# Essentials of College Algebra

**by**Lial, Margaret L.; Hornsby, John E.; Schneider, David I.

### 9780321664990

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## Summary

## Author Biography

**Marge Lial** has always been 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, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced 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 of 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.

## Table of Contents

R. Review of Basic Concepts

Sets

Real Numbers and Their Properties

Polynomials

Factoring Polynomials

Rational Expressions

Rational Exponents

Radical Expressions

1. Equations and Inequalities

Linear Equations

Applications and Modeling with Linear Equations

Complex Numbers

Quadratic Equations

Applications and Modeling with Quadratic Equations

Other Types of Equations and Applications

Inequalities

Absolute Value Equations and Inequalities

2. Graphs and Functions

Rectangular Coordinates and Graphs

Circles

Functions

Linear Functions

Equations of Lines; Curve Fitting

Graphs of Basic Functions

Graphing Techniques

Function Operations and Composition

3. Polynomial and Rational Functions

Quadratic Functions and Models

Synthetic Division

Zeros of Polynomial Functions

Polynomial Functions: Graphs, Applications, and Models

Rational Functions: Graphs, Applications, and Models

Variation

4. Inverse, Exponential, and Logarithmic Functions

Inverse Functions

Exponential Functions

Logarithmic Functions

Evaluating Logarithms and the Change-of-Base Theorem

Exponential and Logarithmic Equations

Applications and Models of Exponential Growth and Decay

5. Systems and Matrices

Systems of Linear Equations

Matrix Solution of Linear Systems

Determinant Solution of Linear Systems

Partial Fractions

Nonlinear Systems of Equations

Systems of Inequalities and Linear Programming

Properties of Matrices

Matrix Inverses

Glossary

Solutions to Selected Exercises

Answers to Selected Exercises

Index of Applications

Index