Beginning and Intermediate Algebra with Applications & Visualization

Gary Rockswold is a professor of mathematics at Minnesota State University—Mankato. He received his BA in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State. He was elected to the honor societies of Phi Beta Kappa, Phi Kappa Phi, and Sigma Xi. He has been a principal investigator at the Minnesota Supercomputer Institute and has published several research articles discussing parallel processing and numerical analysis. He is also the author or coauthor of more than 10 current textbooks. At regional and national meetings, he has given numerous presentations related to teaching mathematics. During his thirty-five-year career, Gary has taught mathematics, physical science, astronomy, and computer science at a variety of student levels, ranging from junior high to graduate. Making mathematics meaningful and relevant for students at the developmental and precalculus levels is of special interest to him. He also has a passion for professing mathematics and for communicating the amazing impact that mathematics has on our society.   Terry Krieger has taught mathematics for over fifteen years at the middle school, high school, vocational, community college, and university levels. He graduated summa cum laude from Bemidji State University in Bemidji, Minnesota with a BA in secondary mathematics education. 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. Outside of teaching, Terry enjoys wilderness camping, trout fishing and home improvement projects. His past experiences include running two marathons, climbing Mt. Kilimanjaro, and watching the sunset from the banks of the Nile. He currently resides in Rochester, Minnesota with his wife and family. Terry has been involved with various aspects of mathematics textbook publication for more than ten years.

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

 

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

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

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

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

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)

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

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

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

Chapters 1-9 Cumulative Review Exercises

 

10. Radical Expressions and Functions

10.1 Radical Expressions and Rational Exponents

10.2 Simplifying Radical Expressions

10.3 Operations on Radical Expressions

10.4 Radical Functions

10.5 Equations involving Radical Expressions

10.6 Complex Numbers

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

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

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

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

Chapters 1-14 Cumulative Review Exercises

 

Appendix A. Using the Graphing Calculator

Appendix B. Sets

Appendix C. Linear Programming

Appendix D. Synthetic Division