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Precalculus with Modeling and Visualization, 3/E
Gary K. Rockswold, Minnesota State University, Mankato

ISBN-10: 0321279077
ISBN-13: 9780321279071

Publisher: Addison-Wesley
Copyright: 2006
Format: Cloth; 1216 pp
Published: 03/09/2005

Suggested retail price: $153.33
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Gary Rockswold focuses on teaching algebra in context, answering the question, “Why am I learning this?” and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.

  • Applications: The author believes that students become more effective problem-solvers by being exposed to applications throughout the course. Therefore, a wide variety of unique, data-based, contemporary applications are included in nearly every section.
  • Making Connections: This feature points out how concepts presented throughout the course are interrelated. It also provides students with a perspective on how previously learned material applies to the new material they have learned.
  • Checking Basic Concepts: This feature consists of a small set of exercises provided after every two sections. These exercises can be used by students for review purposes, or by the instructor as group activities. They require 10-15 minutes to complete and could be used during class if time is available.
  • End of Chapter Material: Each chapter ends with a summary of key concepts, review exercises, and extended and discovery exercises.
  • Chapter R Reference: Basic Concepts from Algebra and Geometry: This contains much of the material from intermediate algebra and basic geometry in a separate appendix at the back of the text. This material is referenced by Algebra and Geometry Review Notes in the margins of the text.
  • Graphing Calculator Appendix: This allows students to work more easily on their own with the calculator and frees up class time for the instructor. This material is referenced by Graphing Calculator Help Notes in the margins of the text.

  • Chapter R now includes more on radicals and rational expressions.
  • Over 90 additional Examples are included in the text, on topics that students find particularly challenging or confusing.
  • Over 2,000 additional Exercises have been added to the text to allow students even more opportunity for practice and review. In addition, every exercise set has been revised to ensure that there are sufficient types of exercises for each mathematical concept and that there is a pairing of odd and even numbered exercises. They have been carefully graded from easy to difficult.
  • The data in the applications has been updated for currency and improved relevancy.
  • A new Now Try label appears at the end of every example, directing students to a similar exercise so they can practice what they have just learned.
  • Cumulative Reviews, which appear every few chapters, require students to understand and use multiple skills from various chapters together. This is an excellent test of comprehension of key concepts in the course.
  • New sections covering mathematical induction and solving linear systems in three variables without matrices have been added. Also, there is more coverage of partial fractions and rotation of axes.
  • Chapter 2 has been reduced to five sections with the midpoint formula now presented in section 1.2 with the distance formula.
  • Several topics have been expanded for greater clarity. These include graphing by hand, calculating the average rate of change, finding the difference quotient, maximizing and minimizing quadratic functions, evaluating function notation, solving equations reducible to quadratic form, graphing rational functions with holes, solving nonlinear equations and inequalities, completing the square, writing functions and formulas to solve applications, and transforming graphs to model data.

Chapter 1: INTRODUCTION TO FUNCTIONS AND GRAPHS   

1.1 Numbers, Data, and Problem Solving

        Sets of Numbers

        Scientific Notation

        Problem Solving

1.2 Visualization of Data

        One-Variable Data

        Two Variable Data

        The Distance Formula

        The Midpoint Formula

        Graphing with a Calculator (Optional)

Checking Basic Concepts for Sections 1.1 and 1.2   

1.3 Functions and Their Representations

        Basic Concepts

        Representations of Functions

        Formal Definition of a Function

        Graphing Calculators and Functions (Optional)

        Identifying Functions   

1.4 Types of Functions and Their Rates of Change

        Constant Functions

        Linear Functions

        Slope as a Rate of Change

        Nonlinear Functions

        Average Rate of Change

        The Difference Quotient

Checking Basic Concepts for Sections 1.3 and 1.4

Chapter 1 Summary 

Chapter 1 Review Exercises

Chapter 1 Extended and Discovery Exercises   

 

Chapter 2: LINEAR FUNCTIONS AND EQUATIONS   

2.1 Linear Functions and Models

        Exact and Approximate Models

        Representations of Linear Functions

        Modeling with Linear Functions

        Linear Regression (Optional)

2.2 Equations of Lines   

        Forms for Equations of Lines

        Determining Intercepts

        Horizontal, Vertical, Parallel, and Perpendicular Lines

        Modeling Data (Optional)

        Interpolation and Extrapolation

        Direct Variation

Checking Basic Concepts for Sections 2.1 and 2.2

2.3 Linear Equations

        Equations

        Symbolic Solutions

        Graphical and Numerical Solutions

        Problem-Solving Strategies  

2.4 Linear Inequalities

        Inequalities

        Interval Notion

        Techniques for Solving Inequalities

        Compound Inequalities

Checking Basic Concepts for Sections 2.3 and 2.4   

2.5 Piecewise-Defined Functions

        Evaluating and Graphing Piecewise-Defined Functions

        The Greatest Integer Function

        The Absolute Value Function

        Equations and Inequalities Involving Absolute Values

Checking Basic Concepts for Section 2.5   

Chapter 2 Summary   

Chapter 2 Review Exercises   

Chapter 2 Extended and Discovery Exercises

 

