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by Richard N. Aufmann, Vernon C. Barker and Richard D. Nation

Edition: 5TH 05Copyright: 2005

Publisher: Houghton Mifflin Harcourt

Published: 2005

International: No

Richard N. Aufmann, Vernon C. Barker and Richard D. Nation

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This text provides a supportive environment to help students successfully learn the content of a standard algebra and trigonometry course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success.

Many new components added to this edition of College Algebra and Trigonometry have been designed to help students diagnose and review weak algebra skills. Prerequisite review is include in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge.

**P. Preliminary Concepts**

Section P.1 The Real Number System

Section P.2 Integer and Rational Number Exponents

Section P.3 Polynomials

Section P.4 Factoring

Section P.5 Rational Expressions

Section P.6 Complex Numbers

Exploring Concepts with Technology: Can You Trust Your Calculator?

**1. Equations and Inequalities**

Section 1.1 Linear and Absolute Value Equations

Section 1.2 Formulas and Applications

Section 1.3 Quadratic Equations

Section 1.4 Other Types of Equations

Section 1.5 Inequalities

Section 1.6 Variation and Applications

Exploring Concepts with Technology: Use a Graphing Calculator to Solve Equations

**2. Functions and Graphs**

Section 2.1 A Two-Dimensional Coordinate System and Graphs

Section 2.2 Introduction to Functions

Section 2.3 Linear Functions

Section 2.4 Quadratic Functions

Section 2.5 Properties of Graphs

Section 2.6 The Algebra of Functions

Section 2.7 Modeling Data Using Regression

Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator

**3. Polynomial and Rational Functions**

Section 3.1 The Remainder Theorem and the Factor Theorem

Section 3.2 Polynomial Functions of Higher Degree

Section 3.3 Zeros of Polynomial Functions

Section 3.4 The Fundamental Theorem of Algebra

Section 3.5 Graphs of Rational Functions and Their Applications

Exploring Concepts with Technology: Finding Zeros of a Polynomial Using Mathematica

**4. Exponential and Logarithmic Functions**

Section 4.1 Inverse Functions

Section 4.2 Exponential Functions and Their Applications

Section 4.3 Logarithmic Functions and Their Applications

Section 4.4 Logarithms and Logarithmic Scales

Section 4.5 Exponential and Logarithmic Equations

Section 4.6 Exponential Growth and Decay

Section 4.7 Modeling Data with Exponential and Logarithmic Functions

Exploring Concepts with Technology: Using a Semi-Log Graph to Model Exponential Decay

**5. Trigonometric Functions**

Section 5.1 Angles and Arcs

Section 5.2 Trigonometric Functions of Acute Angles

Section 5.3 Trigonometric Functions of Any Angle

Section 5.4 Trigonometric Functions of Real Numbers

Section 5.5 Graphs of the Sine and Cosine Functions

Section 5.6 Graphs of the Other Trigonometric Functions

Section 5.7 Graphing Techniques

Section 5.8 Harmonic Motion--An Application of the Sine and Cosine Functions

Exploring Concepts with Technology: Sinusoidal Families

**6. Trigonometric Identities and Equations**

Section 6.1 Verification of Trigonometric Identities

Section 6.2 Sum, Difference, and Cofunction Identities

Section 6.3 Double- and Half-Angle Identities

Section 6.4 Identities Involving the Sum of Trigonometric Functions

Section 6.5 Inverse Trigonometric Functions

Section 6.6 Trigonometric Equations

Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials

**7. Applications of Trigonometry**

Section 7.1 The Law of Sines

Section 7.2 The Law of Cosines and Area

Section 7.3 Vectors

Section 7.4 Trigonometric Form of Complex Numbers

Section 7.5 De Moivre's Theorem

Exploring Concepts with Technology: Optimal Branching of Arteries

**8. Topics in Analytic Geometry**

Section 8.1 Parabolas

Section 8.2 Ellipses

Section 8.3 Hyperbolas

Section 8.4 Rotation of Axes

Section 8.5 Introduction to Polar Coordinates

Section 8.6 Polar Equations of the Conics

Section 8.7 Parametric Equations

Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Roots of z

**9. Systems of Equations**

Section 9.1 Systems of Linear Equations in Two Variables

Section 9.2 Systems of Linear Equations in More Than Two Variables

Section 9.3 Nonlinear Systems of Equations

Section 9.4 Partial Fractions

Section 9.5 Inequalities in Two Variables and Systems of Inequalities

Section 9.6 Linear Programming

Exploring Concepts with Technology: Ill-Conditioned Systems of

Equations

**10. Matrices**

Section 10.1 Gaussian Elimination Method

Section 10.2 The Algebra of Matrices

Section 10.3 The Inverse of a Matrix

Section 10.4 Determinants

Section 10.5 Cramer's Rule

Exploring Concepts with Technology: Stochastic Matrices

**11. Sequences, Series, and Probability**

Section 11.1 Infinite Sequences and Summation Notation

Section 11.2 Arithmetic Sequences and Series

Section 11.3 Geometric Sequences and Series

Section 11.4 Mathematical Induction

Section 11.5 The Binomial Theorem

Section 11.6 Permutations and Combinations

Section 11.7 Introduction to Probability

Exploring Concepts with Technology: Mathematical Expectation

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Summary

This text provides a supportive environment to help students successfully learn the content of a standard algebra and trigonometry course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success.

