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by Gary K. Rockswold and Terry A. Krieger

Edition: 05Copyright: 2005

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

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Beginning and Intermediate Algebra with Applications and Visualization offers an innovative approach to the beginning and intermediate algebra curriculum that allows students to gain both skills and understanding. This text not only prepares students for future mathematics courses, but it also demonstrates to students the relevance of mathematics. This approach increases student interest, motivation, and the likelihood for success. Many students think in visual, concrete terms and not abstractly. This text helps students learn mathematics better by moving from the concrete to the abstract. It makes use of multiple representations (verbal, graphical, numerical, and symbolic), applications, visualization, and technology.

**1. Introduction to Algebra. **

Numbers, Variables, and Algebraic Expressions.

Fractions.

Exponents and Order of Operations.

Real Numbers and the Number Line.

Addition and Subtraction of Real Numbers.

Multiplication and Division of Real Numbers.

Properties of Real Numbers.

Simplifying and Writing Algebraic Expressions.

**2. Linear Equations and Inequalities. **

Introduction to Equations.

Linear Equations.

Introduction to Problem Solving.

Formulas.

Linear Inequalities.

**3. Graphing Equations. **

Introduction to Graphing.

Linear Equations in Two Variables.

More Graphing of Lines.

Slope and Rates of Change.

Slope-Intercept Form.

Point-Slope Form.

Introduction to Modeling.

**4. Systems of Linear Equations in Two Variables. **

Solving Systems of Linear Equations Graphically and Numerically.

Solving Systems of Linear Equations by Substitution.

Solving Systems of Linear Equations by Elimination.

Systems of Linear Inequalities.

**5. Polynomials and Exponents. **

Addition and Subtraction of Polynomials.

Rules for Exponents.

Multiplication of Polynomials.

Special Products.

Integer Exponents and the Quotient Rule.

Division of Polynomials.

**6. Factoring Polynomials and Solving Equations. **

Introduction to Factoring.

Factoring Trinomials (I).

Factoring Trinomials (II).

Special Types of Factoring.

Solving Equations by Factoring.

Factoring Polynomials.

**7. Rational Expressions. **

Introduction to Rational Expressions.

Multiplication and Division of Rational Expressions.

Addition and Subtraction of Rational Expressions (I).

Addition and Subtraction of Rational Expressions (II).

Complex Fractions.

Rational Equations and Formulas.

Proportions and Variation.

**8. Linear Functions and Models. **

Functions and Their Representations.

Linear Functions.

Compound Inequalities.

Other Functions and Their Properties.

Absolute Value Equations and Inequalities.

**9. Matrices and Systems of Linear Equations. **

Systems Equations in Three Variables.

Matrix Solutions of Linear Systems.

Determinants.

**10. Radical Expressions and Functions. **

Radical Expressions and Rational Exponents.

Simplifying Radical Expressions.

Operations on Radical Expressions.

Radical Functions.

Equations Involving Radical Expressions.

Complex Number.

**11. Quadratic Functions and Equations. **

Quadratic Functions and Their Graphs.

Parabolas and Modeling.

Quadratic Equations.

The Quadratic Formula.

Quadratic Inequalities.

Equations in Quadratic Form.

**12. Exponential and Logarithmic Functions. **

Composite and Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Properties of Logarithms.

Exponential and Logarithmic Equations.

**13. Conic Sections. **

Parabolas and Circles.

Ellipses and Hyperbolas.

Nonlinear Systems of Equations and Inequalities.

**14. Sequences and Series. **

Sequences.

Arithmetic and Geometric Sequences.

Series.

The Binomial Theorem.

Graphing Calculator Appendix.

Summary

Beginning and Intermediate Algebra with Applications and Visualization offers an innovative approach to the beginning and intermediate algebra curriculum that allows students to gain both skills and understanding. This text not only prepares students for future mathematics courses, but it also demonstrates to students the relevance of mathematics. This approach increases student interest, motivation, and the likelihood for success. Many students think in visual, concrete terms and not abstractly. This text helps students learn mathematics better by moving from the concrete to the abstract. It makes use of multiple representations (verbal, graphical, numerical, and symbolic), applications, visualization, and technology.

Table of Contents

**1. Introduction to Algebra. **

Numbers, Variables, and Algebraic Expressions.

Fractions.

Exponents and Order of Operations.

Real Numbers and the Number Line.

Addition and Subtraction of Real Numbers.

Multiplication and Division of Real Numbers.

Properties of Real Numbers.

Simplifying and Writing Algebraic Expressions.

**2. Linear Equations and Inequalities. **

Introduction to Equations.

Linear Equations.

Introduction to Problem Solving.

Formulas.

Linear Inequalities.

**3. Graphing Equations. **

Introduction to Graphing.

Linear Equations in Two Variables.

More Graphing of Lines.

Slope and Rates of Change.

Slope-Intercept Form.

Point-Slope Form.

Introduction to Modeling.

**4. Systems of Linear Equations in Two Variables. **

Solving Systems of Linear Equations Graphically and Numerically.

Solving Systems of Linear Equations by Substitution.