Chapter 1-2 Cumulative Review Exercises

 

Chapter 3: QUADRATIC FUNCTIONS AND EQUATIONS

3.1 Quadratic Functions and Models

        Basic Concepts

        Completing the Square and the Vertex Formula

        Applications and Models

        Quadratic Regression (Optional)

3.2 Quadratic Equations and Problem Solving

        Basic Concepts

        Solving Quadratic Equations

        Problem Solving

Checking Basic Concepts for Sections 3.1 and 3.2 

3.3 Quadratic Inequalities

        Graphical Solutions

        Symbolic Solutions

3.4 Transformations of Graphs   

        Vertical and Horizontal Translations

        Stretching and Shrinking

        Reflection of Graphs

        Combining Transformations

        Modeling with Transformations (Optional)

Checking Basic Concepts for Sections 3.3 and 3.4

Chapter 3 Summary   

Chapter 3 Review Exercises   

Chapter 3 Extended and Discovery Exercises

 

Chapter 4: NONLINEAR FUNCTIONS AND EQUATIONS   

4.1 Nonlinear Functions and Their Graphs   

        Polynomial Functions

        Increasing and Decreasing Functions

        Extrema of Nonlinear Functions

        Symmetry

4.2 Polynomial Functions and Models   

        Graphs of Polynomial Functions

        Piecewise-Defined Polynomial Functions

        Polynomial Regression (Optional)

Checking Basic Concepts for Sections 4.1 and 4.2   

4.3 Real Zeros of Polynomial Functions   

        Division of Polynomials

        Factoring Polynomials

        Graphs and Multiple Zeros

        Rational Zeros

        Polynomial Equations

 4.4 The Fundamental Theorem of Algebra   

        Complex Numbers

        Quadratic Equations with Complex Solutions

        Fundamental Theorem of Algebra

        Polynomial Equations with Complex Solutions

Checking Basic Concepts for Sections 4.3 and 4.4   

4.5 Rational Functions and Models   

        Rational Functions

        Vertical Asymptotes

        Horizontal Asymptotes

        Identifying Asymptotes

        Rational Equations

        Variation

4.6 Polynomial and Rational Inequalities   

        Polynomial Inequalities

        Rational Inequalities

Checking Basic Concepts for Sections 4.5 and 4.6   

4.7 Power Functions and Radical Equations   

        Rational Exponents and Radical Notation

        Power Functions and Models

        Equations Involving Rational Exponents

        Equations Involving Radicals

        Power Regression (Optional)

Checking Basic Concepts for Section 4.7   

Chapter 4 Summary

Chapter 4 Review Exercises   

Chapter 4 Extended and Discovery Exercises   

 

Chapters 1-4 Cumulative Review Exercises

 

Chapter 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS   

5.1 Combining Functions   

        Arithmetic Operations on Functions

        Composition of Functions

5.2 Inverse Functions and Their Representations   

        Inverse Operations

        One-to-One Functions

        Symbolic Representations of Inverse Functions

        Other Representations of Inverse Functions

Checking Basic Concepts for Sections 5.1 and 5.2    

5.3 Exponential Functions and Models   

        Linear and Exponential Growth

        Exponential Models

        Compound Interest

        The Natural Exponential Function

5.4 Logarithmic Functions and Models   

        The Common Logarithmic Function

        Basic Equations

        Logarithms with Other Bases

        General Logarithmic Equations

Checking Basic Concepts for Sections 5.3 and 5.4   

5.5 Properties of Logarithms   

        Basic Properties of Logarithms

        Change of Base Formula

5.6 Exponential and Logarithmic Equations   

        Exponential Equations

        Logarithmic Equations

Checking Basic Concepts for 5.5 and 5.6   

5.7 Constructing Nonlinear Models   

        Exponential Model

        Logarithmic Model

        Logistic Model

Checking Basic Concepts for Section 5.7   

Chapter 5 Summary   

Chapter 5 Review Exercises   

Chapter 5 Extended and Discovery Exercises

 

Chapter 6: TRIGONOMETRIC FUNCTIONS   

6.1 Angles and Their Measure   

        Angles

        Degree Measure

        Radian Measure

        Arc Length

        Area of a Sector

6.2 Right Triangle Trigonometry   

        Basic Concepts of Trigonometric Functions

        Applications of Right Triangle Trigonometry

        Complementary Angles and Cofunctions

Checking Basic Concepts for 6.1 and 6.2   

6.3 The Sine and Cosine Functions and Their Graphs  

        Definitions

        The Unit Circle

        Representations of the Sine and the Cosine Functions

        Applications of the Sine and Cosine Functions

        Modeling with the Sine Function (Optional)