Many new components added to this edition of College Algebra and Trigonometry have been designed to help students diagnose and review weak algebra skills. Prerequisite review is include in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge.

Table of Contents

**P. Preliminary Concepts**

Section P.1 The Real Number System

Section P.2 Integer and Rational Number Exponents

Section P.3 Polynomials

Section P.4 Factoring

Section P.5 Rational Expressions

Section P.6 Complex Numbers

Exploring Concepts with Technology: Can You Trust Your Calculator?

**1. Equations and Inequalities**

Section 1.1 Linear and Absolute Value Equations

Section 1.2 Formulas and Applications

Section 1.3 Quadratic Equations

Section 1.4 Other Types of Equations

Section 1.5 Inequalities

Section 1.6 Variation and Applications

Exploring Concepts with Technology: Use a Graphing Calculator to Solve Equations

**2. Functions and Graphs**

Section 2.1 A Two-Dimensional Coordinate System and Graphs

Section 2.2 Introduction to Functions

Section 2.3 Linear Functions

Section 2.4 Quadratic Functions

Section 2.5 Properties of Graphs

Section 2.6 The Algebra of Functions

Section 2.7 Modeling Data Using Regression

Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator

**3. Polynomial and Rational Functions**

Section 3.1 The Remainder Theorem and the Factor Theorem

Section 3.2 Polynomial Functions of Higher Degree

Section 3.3 Zeros of Polynomial Functions

Section 3.4 The Fundamental Theorem of Algebra

Section 3.5 Graphs of Rational Functions and Their Applications

Exploring Concepts with Technology: Finding Zeros of a Polynomial Using Mathematica

**4. Exponential and Logarithmic Functions**

Section 4.1 Inverse Functions

Section 4.2 Exponential Functions and Their Applications

Section 4.3 Logarithmic Functions and Their Applications

Section 4.4 Logarithms and Logarithmic Scales

Section 4.5 Exponential and Logarithmic Equations

Section 4.6 Exponential Growth and Decay

Section 4.7 Modeling Data with Exponential and Logarithmic Functions

Exploring Concepts with Technology: Using a Semi-Log Graph to Model Exponential Decay

**5. Trigonometric Functions**

Section 5.1 Angles and Arcs

Section 5.2 Trigonometric Functions of Acute Angles

Section 5.3 Trigonometric Functions of Any Angle

Section 5.4 Trigonometric Functions of Real Numbers

Section 5.5 Graphs of the Sine and Cosine Functions

Section 5.6 Graphs of the Other Trigonometric Functions

Section 5.7 Graphing Techniques

Section 5.8 Harmonic Motion--An Application of the Sine and Cosine Functions

Exploring Concepts with Technology: Sinusoidal Families

**6. Trigonometric Identities and Equations**

Section 6.1 Verification of Trigonometric Identities

Section 6.2 Sum, Difference, and Cofunction Identities

Section 6.3 Double- and Half-Angle Identities

Section 6.4 Identities Involving the Sum of Trigonometric Functions

Section 6.5 Inverse Trigonometric Functions

Section 6.6 Trigonometric Equations

Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials

**7. Applications of Trigonometry**

Section 7.1 The Law of Sines

Section 7.2 The Law of Cosines and Area

Section 7.3 Vectors

Section 7.4 Trigonometric Form of Complex Numbers

Section 7.5 De Moivre's Theorem

Exploring Concepts with Technology: Optimal Branching of Arteries

**8. Topics in Analytic Geometry**

Section 8.1 Parabolas

Section 8.2 Ellipses

Section 8.3 Hyperbolas

Section 8.4 Rotation of Axes

Section 8.5 Introduction to Polar Coordinates

Section 8.6 Polar Equations of the Conics

Section 8.7 Parametric Equations

Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Roots of z

**9. Systems of Equations**

Section 9.1 Systems of Linear Equations in Two Variables

Section 9.2 Systems of Linear Equations in More Than Two Variables

Section 9.3 Nonlinear Systems of Equations

Section 9.4 Partial Fractions

Section 9.5 Inequalities in Two Variables and Systems of Inequalities

Section 9.6 Linear Programming

Exploring Concepts with Technology: Ill-Conditioned Systems of

Equations

**10. Matrices**

Section 10.1 Gaussian Elimination Method

Section 10.2 The Algebra of Matrices

Section 10.3 The Inverse of a Matrix

Section 10.4 Determinants

Section 10.5 Cramer's Rule

Exploring Concepts with Technology: Stochastic Matrices

**11. Sequences, Series, and Probability**

Section 11.1 Infinite Sequences and Summation Notation

Section 11.2 Arithmetic Sequences and Series

Section 11.3 Geometric Sequences and Series

Section 11.4 Mathematical Induction

Section 11.5 The Binomial Theorem

Section 11.6 Permutations and Combinations

Section 11.7 Introduction to Probability

Exploring Concepts with Technology: Mathematical Expectation

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2005

International: No

Published: 2005

International: No

Many new components added to this edition of College Algebra and Trigonometry have been designed to help students diagnose and review weak algebra skills. Prerequisite review is include in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge.

