College Algebra with Modeling & Visualization

Showing why math matters

Gary Rockswold doesn’t just mention real-world examples; he teaches mathematical concepts through those applications. For example, if we look at Facebook usage over time, what might that tell us about linear growth and predictions? In this way, students learn the concepts in the context of the world they know, which leads to better understanding and retention. From there, the author shows a connection between application, modeling, and visualization. Rockswold is 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). The 6th Edition emphasizes conceptual understanding with new in-chapter features and assignment options, while at the same time providing tools to empower instructors to make their classroom more active through collaboration and group work.

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MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. The 6th Edition continues to expand the comprehensive auto-graded exercise options. The pre-existing exercises were carefully reviewed, vetted, and improved using aggregated student usage and performance data over time. In addition, MyLab Math includes new options to support conceptual learning, visualization, and student preparedness. 

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Gary Rockswold has taught mathematics, computer science, and physical science at a wide variety of levels, including high school, undergraduate, and graduate students for over 30 years. He received his bachelor’s degree from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator of parallel computing at the Minnesota Supercomputer Institute and is an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author and has published numerous mathematics textbooks for Pearson Education at both the developmental and collegiate levels. His motivation for writing is to make mathematics more inclusive for a greater number of students by presenting mathematics in a contextual, meaningful way.

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. Systems of Equations and Inequalities

6.1 Functions and Systems of Equations in Two Variables

6.2 Systems of Inequalities in Two Variables

               Checking Basic Concepts for Sections 6.1 and 6.2

6.3 Systems of Linear Equations in Three Variables

6.4 Solutions to Linear Systems Using Matrices

               Checking Basic Concepts for Sections 6.3 and 6.4

6.5 Properties and Applications of Matrices

6.6 Inverses of Matrices

               Checking Basic Concepts for Sections 6.5 and 6.6

6.7 Determinants

               Checking Basic Concepts for Section 6.7

               Chapter 6 Summary

               Chapter 6 Review Exercises

               Chapter 6 Extended and Discovery Exercises

               Chapters 1-6 Cumulative Review Exercises

7. Conic Sections

7.1 Parabolas

7.2 Ellipses

               Checking Basic Concepts for Sections 7.1 and 7.2

7.3 Hyperbolas

               Checking Basic Concepts for Section 7.3

               Chapter 7 Summary

               Chapter 7 Review Exercises

               Chapter 7 Extended and Discovery Exercises

8. Further Topics in Algebra

8.1 Sequences

8.2 Series

               Checking Basic Concepts for Sections 8.1 and 8.2

8.3 Counting

8.4 The Binomial Theorem

               Checking Basic Concepts for Sections 8.3 and 8.4

8.5 Mathematical Induction

8.6 Probability

               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

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: Collaborative Activities

Appendix B: A Library of Functions

Appendix C: Partial Fractions

Appendix D: Percent Change and Exponential Functions

Bibliography

Answers to Selected Exercises

Photo Credits

Index of Applications

Index

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