College Algebra Essentials

By Julie Miller



When Julie Miller began writing her successful developmental math series, one of her primary goals was to bridge the gap between preparatory courses and college algebra. For thousands of students, the Miller/O’Neill/Hyde (or M/O/H) series has provided a solid foundation in developmental mathematics. With the Miller College Algebra series, Julie has carried forward her clear, concise writing style; highly effective pedagogical features; and complete author-created technological package to students in this course area.

The main objectives of the college algebra series are three-fold:

-Provide students with a clear and logical presentation of -the basic concepts that will prepare them for continued study in mathematics.

-Help students develop logical thinking and problem-solving skills that will benefit them in all aspects of life.

-Motivate students by demonstrating the significance of mathematics in their lives through practical applications.

TABLE OF CONTENTS

Chapter R: Review of Prerequisites
Section R.1 Sets and the Real Number Line
Section R.2 Models, Algebraic Expressions, and Properties of Real Numbers
Section R.3 Integer Exponents and Scientific Notation
Section R.4 Rational Exponents and Radicals
Section R.5 Polynomials and Multiplication of Radicals
Problem Recognition Exercises: Simplifying Algebraic Expressions
Section R.6 Factoring
Section R.7 Rational Expressions and More Operations on Radicals

Chapter 1: Equations and Inequalities
Section 1.1 Linear Equations and Rational Equations
Section 1.2 Applications and Modeling with Linear Equations
Section 1.3 Complex Numbers
Section 1.4 Quadratic Equations
Problem Recognition Exercises: Simplifying Expressions versus Solving Equations
Section 1.5 Applications of Quadratic Equations
Section 1.6 More Equations and Applications
Section 1.7 Linear Inequalities and Compound Inequalities
Section 1.8 Absolute Value Equations and Inequalities
Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities

Chapter 2: Functions and Graphs
Section 2.1 The Rectangular Coordinate System and Graphing Utilities
Section 2.2 Circles
Section 2.3 Functions and Relations
Section 2.4 Linear Equations in Two Variables and Linear Functions
Section 2.5 Applications of Linear Equations and Modeling
Problem Recognition Exercises: Comparing Graphs of Equations
Section 2.6 Transformation of Graphs
Section 2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions
Section 2.8 The Algebra of Functions

Chapter 3: Polynomial and Rational Functions
Section 3.1 Quadratic Functions and Applications
Section 3.2 Introduction to Polynomial Functions
Section 3.3 Division of Polynomials and the Remainder and Factor Theorems
Section 3.4 Zeros of Polynomials
Section 3.5 Rational Functions
Problem Recognition Exercises: Polynomial and Rational Functions
Section 3.6 Polynomial and Rational Inequalities
Problem Recognition Exercises: Solving Equations and Inequalities
Section 3.7 Variation

Chapter 4: Exponential and Logarithmic Functions
Section 4.1 Inverse Functions
Section 4.2 Exponential Functions
Section 4.3 Logarithmic Functions
Problem Recognition Exercises: Analyzing Functions
Section 4.4 Properties of Logarithms
Section 4.5 Exponential and Logarithmic Equations
Section 4.6 Modeling with Exponential and Logarithmic Functions

Chapter 5: Systems of Equations and Inequalities
Section 5.1 Systems of Linear Equations in Two Variables and Applications
Section 5.2 Systems of Linear Equations in Three Variables and Applications
Section 5.3 Partial Fraction Decomposition
Section 5.4 Systems of Nonlinear Equations in Two Variables
Section 5.5 Inequalities and Systems of Inequalities in Two Variables
Problem Recognition Exercises: Equations and Inequalities in Two Variables
Section 5.6 Linear Programming



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