6.4 Other Trigonometric Functions and Their Graphs   

        Definitions and Basic Identities

        Representations of Other Trigonometric Functions

        Applications of Trigonometric Functions

Checking Basic Concepts for Sections 6.3 and 6.4   

6.5 Graphing Trigonometric Functions

        Transformations of Trigonometric Graphs

        Graphing Trigonometric Functions by Hand

        Simple Harmonic Motion

        Models Involving Trigonometric Functions (Optional)

6.6 Inverse Trigonometric Functions   

        Review of Inverses

        The Inverse Sine Function

        The Inverse Cosine Function

        The Inverse Tangent Function

        Solving Triangles and Equations

Checking Basic Concepts for Sections 6.5 and 6.6

Chapter 6 Summary   

Chapter 6 Review Exercises   

Chapter 6 Extended and Discovery Exercises

 

Chapters 1-6 Cumulative Review Exercises

 

Chapter 7: TRIGONOMETRIC IDENTITIES AND EQUATIONS   

7.1 Fundamental Identities   

        Reciprocal and Quotient Identities

        Pythagorean Identities

        Negative-Angle Identities

7.2 Verifying Identities   

        Simplifying Trigonometric Expressions

        Verification of Identities

Checking Basic Concepts for Section 7.1 and 7.2

7.3 Trigonometric Equations

        Reference Angles

        Solving Trigonometric Equations

        Solving Inverse Trigonometric Equations

7.4 Sum and Difference Identities   

        Sum and Difference Identities for Cosine

        Other Sum and Difference Identities

Checking Basic Concepts for Section 7.3 and 7.4   

7.5 Multiple-Angle Identities   

        Double-Angle Identities

        Half-Angle Formulas

        Solving Equations

        Product-to-Sum and Sum-to-Product Identities

Checking Basic Concepts for Section 7.5

Chapter 7 Summary   

Chapter 7 Review Exercises   

Chapter 7 Extended and Discovery Exercises

 

Chapter 8: FURTHER TOPICS IN TRIGONOMETRY

8.1 Law of Sines

        Oblique Triangles

        Solving Triangles

        The Ambiguous Case

8.2 Law of Cosines   

        Derivation of the Law of Cosines

        Solving Triangles

        Area Formulas

Checking Basic Concepts for Sections 8.1 and 8.2   

8.3 Vectors   

        Basic Concepts

        Operations on Vectors

        The Dot Product

        Work

8.4 Parametric Equations   

        Basic Concepts

        Applications of Parametric Equations

Checking Basic Concepts for Sections 8.3 and 8.4   

8.5 Polar Equations

        The Polar Coordinate System

        Graphs of Polar Equations

        Graphing Calculators and Polar Equations (Optional)

        Solving Polar Equations

8.6 Trigonometric Form and Roots of Complex Numbers   

        Trigonometric Form

        Products and Quotients of Complex Numbers

        De Moivre’s Theorem

        Roots of Complex Numbers

Checking Basic Concepts for Sections 8.5 and 8.6   

Chapter 8 Summary   

Chapter 8 Review Exercises   

Chapter 8 Extended and Discovery Exercises

 

Chapters 1-8 Cumulative Review Exercises

           

Chapter 9: SYSTEMS OF EQUATIONS AND INEQUALITIES   

9.1 Functions and Equations in Two Variables   

        Functions of Two Variables

        Systems of Equations

        The Method of Substitution

        Graphical and Numerical Methods

        Joint Variation

9.2 Systems of Equations and Inequalities in Two Variables   

        Types of Linear Systems in Two Variables

        The Elimination Method

        Systems of Linear and Nonlinear Inequalities

        Linear Programming

Checking Basic Concepts for 9.1 and 9.2   

9.3 Systems of Linear Equations in Three Variables   

        Basic Concepts

        Solving with Elimination and Substitution

        Systems with No Solutions

        Systems with Infinitely Many Solutions

9.4 Solutions to Linear Systems Using Matrices   

        Representing Systems of Linear Equations with Matrices

        Row-Echelon Form

        Gaussian Elimination

        Solving Systems of Linear Equations with Technology (Optional)

Checking Basic Concepts for Sections 9.3 and 9.4   

9.5 Properties and Applications of Matrices   

        Matrix Notation

        Sums, Differences, and Scalar Multiples of Matrices

        Matrix Products

        Technology and Matrices (Optional)

