Essentials of College Algebra

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Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland–College Park. His hobbies include travel, dancing, bicycling, and hiking.

Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a bachelor’s degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri–Rolla, the second in Adult Education from the University of Missouri–St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding.

Preface   

Resources for Success   

R: Review of Basic Concepts

R.1 Sets

R.2 Real Numbers and Their Properties

R.3 Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Rational Exponents

R.7 Radical Expressions

1: Equations and Inequalities

1.1 Linear Equations

1.2 Applications and Modeling with Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications and Modeling with Quadratic Equations

1.6 Other Types of Equations and Applications

1.7 Inequalities

1.8 Absolute Value Equations and Inequalities

2: Graphs and Functions

2.1 Rectangular Coordinates and Graphs

2.2 Circles

2.3 Functions

2.4 Linear Functions

2.5 Equations of Lines and Linear Models

2.6 Graphs of Basic Functions

2.7 Graphing Techniques

2.8 Function Operations and Composition

3: Polynomials and Rational Functions

3.1 Quadratic Functions and Models

3.2 Synthetic Division

3.3 Zeros of Polynomial Functions

3.4 Polynomial Functions: Graphs, Applications, and Models

3.5 Rational Functions: Graphs, Applications, and Models

3.6 Variation

4: Inverse, Exponential, and Logarithmic Functions

4.1 Inverse Functions

4.2 Exponential Functions

4.3 Logarithmic Functions

4.4 Evaluating Logarithms and the Change-of-Base Theorem

4.5 Exponential and Logarithmic Equations

4.6 Applications and Models of Exponential Growth and Decay

5: Systems and Matrices

5.1 Systems of Linear Equations

5.2 Matrix Solution of Linear Systems

5.3 Determinant Solution of Linear Systems

5.4 Partial Fractions

5.5 Nonlinear Systems of Equations

5.6 Systems of Inequalities and Linear Programming

5.7 Properties of Matrices

5.8 Matrix Inverses

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