9780321826121

By connecting applications, modeling, and visualization, Gary Rockswold motivates students to learn mathematics in the context of their experiences. In order to both learn and retain the material, students must see a connection between the concepts and their real lives. In this new edition, connections are taken to a new level with “See the Concept” features, where students make important connections through detailed visualizations that deepen understanding.

Rockswold is also known for presenting the concept of a function as a unifying theme, with an emphasis on the rule of four (verbal, graphical, numerical, and symbolic representations). A flexible approach allows instructors to strike their own balance of skills, rule of four, applications, modeling, and technology.

Dr. Gary Rockswold has taught 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 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.

1. Introduction to Functions and Graphs

1.1 Numbers, Data, and Problem Solving

1.2 Visualizing and Graphing Data

Checking Basic Concepts for Sections 1.1 and 1.2

1.3 Functions and Their Representations

1.4 Types of Functions and Their Rates of Change

Checking Basic Concepts for Sections 1.3 and 1.4

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Extended and Discovery Exercises

2. Linear Functions and Equations

2.1 Equations of Lines

2.2 Linear Equations

Checking Basic Concepts for Sections 2.1 and 2.2

2.3 Linear Inequalities

2.4 More Modeling with Functions

Checking Basic Concepts for Sections 2.3 and 2.4

2.5 Absolute Value Equations and Inequalities

Checking Basic Concepts for Section 2.5

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Extended and Discovery Exercises

Chapters 1-2 Cumulative Review Exercises

3. Quadratic Functions and Equations

3.1 Quadratic Functions and Models

3.2 Quadratic Equations and Problem Solving

Checking Basic Concepts for Sections 3.1 and 3.2

3.3 Complex Numbers

3.4 Quadratic Inequalities

Checking Basic Concepts for Sections 3.3 and 3.4

3.5 Transformations of Graphs

Checking Basic Concepts for Section 3.5

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Extended and Discovery Exercises

4. More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

4.2 Polynomial Functions and Models

Checking Basic Concepts for Sections 4.1 and 4.2

4.3 Division of Polynomials

4.4 Real Zeros of Polynomial Functions

Checking Basic Concepts for Sections 4.3 and 4.4

4.5 The Fundamental Theorem of Algebra

4.6 Rational Functions and Models

Checking Basic Concepts for Sections 4.5 and 4.6

4.7 More Equations and Inequalities

4.8 Radical Equations and Power Functions

Checking Basic Concepts for Sections 4.7 and 4.8

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Extended and Discovery Exercises

Chapters 1-4 Cumulative Review Exercises

5. Exponential and Logarithmic Functions

5.1 Combining Functions

5.2 Inverse Functions and Their Representations

Checking Basic Concepts for Sections 5.1 and 5.2

5.3 Exponential Functions and Models

5.4 Logarithmic Functions and Models

Checking Basic Concepts for Sections 5.3 and 5.4

5.5 Properties of Logarithms

5.6 Exponential and Logarithmic Equations

Checking Basic Concepts for Sections 5.5 and 5.6

5.7 Constructing Nonlinear Models

Checking Basic Concepts for Section 5.7

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Extended and Discovery Exercises

6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Right Triangle Trigonometry

Checking Basic Concepts for Sections 6.1 and 6.2

6.3 The Sine and Cosine Functions and Their Graphs

6.4 Other Trigonometric Functions and Their Graphs

Checking Basic Concepts for Sections 6.3 and 6.4

6.5 Graphing Trigonometric Functions

6.6 Inverse Trigonometric Functions

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

7. Trigonometric Identities and Equations

7.1 Fundamental Identities

7.2 Verifying Identities

Checking Basic Concepts for Sections 7.1 and 7.2

7.3 Trigonometric Equations

7.4 Sum and Difference Identities

Checking Basic Concepts for Sections 7.3 and 7.4

7.5 Multiple-Angle Identities

Checking Basic Concepts for Section 7.5

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Extended and Discovery Exercises

8. Further Topics in Trigonometry

8.1 Law of Sines

8.2 Law of Cosines

Checking Basic Concepts for Sections 8.1 and 8.2

8.3 Vectors

8.4 Parametric Equations

Checking Basic Concepts for Sections 8.3 and 8.4

8.5 Polar Equations

8.6 Trigonometric Form and 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

9. Systems of Equations and Inequalities

9.1 Functions and Systems of Equations in Two Variables

9.2 Systems of Inequalities in Two Variables

Checking Basic Concepts for Sections 9.1 and 9.2

9.3 Systems of Linear Equations in Three Variables

9.4 Solutions to Linear Systems Using Matrices

Checking Basic Concepts for Sections 9.3 and 9.4

9.5 Properties and Applications of Matrices

9.6 Inverses of Matrices

Checking Basic Concepts for Sections 9.5 and 9.6

9.7 Determinants

Checking Basic Concepts for Section 9.7

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Extended and Discovery Exercises

Chapters 1-9 Cumulative Review Exercises

10. Conic Sections

10.1 Parabolas

10.2 Ellipses

Checking Basic Concepts for Sections 10.1 and 10.2

10.3 Hyperbolas

Checking Basic Concepts for Section 10.3

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Extended and Discovery Exercises

11. Further Topics in Algebra

11.1 Sequences

11.2 Series

Checking Basic Concepts for Sections 11.1 and 11.2

11.3 Counting

11.4 The Binomial Theorem

Checking Basic Concepts for Sections 11.3 and 11.4

11.5 Mathematical Induction

11.6 Probability

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

R. Reference: Basic Concepts from Algebra and Geometry

R.1 Formulas from Geometry

R.2 Integer Exponents

R.3 Polynomial Expressions

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Radical Notation and Rational Exponents

R.7 Radical Expressions

Appendix A: Using the Graphing Calculator

Appendix B: A Library of Functions

Appendix C: Partial Fractions

Appendix D: Percent Change and Exponential Functions

Appendix E: Rotation of Axes

Bibliography

Answers to Selected Exercises

Photo Credits

Index of Applications

Index

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Algebra and Trigonometry with Modeling & Visualization

Algebra and Trigonometry with Modeling & Visualization

0321826124

Summary

Author Biography

Table of Contents

Supplemental Materials