Solving Systems of Linear Equations by Elimination.

Systems of Linear Inequalities.

**5. Polynomials and Exponents. **

Addition and Subtraction of Polynomials.

Rules for Exponents.

Multiplication of Polynomials.

Special Products.

Integer Exponents and the Quotient Rule.

Division of Polynomials.

**6. Factoring Polynomials and Solving Equations. **

Introduction to Factoring.

Factoring Trinomials (I).

Factoring Trinomials (II).

Special Types of Factoring.

Solving Equations by Factoring.

Factoring Polynomials.

**7. Rational Expressions. **

Introduction to Rational Expressions.

Multiplication and Division of Rational Expressions.

Addition and Subtraction of Rational Expressions (I).

Addition and Subtraction of Rational Expressions (II).

Complex Fractions.

Rational Equations and Formulas.

Proportions and Variation.

**8. Linear Functions and Models. **

Functions and Their Representations.

Linear Functions.

Compound Inequalities.

Other Functions and Their Properties.

Absolute Value Equations and Inequalities.

**9. Matrices and Systems of Linear Equations. **

Systems Equations in Three Variables.

Matrix Solutions of Linear Systems.

Determinants.

**10. Radical Expressions and Functions. **

Radical Expressions and Rational Exponents.

Simplifying Radical Expressions.

Operations on Radical Expressions.

Radical Functions.

Equations Involving Radical Expressions.

Complex Number.

**11. Quadratic Functions and Equations. **

Quadratic Functions and Their Graphs.

Parabolas and Modeling.

Quadratic Equations.

The Quadratic Formula.

Quadratic Inequalities.

Equations in Quadratic Form.

**12. Exponential and Logarithmic Functions. **

Composite and Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Properties of Logarithms.

Exponential and Logarithmic Equations.

**13. Conic Sections. **

Parabolas and Circles.

Ellipses and Hyperbolas.

Nonlinear Systems of Equations and Inequalities.

**14. Sequences and Series. **

Sequences.

Arithmetic and Geometric Sequences.

Series.

The Binomial Theorem.

Graphing Calculator Appendix.

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

Published: 2005

International: No

**1. Introduction to Algebra. **

Numbers, Variables, and Algebraic Expressions.

Fractions.

Exponents and Order of Operations.

Real Numbers and the Number Line.

Addition and Subtraction of Real Numbers.

Multiplication and Division of Real Numbers.

Properties of Real Numbers.

Simplifying and Writing Algebraic Expressions.

**2. Linear Equations and Inequalities. **

Introduction to Equations.

Linear Equations.

Introduction to Problem Solving.

Formulas.

Linear Inequalities.

**3. Graphing Equations. **

Introduction to Graphing.

Linear Equations in Two Variables.

More Graphing of Lines.

Slope and Rates of Change.

Slope-Intercept Form.

Point-Slope Form.

Introduction to Modeling.

**4. Systems of Linear Equations in Two Variables. **

Solving Systems of Linear Equations Graphically and Numerically.

Solving Systems of Linear Equations by Substitution.

Solving Systems of Linear Equations by Elimination.

Systems of Linear Inequalities.

**5. Polynomials and Exponents. **

Addition and Subtraction of Polynomials.

Rules for Exponents.

Multiplication of Polynomials.

Special Products.

Integer Exponents and the Quotient Rule.

Division of Polynomials.

**6. Factoring Polynomials and Solving Equations. **

Introduction to Factoring.

Factoring Trinomials (I).

Factoring Trinomials (II).

Special Types of Factoring.

Solving Equations by Factoring.

Factoring Polynomials.

**7. Rational Expressions. **

Introduction to Rational Expressions.

Multiplication and Division of Rational Expressions.

Addition and Subtraction of Rational Expressions (I).

Addition and Subtraction of Rational Expressions (II).

Complex Fractions.

Rational Equations and Formulas.

Proportions and Variation.

**8. Linear Functions and Models. **

Functions and Their Representations.

Linear Functions.

Compound Inequalities.

Other Functions and Their Properties.

Absolute Value Equations and Inequalities.

**9. Matrices and Systems of Linear Equations. **

Systems Equations in Three Variables.

Matrix Solutions of Linear Systems.

Determinants.

**10. Radical Expressions and Functions. **

Radical Expressions and Rational Exponents.

Simplifying Radical Expressions.

Operations on Radical Expressions.

Radical Functions.

Equations Involving Radical Expressions.

Complex Number.

**11. Quadratic Functions and Equations. **

Quadratic Functions and Their Graphs.

Parabolas and Modeling.

Quadratic Equations.

The Quadratic Formula.

Quadratic Inequalities.

Equations in Quadratic Form.

**12. Exponential and Logarithmic Functions. **

Composite and Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Properties of Logarithms.

Exponential and Logarithmic Equations.

**13. Conic Sections. **

Parabolas and Circles.

Ellipses and Hyperbolas.

Nonlinear Systems of Equations and Inequalities.

**14. Sequences and Series. **

Sequences.

Arithmetic and Geometric Sequences.

Series.

The Binomial Theorem.

Graphing Calculator Appendix.