Beginning and Intermediate Algebra with Applications & Visualization

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. He has taught not only at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing and is currently an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author for Pearson Education and has over 10 current textbooks at the developmental and precalculus levels. His developmental coauthor and friend is Terry Krieger. They have been working together for over a decade. Making mathematics meaningful for students and professing the power of mathematics are special passions for Gary. In his spare time he enjoys sailing, doing yoga, and spending time with his family.   Additional information about Gary Rockswold can be found at www.garyrockswold.net.   Terry Krieger has taught mathematics for 18 years at the middle school, high school, vocational, community college and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University - Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia, and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry is currently teaching at Rochester Community and Technical College in Rochester, Minnesota. He has been involved with various aspects of mathematics textbook publication for more than 14 years and has joined his friend Gary Rockswold as coauthor of a developmental math series published by Pearson Education. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing.

1. Introduction to Algebra

1.1 Numbers, Variables, and Expressions

1.2 Fractions

1.3 Exponents and Order of Operations

1.4 Real Numbers and the Number Line

1.5 Addition and Subtraction of Real Numbers

1.6 Multiplication and Division of Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying and Writing Algebraic Expressions

Summary - Review Exercises - Test - Extended and Discovery Exercises

 

2. Linear Equations and Inequalities

2.1 Introduction to Equations

2.2 Linear Equations

2.3 Introduction to Problem Solving

2.4 Formulas

2.5 Linear Inequalities

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-2 Cumulative Review

 

3. Graphing Equations

3.1 Introduction to Graphing

3.2 Linear Equations in Two Variables

3.3 More Graphing of Lines

3.4 Slope and Rates of Change

3.5 Slope-Intercept Form

3.6 Point-Slope Form

3.7 Introduction to Modeling

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-3 Cumulative Review

 

4. Systems of Linear Equations in Two Variables

4.1 Solving Systems of Linear Equations Graphically and Numerically

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

4.4 Systems of Linear Inequalities

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-4 Cumulative Review

 

5. Polynomials and Exponents

5.1 Rules for Exponents

5.2 Addition and Subtraction of Polynomials

5.3 Multiplication of Polynomials

5.4 Special Products

5.5 Integer Exponents and the Quotient Rule

5.6 Division of Polynomials

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-5 Cumulative Review

 

6. Factoring Polynomials and Solving Equations

6.1 Introduction to Factoring

6.2 Factoring Trinomials I (x2 + bx + c)

6.3 Factoring Trinomials II (ax2 + bx + c)

6.4 Special Types of Factoring

6.5 Summary of Factoring

6.6 Solving Equations by Factoring I (Quadratics)

6.7 Solving Equations by Factoring II (Higher Degree)

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-6 Cumulative Review Exercises

 

7. Rational Expressions

7.1 Introduction to Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction with Like Denominators

7.4 Addition and Subtraction with Unlike Denominators

7.5 Complex Fractions

7.6 Rational Equations and Formulas

7.7 Proportions and Variation

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-7 Cumulative Review

 

8. Introduction to Functions

8.1 Functions and Their Representations

8.2 Linear Functions

8.3 Compound Inequalities

8.4 Other Functions and Their Properties

8.5 Absolute Value Equations and Inequalities

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-8 Cumulative Review

 

9. Systems of Linear Equations

9.1 Systems of Linear Equations in Three Variables

9.2 Matrix Solutions of Linear Systems

9.3 Determinants

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-9 Cumulative Review Exercises

 

10. Radical Expressions and Functions

10.1 Radical Expressions and Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Operations on Radical Expressions

10.5 More Radical Functions

10.6 Equations Involving Radical Expressions

10.7 Complex Numbers

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-10 Cumulative Review

 

11. Quadratic Functions and Equations

11.1 Quadratic Functions and Their Graphs

11.2 Parabolas and Modeling

11.3 Quadratic Equations

11.4 The Quadratic Formula

11.5 Quadratic Inequalities

11.6 Equations in Quadratic Form

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-11 Cumulative Review

 

12. Exponential and Logarithmic Functions

12.1 Composite and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithms

12.5 Exponential and Logarithmic Equations

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-12 Cumulative Review Exercises

 

13. Conic Sections

13.1 Parabolas and Circles

13.2 Ellipses and Hyperbolas

13.3 Nonlinear Systems of Equations and Inequalities

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-13 Cumulative Review

 

14. Sequences and Series

14.1 Sequences

14.2 Arithmetic and Geometric Sequences

14.3 Series

14.4 The Binomial Theorem

Summary - Review Exercises - Test - Extended and Discovery Exercises

Chapters 1-14 Cumulative Review Exercises

 

Appendix A. Using the Graphing Calculator

Appendix B. Sets

Appendix C. Linear Programming

Appendix D. Synthetic Division

Bibliography

Answers to Selected Exercises

Photo Credits

Glossary

Index