9.6 Inverses of Matrices   

        Matrix Inverses

        Finding Inverses Symbolically

        Representing Linear Systems with Matrix Equations

        Solving Linear Systems with Inverses

Checking Basic Concepts for Sections 9.5 and 9.6    

9.7 Determinants   

        Definition and Calculation of Determinants

        Area of Regions

        Cramer’s Rule

        Limitations on the Method of Cofactors and Cramer’s Rule

Checking Basic Concepts for Section 9.7

Chapter 9 Summary   

Chapter 9 Review Exercises   

Chapter 9 Extended and Discovery Exercise

 

Chapter 10: CONIC SECTIONS   

10.1 Parabolas   

        Equations and Graphs of Parabolas

        Reflective Property of Parabolas

        Translations of Parabolas

10.2 Ellipses   

        Equations and Graphs of Ellipses

        Reflective Property of Ellipses

        Translations of Ellipses

        Circles

        Solving Systems of Equations and Inequalities

Checking Basic Concepts for Section 10.1 and 10.2   

10.3 Hyperbolas   

        Equations and Graphs of Hyperbolas

        Reflective Property of Hyperbolas

        Translations of Hyperbolas

        Solving Systems of Nonlinear Equations

Checking Basic Concepts for Section 10.3

Chapter 10 Summary

Chapter 10 Review Exercises   

Chapter 10 Extended and Discovery Exercises

 

Chapter 11: FURTHER TOPICS IN ALGEBRA    

11.1 Sequences   

        Basic Concepts

        Representations of Sequences

        Arithmetic Sequences

        Geometric Sequences

11.2 Series   

        Basic Concepts

        Arithmetic Series

        Geometric Series

        Summation Notation

Checking Basic Concepts for Sections 11.1 and 11.2   

11.3 Counting   

        Fundamental Counting Principle

        Permutations

        Combinations

11.4 The Binomial Theorem   

        Derivation of the Binomial Theorem

        Pascal’s Triangle

Checking Basic Concepts for Sections 11.3 and 11.4   

11.5 Mathematical Induction   

        Mathematical Induction

        Proving Statements

        Generalized Principle of Mathematical Induction

11.6 Probability   

        Definition of Probability

        Compound Events

        Independent and Dependent Events

Checking Basic Concepts for Sections 11.5 and 11.6   

Chapter 11 Summary   

Chapter 11 Review Exercises   

Chapter 11 Extended and Discovery Exercises

 

Chapters 1-11 Cumulative Review Exercises

           

Chapter R: REFERENCE- BASIC CONCEPTS FROM ALGEBRA AND GEOMETRY

R.1 Formulas from Geometry   

        Geometric Shapes in a Plane

        The Pythagorean Theorem

        Three-Dimensional Objects

        Similar Triangles

        A Summary of Geometric Formulas

R.2 Circles   

        Equations and Graphs of Circles

        Finding the Center and Radius of a Circle

R.3 Integer Exponents   

        Bases and Positive Exponents

        Zero and Negative Exponents

        Product, Quotient, and Power Rules

R.4 Polynomial Expressions   

        Addition and Subtraction of Monomials

        Addition and Subtraction of Polynomials

        Distributive Properties

        Multiplying Polynomials

        Some Special Products

R.5 Factoring Polynomials   

        Common Factors

        Factoring by Grouping

        Factoring x2 + bx + c

        Factoring Trinomials by Grouping

        Factoring Trinomials with FOIL

        Difference of Two Squares

        Perfect Square Trinomials

        Sum and Difference of Two Cubes

R.6 Rational Expressions   

        Simplifying Rational Expressions

        Multiplication and Division of Rational Expressions

        Least Common Multiples

        Common Denominators

        Addition and Subtraction of Rational Expressions

        Clearing Fractions

        Complex Fractions

R.7 Radical Notation and Rational Exponents   

        Radical Notation

        Rational Exponents

        Properties of Rational Exponents 

R.8 Radical Expressions   

        Product Rule for Radical Expressions

        Quotient Rule for Radical Expressions

        Addition and Subtraction

        Multiplication

        Rationalizing the Denominator

 

APPENDIX A: A Library of Functions   

APPENDIX B: Using the Graphing Calculator  

APPENDIX C: Partial Fractions

APPENDIX D: Rotation of Axes

 

Bibliography

Answers to Selected Exercises

Index of Applications

Index

 

Gary Rockswold- Dr. Gary Rockswold has been teaching mathematics for 25 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics and the chair of the mathematics department. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science. Outside of mathematics, he enjoys spending time with his wife and two children.

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    Gary Rockswold focuses on teaching algebra in context, answering the question, “Why am I learning this?” and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.

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    Brief Description | Buy from myPearsonStore

    • Gary Rockswold focuses on teaching algebra in context, answering the question, “Why am I learning this?” and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.

  • 0321279077Precalculus with Modeling and Visualization, 3/E
    Rockswold
    © 2006 | Addison-Wesley | Cloth; 1216 pages | Instock
    ISBN-10: 0321279077 | ISBN-13: 9780321279071
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