by Gary Rockswold and Terry Krieger
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Intermediate Algebra with Applications and Visualization, Second Edition, offers an innovative approach to the 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. The early introduction of functions and graphs allows the instructor to use applications and visualization to present mathematical topics. Real data, graphs, and tables play an important role in the course, giving meaning to the numbers and equations that students encounter. 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. Real Numbers and Algebra.
Describing Data with Sets of Numbers.
Operations on Real Numbers.
Integer Exponents.
Variables, Equations, and Formulas.
Introduction to Graphing.
2. Linear Functions and Models.
Functions and Their Representations.
Linear Functions.
The Slope of a Line.
Equations of Lines and Linear Models.
3. Linear Equations and Inequalities.
Linear Equations.
Introduction to Problem Solving.
Linear Inequalities.
Compound Inequalities.
Absolute Value Equations and Inequalities.
4. Systems of Linear Equations.
Systems of Linear Equations in Two Variables.
The Substitution and Elimination Methods.
Systems of Linear Inequalities.
Introduction to Linear Programming.
Systems of Linear Equations in Three Variables.
Matrix Solutions of Linear Systems.
Determinants.
5. Polynomial Expressions and Functions.
Polynomial Functions.
Multiplication of Polynomials.
Factoring Polynomials.
Factoring Trinomials.
Special Types of Factoring.
Polynomial Equations.
6. Rational Expressions and Functions.
Introduction to Rational Functions and Equations.
Multiplication and Division of Rational Expressions.
Addition and Subtraction of Rational Expressions.
Rational Equations.
Complex Fractions.
Modeling with Proportions and Variation.
Division of Polynomials.
7. Radical Expressions and Functions.
Radical Expressions and Rational Exponents.
Simplifying Radical Expressions.
Operations on Radical Expressions.
Radical Functions.
Equations Involving Radical Expressions.
Complex Numbers.
8. Quadratic Functions and Equations.
Quadratic Functions and Their Graphs.
Parabolas and Modeling.
Quadratic Equations.
The Quadratic Formula.
Quadratic Inequalities.
Equations in Quadratic Form.
9. Exponential and Logarithmic Functions.
Composite and Inverse Functions.
Exponential Functions.
Logarithmic Functions.
Properties of Logarithms.
Exponential and Logarithmic Equations.
10. Conic Sections.
Parabolas and Circles.
Ellipses and Hyperbolas.
Nonlinear Systems of Equations and Inequalities.
11. Sequences and Series.
Sequences.
Arithmetic and Geometric Sequences.
Series.
The Binomial Theorem.
Graphing Calculator Appendix.
Glossary.
Bibliography.
Answers to Selected Exercises.
Index.
Gary Rockswold and Terry Krieger
ISBN13: 978-0321158925Intermediate Algebra with Applications and Visualization, Second Edition, offers an innovative approach to the 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. The early introduction of functions and graphs allows the instructor to use applications and visualization to present mathematical topics. Real data, graphs, and tables play an important role in the course, giving meaning to the numbers and equations that students encounter. 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. Real Numbers and Algebra.
Describing Data with Sets of Numbers.
Operations on Real Numbers.
Integer Exponents.
Variables, Equations, and Formulas.
Introduction to Graphing.
2. Linear Functions and Models.
Functions and Their Representations.
Linear Functions.
The Slope of a Line.
Equations of Lines and Linear Models.
3. Linear Equations and Inequalities.
Linear Equations.
Introduction to Problem Solving.
Linear Inequalities.
Compound Inequalities.
Absolute Value Equations and Inequalities.
4. Systems of Linear Equations.
Systems of Linear Equations in Two Variables.
The Substitution and Elimination Methods.
Systems of Linear Inequalities.
Introduction to Linear Programming.
Systems of Linear Equations in Three Variables.
Matrix Solutions of Linear Systems.
Determinants.
5. Polynomial Expressions and Functions.
Polynomial Functions.
Multiplication of Polynomials.
Factoring Polynomials.
Factoring Trinomials.
Special Types of Factoring.
Polynomial Equations.
6. Rational Expressions and Functions.
Introduction to Rational Functions and Equations.
Multiplication and Division of Rational Expressions.
Addition and Subtraction of Rational Expressions.
Rational Equations.
Complex Fractions.
Modeling with Proportions and Variation.
Division of Polynomials.
7. Radical Expressions and Functions.
Radical Expressions and Rational Exponents.
Simplifying Radical Expressions.
Operations on Radical Expressions.
Radical Functions.
Equations Involving Radical Expressions.
Complex Numbers.
8. Quadratic Functions and Equations.
Quadratic Functions and Their Graphs.
Parabolas and Modeling.
Quadratic Equations.
The Quadratic Formula.
Quadratic Inequalities.
Equations in Quadratic Form.
9. Exponential and Logarithmic Functions.
Composite and Inverse Functions.
Exponential Functions.
Logarithmic Functions.
Properties of Logarithms.
Exponential and Logarithmic Equations.
10. Conic Sections.
Parabolas and Circles.
Ellipses and Hyperbolas.
Nonlinear Systems of Equations and Inequalities.
11. Sequences and Series.
Sequences.
Arithmetic and Geometric Sequences.
Series.
The Binomial Theorem.
Graphing Calculator Appendix.
Glossary.
Bibliography.
Answers to Selected Exercises.
Index.