Intermediate Algebra Through Applications

Geoffrey Akst and Sadie Bragg have worked together for many years as professors of mathematics at Borough of Manhattan Community College/City University of New York. They met as graduate students at Teachers College, Columbia University, where they were both working on degrees in the teaching of college mathematics. The emphasis on applications in their texts reflects a concern they share for helping students understand why the topics to be studied are useful. Dr. Akst for years has begun his classes with the payoff question:¿ Why is this material worth learning? A native New Yorker, he enjoys surfing the Web, listening to good music, and traveling to exciting places. Dr. Bragg, who began her career in math education as a high school geometry teacher, credits her teachers with inspiring her love for mathematics and an appreciation of its utility. A transplanted Virginian, she spends her time with her family and her beautiful grandchildren.

Preface

1. Algebra Basics

1.1 Introduction to Real Numbers

1.2 Operations with Real Numbers

1.3 Properties of Real Numbers

1.4 Laws of Exponents and Scientific Notation

1.5 Algebraic Expressions: Translating, Evaluating, and Simplifying

2. Linear Equations and Inequalities

2.1 Solving Linear Equations

2.2 Solving Literal Equations and Formulas

2.3 Solving Linear Inequalities

2.4 Solving Compound Inequalities

2.5 Solving Absolute Value Equations and Inequalities

3. Graphs, Linear Equations and Inequalities, and Functions

3.1 The Rectangular Coordinate System

3.2 Slope

3.3 Graphing Linear Equations

3.4 More on Graphing Linear Equations

3.5 Graphing Linear Inequalities

3.6 Introduction to Functions

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations Algebraically

4.3 Solving Systems of Linear Equations in Three Variables

4.4 Solving Systems of Linear Equations by Using Matrices

4.5 Solving Systems of Linear Inequalities

5. Polynomials

5.1 Addition and Subtraction of Polynomials

5.2 Multiplication of Polynomials

5.3 Division of Polynomials

5.4 The Greatest Common Factor and Factoring by Grouping

5.5 Factoring Trinomials

5.6 Special Factoring

5.7 Solving Quadratic Equations by Factoring

6. Rational Expressions and Equations

6.1 Multiplication and Division of Rational Expressions

6.2 Addition and Subtraction of Rational Expressions

6.3 Complex Rational Expressions

6.4 Solving Rational Equations

6.5 Variation

7. Radical Expressions and Equations

7.1 Radical Expressions and Rational Exponents

7.2 Simplifying Radical Expressions

7.3 Addition and Subtraction of Radical Expressions

7.4 Multiplication and Division of Radical Expressions

7.5 Solving Radical Equations

7.6 Complex Numbers

8. Quadratic Equations, Functions, and Inequalities

8.1 Solving Quadratic Equations: The Square Root Property of Equality; Completing the Square

8.2 Solving Quadratic Equations: The Quadratic Formula

8.3 More on Quadratic Equations

8.4 Graphing Quadratic Functions

8.5 Solving Quadratic and Rational Inequalities

9. Exponential and Logarithmic Functions

9.1 The Algebra of Functions and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Common Logarithms, Natural Logarithms, and Change of Base

9.6 Exponential and Logarithmic Equations

10. Conic Sections

10.1 Introduction to Conics; The Parabola

10.2 The Circle

10.3 The Ellipse and the Hyperbola

10.4 Solving Nonlinear Systems of Equations

10.5 Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities

Appedixes

A.1 Table of Symbols

A.2 Introduction to Graphing Calculators

A.3 Determinants and Cramer’s Rule

A.4 Synthetic Division

Answers

Glossary

Index

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