College Algebra and Trigonometry

by Aufmann, Richard N.; Barker, Vernon C.; Nation, Richard D.

• ISBN13: 9780618825158
• ISBN10: 0618825150
• Edition: 6th
• Format: Hardcover
• Copyright: 2007-01-19
• Publisher: Brooks Cole

Summary

Accessible to students and flexible for instructors,College Algebra and Trigonometry,Sixth Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. Additional program components that support student success include Eduspace tutorial practice, online homework, SMARTHINKING Live Online Tutoring, and Instructional DVDs. The authors' provenAufmann Interactive Methodallows students to try a skill as it is presented in example form. This interaction between the examples andTry Exercisesserves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Sixth Edition,Review Notesare featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts. Updated!End-of-chapter exercises--Assessing Concepts--have been revised to include more question types including fill-in-the-blank, multiple choice, and matching. Revised!Prepare for This Sectionexercises, formerlyPrepare for the Next Section,have been moved from the end of each chapter to the beginning of each chapter and afford students the opportunity to test their understanding of prerequisite skills about to be covered. New!Calculus Connectionicons have been added to indicate topics that will be revisited in subsequent courses, laying the groundwork for further study. New!A Quantitative Reasoning feature demonstrates math solutions to real-world problems and is compliant with MAA Guidelines and AMATYC 2006 Crossroads Revisited. Applicationsrequire students to use problem-solving strategies and new skills to solve practical problems. Covering topics from many disciplines, including agriculture, business, chemistry, education, and sociology, these problems demonstrate to students the practicality and value of algebra. Noted by a pie chart icon,Real Dataexamples and exercises require students to analyze and construct mathematical models from actual situations. Appearing throughout the text,Integrating Technologynotes offer relevant information about using graphing calculators as an alternative way to solve a problem. Step-by-step instructions allow students to use technology with confidence. Exploring Concepts with Technology,an optional end-of-chapter feature, uses technology (graphing calculators, CAS, etc.) to explore ideas covered in the chapter. These investigations can be used in a variety of ways, such as group projects or extra-credit assignments. Together withIntegrating Technologytips, this feature makes the text appropriate for courses that allow the use of graphing calculators.

Table of Contents

Preliminary Concepts

The Real Number System

Integer and Rational Number Exponents

Polynomials

Factoring

Rational Expressions

Complex Numbers

Equations and Inequalities

Linear and Absolute Value Equations

Formulas and Applications

Quadratic Equations

Other Types of Equations

Inequalities

Variation and Applications

Functions and Graphs

A Two Dimensional Coordinate System and Graphs

Introduction to Functions

Linear Functions

Quadratic Functions

Properties of Graphs

The Algebra of Functions

Modeling Data Using Regression

Polynomial and Rational Functions

The Remainder Theorem and the Factor Theorem

Polynomial Functions of Higher Degree

Zeros of Polynomial Functions

The Fundamental Theorem of Algebra

Graphs of Rational Functions and Their Applications

Exponential and Logarithmic Functions

Inverse Functions

Exponential Functions and Their Applications

Logarithmic Functions and Their Applications

Properties of Logarithms and Logarithmic Scales

Exponential and Logarithmic Equations

Exponential Growth and Decay

Modeling Data with Exponential and Logarithmic Functions

Trigonometric Functions

Angles and Arcs

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Trigonometric Functions of Real Numbers

Graphs of the Sine and Cosine Functions

Graphs of the Other Trigonometric Functions

Graphing Techniques

Harmonic Motion--An Application of the Sine and Cosine Functions

Trigonometric Identities and Equations

Verification of Trigonometric Identities

Sum, Difference, and Cofunction Identities

Double- and Half-Angle Identities

Identities Involving the Sum of Trigonometric Functions

Inverse Trigonometric Functions

Trigonometric Equations

Applications of Trigonometry

The Law of Sines

The Law of Cosines and Area

Vectors

Trigonometric Form of Complex Numbers

De Moivre's Theorem

Topics in Analytic Geometry

Parabolas

Ellipses

Hyperbolas

Rotation of Axes

Introduction to Polar Coordinates

Polar Equations of the Conics

Parametric Equations

Systems of Equations and Inequalities

Systems of Linear Equations in Two Variables

Systems of Linear Equations in More than Two Variables

Nonlinear Systems of Equations

Partial Fractions

Inequalities in Two Variables and Systems of Inequalities

Linear Programming

Matrices

Gaussian Elimination Method

The Algebra of Matrices

The Inverse of a Matrix

Determinants

Cramer's Rule

Sequences, Series, and Probability

Infinite Sequences and Summation Notation

Arithmetic Sequences and Series

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Permutations and Combinations

Introduction to Probability

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