Essentials of College Algebra with Modeling and Visualization

Dr. Gary Rockswold has taught mathematics for 35 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 professor emeritus at Minnesota State University, Mankato and has been a principal investigator at the Minnesota Supercomputer Institute. 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. His passion is to write and speak about the relevance and amazing impact that mathematics has on our society. Outside of mathematics, he enjoys boating, sailing, and spending time with his wife and two adult children.

1. Introduction to Functions and Graphs

1.1 Numbers, Data, and Problem Solving

1.2 Visualizing and Graphing Data

1.3 Functions and Their Representations

1.4 Types of Functions

1.5 Functions and Their Rates of Change

 

2. Linear Functions and Equations

2.1 Linear Functions and Models

2.2 Equations of Lines

2.3 Linear Equations

2.4 Linear Inequalities

2.5 Absolute Value Equations and Inequalities

 

3. Quadratic Functions and Equations

3.1 Quadratic Functions and Models

3.2 Quadratic Equations and Problem Solving

3.3 Complex Numbers

3.4 Quadratic Inequalities

3.5 Transformations of Graphs

 

4. More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

4.2 Polynomial Functions and Models

4.3 Division of Polynomials

4.4 Real Zeros of Polynomial Functions

4.5 The Fundamental Theorem of Algebra

4.6 Rational Functions and Models

4.7 More Equations and Inequalities

4.8 Radical Equations and Power Functions

 

5. Exponential and Logarithmic Functions

5.1 Combining Functions

5.2 Inverse Functions and Their Representations

5.3 Exponential Functions and Models

5.4 Logarithmic Functions and Models

5.5 Properties of Logarithms

5.6 Exponential and Logarithmic Equations

5.7 Constructing Nonlinear Models

 

6. Systems of Equations and Inequalities

6.1 Functions and Systems of Equations in Two Variables

6.2 Systems of Inequalities in Two Variables

6.3 Systems of Linear Equations in Three Variables

6.4 Solutions to Linear Systems Using Matrices

6.5 Properties and Applications of Matrices

6.6 Inverses of Matrices

6.7 Determinants

 

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