Theorem and Descartes's Rule of Signs.

Radical Functions.

Variation.

Chapter Summary.

Review Exercises.

Practice Test.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions.

Logarithmic Functions.

Properties of Logarithms: Logarithmic Equations.

Common and Natural Logarithms: Exponential Equations and Change of Base.

Applications.

Chapter Summary.

Review Exercises.

Practice.

6. TRIGONOMETRY.

Angle Measurement and Two Special Triangles.

The Trigonometric Functions of a General Angle.

Right Triangle Trigonometry and Applications.

The Trigonometric Functions as Functions of Real Numbers.

Chapter Summary.

Review Exercises.

Practice Test.

7. THE TRIGONOMETRIC FUNCTIONS.

The Sine and Cosine Functions and Their Graphs.

The Tangent, Secant, Cosecant, and Contangent Functions and Their Graphs.

Basic Identities.

Trigonometric Equations.

The Inverse Trigonometric Functions.

Chapter Summary.

Review Exercises.

Practice Test.

8. 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.

Chapter Summary.

Review Exercises.

Practice Test.

9. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.

Elimination and Substitution: 2 X 2 Linear Systems.

Elimination and Gaussian Elimination: 3 X 3 Linear Systems.

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.

Chapter Summary. Review Exercises.

Practice Test.

10. CONIC SECTIONS.

Conic Sections: Circles.

The Parabola. The Ellipse.

The Hyperbola.

Identifying Conic Sections: Degenerate Forms.

Translations and Rotations of Coordinate Axes.

Nonlinear Systems of Equations and Inequalities.

Chapter Summary.

Review Exercises.

Practice Test.

11. SEQUENCE, 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.

Chapter Summary.

Review Exercises.

Practice Test.

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

Published: 2004

International: No

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.

** Benefits: **

- A full four-color presentation provides a crisp, elegant enhancement to the text's pedagogical features, such as the Different Perspectives, Calculator Exploration, and Technology Corner boxes.
- Every new copy of this text is packaged with our suite of online, customizable technology services, giving your students dynamic, flexible online tutorial resources at their fingertips. By entering a PIN code packaged with their textbook, students gain access to text-specific tutorials with step-by-step explanations, exercises and quizzes, and vMentor--live, one-on-one help from an experienced mathematics tutor. For instructors, we offer highly customizable testing, course management, and diagnostic online resources that provide a dynamic way to power your course.
- Our student mastery system also includes the Interactive Video Skillbuilder CD-ROM. Think of it as portable office hours! Free with every copy of this text, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction.
- In addition to robust tutorial services, your students also receive anytime, anywhere access to InfoTrac College Edition. This online library offers the full text of articles from almost 4000 scholarly and popular publications, updated daily and going back as much as 22 years. Both adopters and their students receive unlimited access for four months.
- Functions and Graphs are covered in great depth in Chapters 2 and 3. Section 2.6 is devoted to the interpretation of graphs.
- Different Perspectives boxes appear wherever there is an opportunity to highlight the connection between the algebraic and graphical interpretation of the same idea.
- Applications and Mathematical Modeling are integrated throughout the text. Modeling is introduced in its own section 3.3 with a special concentration of modeling problems in chapters 3, 4, and 5. These sections provide practice in skills necessary for calculus.
- Problem Analysis is presented in a question and answer format that walks students through the process of setting up and solving problems.
- Margin Comments ask questions that help students check their understanding and provide tips to pace the reading of the material.
- Technology Corner boxes have been added to enhance the student's appreciation of the graphing calculator as a technological device and learning aid.
- The margin comments have been expanded to further encourage students to be active learners as they read the text.
- Many examples and exercises have been revised and updated to make them more current.
- The Problem Analysis approach has been applied to additional examples to allow students more opportunities to see how a mathematical problem is approached and analyzed.
- Two interim reviews have been inserted. The first contains exercises covering the material in Chapter 1 through 5, with an emphasis on those topics most critical to being successful in calculus. The second appears after Chapter 8 and consists of exercises that review the trigonometric concepts that are most frequently encountered in calculus.
- New, realistic application problems give students an idea of how the material they are learning can be applied to real situations.
- Greater integration of modeling throughout the text.
- Found in the ANNOTATED INSTRUCTOR'S EDITION, the NEW RESOURCE INTEGRATION GUIDE makes this text eminently teachable by offering a chapter-by-chapter glimpse of how the supplements support the learning system in the text, reducing the time-consuming task of choosing activities or graphing calculator exercises and directing students to valuable study aids.

1. ALGEBRA: THE FUNDAMENTALS.

The Real Numbers.

Operations with Real Numbers.

Polynomials and Rational Expressions.

Exponents and Radicals.

The Complex Numbers.

First-Degree Equations and Inequalities to One Variable.

Absolute Value Equations and Inequalities.

Quadratic Equations and Equations in Quadratic Form.

Quadratic and Rational Inequalities.

Substitution.

Chapter Summary.

Review Exercises.

Practice Test.

2. FUNCTIONS AND GRAPHS: PART I.

The Cartesian Coordinate System: Graphing Straight Lines Functions and Circles.

Slope.

Equations of a Line.

Relations and Functions.

Function Notation.

Relating Equations to Their Graphs.

Introduction to Graph Sketching: Symmetry.

Chapter Summary.

Review Exercises.

Practice Test.

3. FUNCTIONS AND GRAPHS: PART II.

Basic Graphing Principles.

More Graphing Principles: Types of Functions.

Mathematical Modeling: Extracting Functions from Real-Life Situations.

Quadratic Functions.

Operations in Functions.

Inverse Functions.

Chapter Summary.

Review Exercises.

Practice Test.

4. POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS.

Polynomial Functions.

More Polynomial Functions and Mathematical Models.

Polynomial Division, Roots of Polynomials; The Remainder and Factor Theorems.

More on Roots of Polynomial Equations; The Rational Root Theorem and Descartes's Rule of Signs.

Radical Functions.

Variation.

Chapter Summary.

Review Exercises.

Practice Test.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions.

Logarithmic Functions.

Properties of Logarithms: Logarithmic Equations.

Common and Natural Logarithms: Exponential Equations and Change of Base.

Applications.

Chapter Summary.

Review Exercises.

Practice.

6. TRIGONOMETRY.

Angle Measurement and Two Special Triangles.

The Trigonometric Functions of a General Angle.

Right Triangle Trigonometry and Applications.

The Trigonometric Functions as Functions of Real Numbers.

Chapter Summary.

Review Exercises.

Practice Test.

7. THE TRIGONOMETRIC FUNCTIONS.

The Sine and Cosine Functions and Their Graphs.

The Tangent, Secant, Cosecant, and Contangent Functions and Their Graphs.

Basic Identities.

Trigonometric Equations.

The Inverse Trigonometric Functions.

Chapter Summary.

Review Exercises.

Practice Test.

8. 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.

Chapter Summary.

Review Exercises.

Practice Test.

9. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.

Elimination and Substitution: 2 X 2 Linear Systems.

Elimination and Gaussian Elimination: 3 X 3 Linear Systems.

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.

Chapter Summary. Review Exercises.

Practice Test.

10. CONIC SECTIONS.

Conic Sections: Circles.

The Parabola. The Ellipse.

The Hyperbola.

Identifying Conic Sections: Degenerate Forms.

Translations and Rotations of Coordinate Axes.

Nonlinear Systems of Equations and Inequalities.

Chapter Summary.

Review Exercises.

Practice Test.

11. SEQUENCE, 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.

Chapter Summary.

Review Exercises.

Practice Test.