Elementary and Intermediate Algebra

by Dugopolski, Mark

• ISBN13: 9780077224820
• ISBN10: 0077224825
• Edition: 3rd
• Format: Hardcover
• Copyright: 2008-01-09
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

Elementary & Intermediate Algebra, 3eis part of the latest offerings in the successful Dugopolski series in mathematics. The author's goal is to explain mathematical concepts to students in a language they can understand. In this book, students and faculty will find short, precise explanations of terms and concepts written in understandable language. The author uses concrete analogies to relate math to everyday experiences. For example, when the author introduces the Commutative Property of Addition, he uses a concrete analogy that "the price of a hamburger plus a Coke is the same as a Coke plus a hamburger". Given the importance of examples within a math book, the author has paid close attention to the most important details for solving the given topic. Dugopolski includes a double cross-referencing system between the examples and exercise sets, so no matter which one the students start with, they will see the connection to the other. Finally, the author finds it important to not only provide quality, but also a good quantity of exercises and applications. The Dugopolski series is known for providing students and faculty with the most quantity and quality of exercises as compared to any other developmental math series on the market. In completing this revision, Dugopolski feels he has developed the clearest and most concise developmental math series on the market, and he has done so without comprising the essential information every student needs to become successful in future mathematics courses. The book is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone.

Table of Contents

To the student preface

Real Numbers and Their Properties

The Real Numbers

Fractions

Addition and Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Exponential Expressions and the Order of Operations

Algebraic Expressions

Properties of the Real Numbers

Using the Properties to Simplify Expressions

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Critical Thinking

Linear Equations and Inequalities in One Variable

The Addition and Multiplication Properties of Equality

Solving General Linear Equations

More Equations

Formulas

Translating Verbal Expressions into Algebraic Expressions

Number, Geometric, and Uniform Motion Applications

Discount, Investment, and Mixture Applications

Inequalities

Solving Inequalities and Applications

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

A review of Chapters 1-2 • Critical Thinking

Linear Equations and Inequalities in Two Variables

Graphing Lines in the Coordinate Plane

Slope

Equations of Lines in Slope-Intercept Form

The Point-Slope Form

Variations

Graphing Linear Inequalities in Two Variables

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-3 • Critical Thinking

Exponents and Polynomials

The Rules of Exponents

Negative Exponents and Scientific Notation

Addition and Subtraction of Polynomials

Multiplication of Polynomials

Multiplication of Binomials

Special Products

Division of Polynomials

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-4 • Critical Thinking

Factoring

Factoring Out Common Factors

Special Products and Grouping

Factoring the Trinomial ax² + bx + c with a = 1

Factoring the Trinomial ax² + bx + c with a ¿ 1

The Factoring Strategy

Solving Quadratic Equations by Factoring

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-5 • Critical Thinking

Rational Expressions

Reducing Rational Expressions

Multiplication and Division

Finding the Least Common Denominator

Addition and Subtraction

Complex Fractions

Solving Equations with Rational Expressions

Applications of Ratios and Proportions

Applications of Rational Expressions

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-6 • Critical Thinking

Systems of Linear Equations

Solving Systems by Graphing and Substitution

The Addition Method

Systems of Linear Equations in Three Variables

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-7 • Critical Thinking

More on Inequalities

Compound Inequalities in One Variable

Absolute Value Equations and Inequalities

Compound Inequalities in Two Variables

Linear Programming

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-8 • Critical Thinking

Radicals and Rational Exponents

Radicals

Rational Exponents

Adding, Subtracting, and Multiplying Radicals

Quotients, Powers, and Rationalizing Denominators

Solving Equations with Radicals and Exponents

Complex Numbers

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-9 • Critical Thinking

Quadratic Equations and Inequalities

Factoring and Completing the Square

The Quadratic Formula

More on Quadratic Equations

Graphing Parabolas

Quadratic and Rational Inequalities

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-10 • Critical Thinking

Functions

Functions and Relations

Graphs of Functions and Relations

Transformations of Graphs

Graphs of Polynomial Functions

Graphs of Rational Functions

Combining Functions

Inverse Functions

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-11 • Critical Thinking

Exponential and Logarithmic Functions

Exponential Functions and Their Applications

Logarithmic Functions and Their Applications

Properties of Logarithms

Solving Equations and Applications

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-12 • Critical Thinking

Nonlinear Systems and the Conic Sections

Nonlinear Systems of Equations

The Parabola

The Circle

The Ellipse and Hyperbola

Second-Degree Inequalities

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

a review of Chapters 1-13 • Critical Thinking

Sequences and Series

Sequences

Series

Arithmetic Sequences and Series

Geometric Sequences and Series

Binomial Expansions

Wrap-Up • Summary • Enriching Your Mathematical Word Power • Review Exercises •

Test • Making Connections

A Review of Chapter 1-14 • Critical Thinking

Geometry Review Exercises

Sets

Chapters 1-6 Diagnostic Test

Chapters 1-6 Review Answers to

Selected Exercises

Index

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