Introductory and Intermediate Algebra through Applications

by Akst, Geoffrey; Bragg, Sadie

• ISBN13: 9780321535788
• ISBN10: 0321535782
• Edition: 2nd
• Format: Paperback
• Copyright: 2008-01-31
• Publisher: Pearson

Summary

Presented in a clear and concise style, theAkst/Braggseries teaches by example while expanding understanding with applications that are fully integrated throughout the text and exercise sets. Akst/Braggrs"s user-friendly design offers a distinctive side-by-side format that pairs each example and its solution with a corresponding practice exercise. The concise writing style keeps readersrs" interest and attention by presenting the mathematics with minimal distractions, and the motivating real-world applications demonstrate how integral mathematical understanding is to a variety of disciplines, careers, and everyday situations.

Author Biography

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 granddaughter, Maya.

Table of Contents

Prealgebra Review

Exponents and Order of Operations

Factors, Primes, and Least Common Multiples

Fractions

Decimals

Percents

Real Numbers and Algebraic Expressions

Real Numbers and the Real Number Line

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Properties of Real Numbers

Algebraic Expressions, Translations, and Exponents

Simplifying Algebraic Expressions

Translating and Evaluating Algebraic Expressions

Solving Linear Equations and Inequalities

Solving Linear Equations: the Addition Property

Solving Linear Equations: the Multiplication Property

Solving Linear Equations by Combining Properties

Applications of Linear Equations: Formulas

Solving Linear Inequalities

Graphing Linear Equations and Inequalities; Functions

The Rectangular Coordinate System

Graphing Linear Equations

Slope of a Line

Linear Equations and their Graphs

Graphing Linear Inequalities

Introduction to Functions

Systems of Equations and Inequalities

Solving Systems of Linear Equations by Graphing

Solving Systems of Linear Equations by Substitution

Solving Systems of Linear Equations by Elimination

Solving Systems of Linear Inequalities

Exponents and Polynomials

Laws of Exponents

Negative Exponents and Scientific Notation

Addition and Subtraction of Polynomials

Multiplication of Polynomials

Special Products

Division of Polynomials

Factoring Polynomials

Common Factors and Factoring by Grouping

Factoring Trinomials Whose Leading Coefficient is One

Factoring Trinomials Whose Leading Coefficient is not One

Special Factoring

More on Factoring and Factoring Strategies

Solving Quadratic Equations by Factoring

Rational Expressions and Equations

Rational Expressions and Functions

Multiplication and Division of Rational Expressions

Addition and Subtraction of Rational Expressions

Complex Rational Expressions

Solving Rational equations

Ratio and Proportion; Variation

Radical Expressions and Equations

Rational Exponents

Radical Expressions and Functions

Simplifying Radical Expressions

Addition and Subtraction of Radical Expressions

Multiplication and Division of Radical Expressions

Solving Radical Equations

Complex Numbers

Quadratic Equations, Functions, and Inequalities

Solving Quadratic Equations: Square Root Property and Completing the Square

Solving Quadratic Equations: Quadratic Formula

More on Quadratic Equations

Graphing Quadratic Functions

Compound Inequalities and Solving Quadratic and Rational Inequalities

Exponential and Logarithmic Functions

More on Functions the Algebra of Functions

Inverse Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Common Logarithms, Natural Logarithms, and Change of Bases

Exponential and Logarithmic Equations

Conic Sections and Nonlinear Systems

Introduction to Conics the Parabola

The Circle

The Ellipse and the Hyperbola

Solving Nonlinear Systems of Equations

Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities

Appendix A

Review Solving Linear Equations and Inequalities

Absolute Value Equations and Inequalities

More on Systems of Linear Equations

Solving Systems of Linear Equations by Using Matrices

Appendix B

Determinants / Cramer's Rule

Synthetic Division and the Remainder Theorem

Sequences (Arithmetic and Geometric)

Series

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