Elementary and Intermediate Algebra

R. David Gustafson is professor emeritus of mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. In addition to this best-selling college algebra resource with Jeffrey Hughes, he has co-authored Gustafson/Karr/Massey's BEGINNING ALGEBRA; INTERMEDIATE ALGEBRA; BEGINNING AND INTERMEDIATE ALGEBRA; BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH; and the Tussy/Gustafson and Tussy/Gustafson/Koenig Developmental Mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in the American Mathematical Association of Two-Year Colleges (AMATYC) as a Midwest vice president. He has also served as president of IMACC, AMATYC's Illinois affiliate. Professor Gustafson earned a master of arts from Rockford College in Illinois as well as a master of science from Northern Illinois University. Alan Tussy received a Bachelor of Science in Mathematics from the University of Redlands and a Master of Science in Applied Mathematics from California State University, Los Angeles. He has taught across a variety of course and curriculum areas from pre-algebra to differential equations at Arcadia High School and Citrus Community College in Glendora, CA. He has authored best-selling paperback and hardcover developmental mathematic series now in their 6th editions published by Cengage. An extraordinary author, he is dedicated to his students' success and is a relentlessly meticulous and creative visionary who maintains a keen focus on the greatest challenges students of today face in mathematics. He is a well-received conference speaker and has recently focused on mentoring and counseling the next generation of mathematics instructors.

1. AN INTRODUCTION TO ALGEBRA.
Introducing the Language of Algebra. Fractions. The Real Numbers. Adding Real Numbers; Properties of Addition. Subtracting Real Numbers. Multiplying and Dividing Real Numbers; Multiplication and Division Properties. Exponents and Order of Operations. Algebraic Expressions. Simplifying Algebraic Expressions Using Properties of Real Numbers. Chapter Summary. Chapter Test.
2. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING.
Solving Equations Using Properties of Equality. More about Solving Equations. Applications of Percent. Formulas. Problem Solving. More about Problem Solving. Solving Inequalities. Chapter Summary. Chapter Test.
3. GRAPHING LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES; FUNCTIONS.
Graphing Using the Rectangular Coordinate System. Graphing Linear Equations. Intercepts. Slope and Rate of Change. Slope-Intercept Form. Point-Slope Form. Graphing Linear Inequalities. An Introduction to Functions. Chapter Summary. Chapter Test.
4. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.
Solving Systems of Equations by Graphing. Solving Systems of Equations by Substitution. Solving Systems of Equations by Elimination (Addition). Problem Solving Using Systems of Equations. Solving Systems of Linear Inequalities. Chapter Summary. Chapter Test.
5. EXPONENTS AND POLYNOMIALS.
Rules for Exponents. Zero and Negative Exponents. Scientific Notation. Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Special Products. Polynomials. Chapter Summary. Chapter Test.
6. FACTORING AND QUADRATIC EQUATIONS.
The Greatest Common Factor; Factoring by Grouping. Factoring Trinomials of the Form x2 + bx + c. Factoring Trinomials of the Form ax2 + bx + c. Factoring Perfect-Square Trinomials and the Difference of Two Squares. Factoring the Sum and Difference of Two Cubes. A Factoring Strategy. Solving Quadratic Equations by Factoring. Applications of Quadratic Equations. Chapter Summary. Chapter Test.
7. RATIONAL EXPRESSIONS AND EQUATIONS.
Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting with Like Denominators; Least Common Denominators. Adding and Subtracting with Unlike Denominators. Simplifying Complex Fractions. Solving Rational Equations. Problem Solving Using Rational Equations. Ratios, Rates, Proportions and Similar Triangles. Chapter Summary. Chapter Test. Cumulative Review Chapters 1–7.
8. TRANSITION TO INTERMEDIATE ALGEBRA.
Review of Solving Linear Equations, Formulas, and Linear Inequalities; Applications. Functions. Graphs of Functions. Solving Compound Inequalities. Solving Absolute Value Equations and Inequalities. Review of Factoring Methods: GCF, Grouping, Trinomials. Review of Factoring Methods: The Difference of Two Squares; The Sum and Difference of Two Cubes. Review of Rational Expressions and Rational Equations; Rational Functions. Variation. Chapter Summary. Chapter Test.
9. RADICAL EXPRESSIONS AND EQUATIONS.
Radical Expressions and Radical Functions. Rational Exponents. Simplifying and Combining Radical Expressions. Multiplying and Dividing Radical Expressions. Solving Radical Equations. Geometric Applications of Radicals. Complex Numbers. Chapter Summary. Chapter Test.
10. QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES.
The Square Root Property and Completing the Square. The Quadratic Formula. The Discriminant and Equations That Can Be Written in Quadratic Form. Quadratic Functions and Their Graphs. Quadratic and Other Nonlinear Inequalities. Chapter Summary. Chapter Test.
11. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Algebra and Composition of Functions. Inverse Functions. Exponential Functions. Base-e Exponential Functions. Logarithmic Functions. Base-e Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary. Chapter Test.
12. MORE ON SYSTEMS OF EQUATIONS.
Solving Systems of Equations in Two Variables; Applications. Solving Systems of Equations in Three Variables. Problem Solving Using Systems of Three Equations. Solving Systems of Equations Using Matrices. Solving Systems of Equations Using Determinants. Chapter Summary. Chapter Test.
13. CONIC SECTIONS; MORE GRAPHING.
The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Nonlinear Systems of Equations. Chapter Summary. Chapter Test.
14. MISCELLANEOUS TOPICS.
The Binomial Theorem. Arithmetic Sequences and Series. Geometric Sequences and Series. Chapter Summary. Chapter Test. Group Project. Cumulative Review Chapters 8–14.
Appendix 1: Synthetic Division.
Appendix 2: Answers to Selected Problems.