**P. Preliminary Concepts**

Section P.1 The Real Number System

Section P.2 Integer and Rational Number Exponents

Section P.3 Polynomials

Section P.4 Factoring

Section P.5 Rational Expressions

Section P.6 Complex Numbers

Exploring Concepts with Technology: Can You Trust Your Calculator?

**1. Equations and Inequalities**

Section 1.1 Linear and Absolute Value Equations

Section 1.2 Formulas and Applications

Section 1.3 Quadratic Equations

Section 1.4 Other Types of Equations

Section 1.5 Inequalities

Section 1.6 Variation and Applications

Exploring Concepts with Technology: Use a Graphing Calculator to Solve Equations

**2. Functions and Graphs**

Section 2.1 A Two-Dimensional Coordinate System and Graphs

Section 2.2 Introduction to Functions

Section 2.3 Linear Functions

Section 2.4 Quadratic Functions

Section 2.5 Properties of Graphs

Section 2.6 The Algebra of Functions

Section 2.7 Modeling Data Using Regression

Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator

**3. Polynomial and Rational Functions**

Section 3.1 The Remainder Theorem and the Factor Theorem

Section 3.2 Polynomial Functions of Higher Degree

Section 3.3 Zeros of Polynomial Functions

Section 3.4 The Fundamental Theorem of Algebra

Section 3.5 Graphs of Rational Functions and Their Applications

Exploring Concepts with Technology: Finding Zeros of a Polynomial Using Mathematica

**4. Exponential and Logarithmic Functions**

Section 4.1 Inverse Functions

Section 4.2 Exponential Functions and Their Applications

Section 4.3 Logarithmic Functions and Their Applications

Section 4.4 Logarithms and Logarithmic Scales

Section 4.5 Exponential and Logarithmic Equations

Section 4.6 Exponential Growth and Decay

Section 4.7 Modeling Data with Exponential and Logarithmic Functions

Exploring Concepts with Technology: Using a Semi-Log Graph to Model Exponential Decay

**5. Trigonometric Functions**

Section 5.1 Angles and Arcs

Section 5.2 Trigonometric Functions of Acute Angles

Section 5.3 Trigonometric Functions of Any Angle

Section 5.4 Trigonometric Functions of Real Numbers

Section 5.5 Graphs of the Sine and Cosine Functions

Section 5.6 Graphs of the Other Trigonometric Functions

Section 5.7 Graphing Techniques

Section 5.8 Harmonic Motion--An Application of the Sine and Cosine Functions

Exploring Concepts with Technology: Sinusoidal Families

**6. Trigonometric Identities and Equations**

Section 6.1 Verification of Trigonometric Identities

Section 6.2 Sum, Difference, and Cofunction Identities

Section 6.3 Double- and Half-Angle Identities

Section 6.4 Identities Involving the Sum of Trigonometric Functions

Section 6.5 Inverse Trigonometric Functions

Section 6.6 Trigonometric Equations

Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials

**7. Applications of Trigonometry**

Section 7.1 The Law of Sines

Section 7.2 The Law of Cosines and Area

Section 7.3 Vectors

Section 7.4 Trigonometric Form of Complex Numbers

Section 7.5 De Moivre's Theorem

Exploring Concepts with Technology: Optimal Branching of Arteries

**8. Topics in Analytic Geometry**

Section 8.1 Parabolas

Section 8.2 Ellipses

Section 8.3 Hyperbolas

Section 8.4 Rotation of Axes

Section 8.5 Introduction to Polar Coordinates

Section 8.6 Polar Equations of the Conics

Section 8.7 Parametric Equations

Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Roots of z

**9. Systems of Equations**

Section 9.1 Systems of Linear Equations in Two Variables

Section 9.2 Systems of Linear Equations in More Than Two Variables

Section 9.3 Nonlinear Systems of Equations

Section 9.4 Partial Fractions

Section 9.5 Inequalities in Two Variables and Systems of Inequalities

Section 9.6 Linear Programming

Exploring Concepts with Technology: Ill-Conditioned Systems of

Equations

**10. Matrices**

Section 10.1 Gaussian Elimination Method

Section 10.2 The Algebra of Matrices

Section 10.3 The Inverse of a Matrix

Section 10.4 Determinants

Section 10.5 Cramer's Rule

Exploring Concepts with Technology: Stochastic Matrices

**11. Sequences, Series, and Probability**

Section 11.1 Infinite Sequences and Summation Notation

Section 11.2 Arithmetic Sequences and Series

Section 11.3 Geometric Sequences and Series

Section 11.4 Mathematical Induction

Section 11.5 The Binomial Theorem

Section 11.6 Permutations and Combinations

Section 11.7 Introduction to Probability

Exploring Concepts with Technology: Mathematical Expectation