Elementary & Intermediate Algebra, 3e is 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 1 Real Numbers and Their Properties 1.1 The Real Numbers 1.2 Fractions 1.3 Addition and Subtraction of Real Numbers 1.4 Multiplication and Division of Real Numbers 1.5 Exponential Expressions and the Order of Operations 1.6 Algebraic Expressions 1.7 Properties of the Real Numbers 1.8 Using the Properties to Simplify Expressions Chapter 1 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 1 Test * Critical Thinking 2 Linear Equations and Inequalities in One Variable 2.1 The Addition and Multiplication Properties of Equality 2.2 Solving General Linear Equations 2.3 More Equations 2.4 Formulas 2.5 Translating Verbal Expressions into Algebraic Expressions 2.6 Number, Geometric, and Uniform Motion Applications 2.7 Discount, Investment, and Mixture Applications 2.8 Inequalities 2.9 Solving Inequalities and Applications Chapter 2 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 2 Test * Making Connections: A review of Chapters 1-2 * Critical Thinking 3 Linear Equations and Inequalities in Two Variables 3.1 Graphing Lines in the Coordinate Plane 3.2 Slope 3.3 Equations of Lines in Slope-Intercept Form 3.4 The Point-Slope Form 3.5 Variations 3.6 Graphing Linear Inequalities in Two Variables Chapter 3 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 3 Test * Making Connections: a review of Chapters 1-3 * Critical Thinking 4 Exponents and Polynomials 4.1 The Rules of Exponents 4.2 Negative Exponents and Scientific Notation 4.3 Addition and Subtraction of Polynomials 4.4 Multiplication of Polynomials 4.5 Multiplication of Binomials 4.6 Special Products 4.7 Division of Polynomials Chapter 4 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 4 Test * Making Connections: a review of Chapters 1-4 * Critical Thinking 5 Factoring 5.1 Factoring Out Common Factors 5.2 Special Products and Grouping 5.3 Factoring the Trinomial ax^2 + bx + c with a = 1 5.4 Factoring the Trinomial ax^2 + bx + c with a ' 1 5.5 The Factoring Strategy 5.6 Solving Quadratic Equations by Factoring Chapter 5 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 5 Test * Making Connections: a review of Chapters 1-5 * Critical Thinking 6 Rational Expressions 6.1 Reducing Rational Expressions 6.2 Multiplication and Division 6.3 Finding the Least Common Denominator 6.4 Addition and Subtraction 6.5 Complex Fractions 6.6 Solving Equations with Rational Expressions 6.7 Applications of Ratios and Proportions 6.8 Applications of Rational Expressions Chapter 6 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 6 Test * Making Connections: a review of Chapters 1-6 * Critical Thinking 7 Systems of Linear Equations 7.1 Solving Systems by Graphing and Substitution 7.2 The Addition Method 7.3 Systems of Linear Equations in Three Variables Chapter 7 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 7 Test * Making Connections: a review of Chapters 1-7 * Critical Thinking 8 More on Inequalities 8.1 Compound Inequalities in One Variable 8.2 Absolute Value Equations and Inequalities 8.3 Compound Inequalities in Two Variables 8.4 Linear Programming Chapter 8 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 8 Test * Making Connections: a review of Chapters 1-8 * Critical Thinking 9 Radicals and Rational Exponents 9.1 Radicals 9.2 Rational Exponents 9.3 Adding, Subtracting, and Multiplying Radicals 9.4 Quotients, Powers, and Rationalizing Denominators 9.5 Solving Equations with Radicals and Exponents 9.6 Complex Numbers Chapter 9 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 9 Test * Making Connections: a review of Chapters 1-9 * Critical Thinking 10 Quadratic Equations and Inequalities 10.1 Factoring and Completing the Square 10.2 The Quadratic Formula 10.3 More on Quadratic Equations 10.4 Graphing Parabolas 10.5 Quadratic and Rational Inequalities Chapter 10 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 10 Test * Making Connections: a review of Chapters 1-10 * Critical Thinking 11 Functions 11.1 Functions and Relations 11.2 Graphs of Functions and Relations 11.3 Transformations of Graphs 11.4 Graphs of Polynomial Functions 11.5 Graphs of Rational Functions 11.6 Combining Functions 11.7 Inverse Functions Chapter 11 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 11 Test * Making Connections: a review of Chapters 1-11 * Critical Thinking 12 Exponential and Logarithmic Functions 12.1 Exponential Functions and Their Applications 12.2 Logarithmic Functions and Their Applications 12.3 Properties of Logarithms 12.4 Solving Equations and Applications Chapter 12 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 12 Test * Making Connections: a review of Chapters 1-12 * Critical Thinking 13 Nonlinear Systems and the Conic Sections 13.1 Nonlinear Systems of Equations 13.2 The Parabola 13.3 The Circle 13.4 The Ellipse and Hyperbola 13.5 Second-Degree Inequalities Chapter 13 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 13 Test * Making Connections: a review of Chapters 1-13 * Critical Thinking 14 Sequences and Series 14.1 Sequences 14.2 Series 14.3 Arithmetic Sequences and Series 14.4 Geometric Sequences and Series 14.5 Binomial Expansions Chapter 14 Wrap-Up * Summary * Enriching Your Mathematical Word Power * Review Exercises * Chapter 14 Test * Making Connections: A Review of Chapter 1-14 * Critical Thinking Appendix A: Geometry Review Exercises Appendix B: Sets Appendix C: Chapters 1-6 Diagnostic Test Appendix D: Chapters 1-6 Review Answers to Selected Exercises Index
