Algebra For College Students

by Dugopolski, Mark

• ISBN13: 9780072934823
• ISBN10: 0072934824
• Edition: 4th
• Format: Hardcover
• Copyright: 2004-12-01
• Publisher: McGraw-Hill College

Summary

The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems. Every section ending in the text begins with six simple writing exercises. These exercises are designed to get students to review the definitions and rules of the section before doing more traditional exercises.

Table of Contents

The Real Numbers

Sets

The Real Numbers

Operations on the Set of Real Numbers

Evaluating Expressions

Properties of the Real Numbers

Using the Properties

Linear Equations and Inequalities in One Variable

Linear Equations in One Variable

Formulas

Applications

Inequalities

Compound Inequalities

Absolute Value Equations and Inequalities

Linear Equations and Inequalities in Two Variables

Graphing Lines in the Coordinate Plane

Slope of a Line

Three Forms for the Equation of a Line

Linear Inequalities and Their Graphs

Functions and Relations

Systems of Linear Equations

Solving Systems by Graphing and Substitution

The Addition Method

Systems of Linear Equations in Three Variables

Solving Linear Systems Using Matrices

Determinants and Cramer's Rule

Linear Programming

Exponents and Polynomials

Integral Exponents and Scientific Notation

The Power Rules

Polynomials and Polynomial Functions

Multiplying Binomials

Factoring Polynomials

Factoring ax^2 + bx + c

Factoring Strategy

Solving Equations by Factoring

Rational Expressions and Functions

Properties of Rational Expressions and Functions

Multiplication and Division

Addition and Subtraction

Complex Fractions

Division of Polynomials

Solving Equations Involving Rational Expressions

Applications

Radicals and Rational Exponents

Radicals

Rational Exponents

Operations with Radicals

Quotients, Powers, and Rationalizing Denominators

Solving Equations with Radicals and Exponents

Complex Numbers

Quadratic Equations, Functions, and Inequalities

Factoring and Completing the Square

The Quadratic Formula

Quadratic Functions and Their Graphs

More on Quadratic Equations

Quadratic and Rational Inequalities

Additional Function Topics

Graphs of Functions and Relations

Transformations of Graphs

Combining Functions

Inverse Functions

Variation Chapter

Polynomial and Rational Functions

The Factor Theorem

Zeros of a Polynomial Function

The Theory of Equations

Graphs of Polynomial Functions

Graphs of Rational Functions

Exponential and Logarithmic Functions

Exponential Functions and Their Applications

Logarithmic Functions and Their Applications

Properties of Logarithms

Solving Equations and Applications

Nonlinear Systems and the Conic Sections

Nonlinear Systems of Equations

The Parabola

The Circle

The Ellipse and Hyperbola

Second-Degree Inequalities

Sequences and Series

Sequences

Series

Arithmetic Sequences and Series

Geometric Sequences and Series

Binomial Expansions

Counting and Probability

Counting and Permutations

Combinations

Probability

Geometry Review Exercises

Sets

Final Exam Review

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