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Understanding Intermediate Algebra : Algebra for College Students / With CD-ROM

Understanding Intermediate Algebra : Algebra for College Students / With CD-ROM - 5th edition

ISBN13: 978-0534432232

Cover of Understanding Intermediate Algebra : Algebra for College Students / With CD-ROM 5TH 02 (ISBN 978-0534432232)
ISBN13: 978-0534432232
ISBN10: 0534432239
Cover type:
Edition/Copyright: 5TH 02
Publisher: Brooks/Cole Publishing Co.
Published: 2002
International: No

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Understanding Intermediate Algebra : Algebra for College Students / With CD-ROM - 5TH 02 edition

ISBN13: 978-0534432232

Lewis Hirsch and Arthur Goodman

ISBN13: 978-0534432232
ISBN10: 0534432239
Cover type:
Edition/Copyright: 5TH 02
Publisher: Brooks/Cole Publishing Co.

Published: 2002
International: No
Summary

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples - both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

Author Bio

Hirsch, Lewis : Rutgers University

Goodman, Arthur : Queens College of the City University of New York

Table of Contents

1. THE FUNDAMENTAL CONCEPTS

Basic Definitions: The Real Numbers and the Real Number Line
Operations with Real Numbers
Algebraic Expressions
Translating Phrases and Sentences into Algebraic Form
First-Degree Equations and Inequalities
Chapter Summary, Review Exercises, and Practice Test

2. EQUATIONS AND INEQUALITITES

Equations as Mathematical Models
First-Degree Equations and Applications
First-Degree Inequalities and Applications
Absolute-Value Equations and Inequalities
Chapter Summary, Review Exercises, and Practice Test

3. GRAPHING STRAIGHT LINES AND FUNCTIONS

The Rectangular Coordinate System and Graphing Straight Lines
Graphs and Equations
Relations and Functions: Basic Concepts
Function Notation
Interpreting Graphs
Chapter Summary, Review Exercises, and Practice Test
Cumulative Review and Practice Test: Chapters 1-3

4. EQUATIONS OF A LINE AND LINEAR SYSTEMS IN TWO VARIABLES

Straight Lines and Slope
Equations of a Line and Linear Functions as Mathematical Models
Linear Systems in Two Variables
Graphing Linear Inequalities in Two Variables
Chapter Summary, Review Exercises, and Practice Test

5. POLYNOMIAL EXPRESSIONS AND FUNCTIONS

Polynomial Functions as Mathematical Models
Polynomials: Sums, Differences, and Products
General Forms and Special Products
Factoring out the Greatest Common Factor
Factoring Trinomials
Solving Polynomial Equations by Factoring
Polynomial Division
Chapter Summary, Review Exercises, and Practice Test

6. RATIONAL EXPRESSIONS AND FUNCTIONS

Rational Functions
Equivalent Fractions
Multiplication and Division of Rational Expressions
Sums and Differences of Rational Expressions
Mixed Operations and Complex Fractions
Fractional Equations and Inequalities
Literal Equations
Applications: Rational Functions and Equations as Mathematical Models
Chapter Summary, Review Exercises, and Practice Test
Cumulative Review and Practice Test: Chapters 4-6

7. EXPONENTS AND RADICALS

Natural Number and Integer Exponents
Scientific Notation
Rational Exponents and Radical Notation
Simplifying Radical Expressions
Adding and Subtracting Radical Expressions
Multiplying and Dividing Radical Expressions
Radical Functions and Equations
Complex Numbers
Chapter Summary, Review Exercises, and Practice Test

8. QUADRATIC FUNCTIONS AND EQUATIONS

Quadratic Functions as Mathematical Models
Solving Quadratic Equations: The Factoring and Square Root Methods
Solving Quadratic Equations: Completing the Square
Solving Quadratic Equations: The Quadratic Formula
Equations Reducible to Quadratic Form (and More Radical Equations)
Graphing Quadratic Functions
Quadratic and Rational Inequalities
The Distance Formula: Circles
Chapter Summary, Review Exercises, and Practice Test

9. MORE ON FUNCTIONS

More on Function Notation: Split Functions
Composition and the Algebra of Functions
Types of Functions
Inverse Functions
Variation
Chapter Summary, Review Exercises, and Practice Test
Cumulative Review And Practice Test: Chapters 7-9

10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Exponential Functions
Logarithms and Logarithmic Functions
Properties of Logarithms
Common Logarithms, Natural Logarithms, and Change of Base
Exponential and Logarithmic Equations
Applications: Exponential and Logarithmic Functions as Mathematical Models
Chapter Summary, Review Exercises, and Practice Test

11. MORE SYSTEMS OF EQUATIONS AND SYSTEMS OF INEQUALITITIES

3x3 Linear Systems
Solving Linear Systems Using Augmented Matrices
The Algebra of Matrices
Solving Linear Systems Using Matrix Inverses
Determinants and Cramer's Rule
Systems of Linear Inequalities
Nonlinear Systems of Equations
Chapter Summary, Review Exercises, and Practice Test
Cumulative Review And Practice Test: Chapters 10-11
Appendix A: Sets
Appendix B: The Conic Sections
Answers to Selected Exercises and Chapter Tests
Index

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