Algebra and Trigonometry (with Video Skillbuilder CD-ROM and CengageNOW, iLrn Homework Student Version, Personal Tutor with SMARTHINKING Printed Access Card)

by Stewart, James; Redlin, Lothar; Watson, Saleem

• ISBN13: 9780495013570
• ISBN10: 0495013579
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-01-03
• Publisher: Cengage Learning

Summary

This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader.

Table of Contents

Prerequisites

Modeling the Real World

Real Numbers

Integer Exponents

Rational Exponents and Radicals

Algebraic Expressions

Discovery Project: Visualizing a Formula

Factoring Algebraic Expressions

Rational Expressions

Chapter P Review

Chapter P Test

Focus on Problem Solving: General Principles

Equations and Inequalities

Basic Equations

Modeling with Linear Equations

Discovery Project: Equations Through the Ages

Quadratic Equations

Complex Numbers

Other Types of Equations

Inequalities

Absolute Value Equations and Inequalities

Review

Test

Focus on Modeling: Making the Best Decisions

Coordinates and Graphs

The Coordinate Plane

Discovery Project: Visualizing Data

Graphs of Equations in Two Variables

Graphing Calculators: Solving Equations and Inequalities Graphically

Lines

Modeling: Variation

Review

Test

Focus on Modeling: Fitting Lines to Data

Functions

What is a Function? Graphs of Functions

Discovery Project: Relations and Functions

Increasing and Decreasing Functions: Average Rate of Change

Transformations of Functions

Quadratic Functions: Maxima and Minima

Combining Functions

Discovery Project: Iteration and Chaos

One-to-One Functions and Their Inverses

Review

Test

Focus on Modeling: Modeling With Functions

Polynomial and Rational Functions

Polynomial Functions and Their Graphs

Dividing Polynomials

Real Zeros of Polynomials

Discovery Project: Zeroing in on a Zero

Complex Zeros and the Fundamental Theorem of Algebra

Rational Functions

Review

Test

Focus on Modeling: Fitting Polynomial Curves to Data

Exponential and Logarithmic Functions

Exponential Functions

Discovery Project: Exponential Explosion

Logarithmic Functions

Laws of Logarithms

Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Functions

Review

Test

Focus on Modeling: Fitting Exponential and Power Curves to Data

Trigonometric Functions of Angles

Angle Measure

Trigonometry of Right Triangles

Trigonometric Functions of Angles

Discovery Project: Similarity

The Law of Sines

The Law of Cosines

Review

Test

Focus on Modeling: Surveying

Trigonometric Functions of Real Numbers

The Unit Circle

Trigonometric Functions of Real Numbers

Trigonometric Graphs

Discovery Project: Predator-Prey Models

More Trigonometric Graphs

Modeling Harmonic Motion

Review

Test

Focus on Modeling: Fitting Sinusoidal Curves to Data

Analytic Trigonometry

Trigonometric Identities

Addition and Subtraction Formulas

Double-Angle, Half-Angle, and Sum-Product Identities

Inverse Trigonometric Functions

Discovery Project:Where to Sit at the Movies

Trigonometric Equations

Review

Test

Focus on Modeling: Traveling and Standing Waves

Polar Coordinates and Vectors

Polar Coordinates

Graphs of Polar Equations

Polar Form of Complex Numbers; DeMoivre's Theorem

Discovery Project: Fractals

Vectors

The Dot Product

Discovery Project: Sailing Against the Wind

Review

Test

Focus on Modeling: Mapping the World

Systems of Equations and Inequalities

Systems of Equations

Systems of Linear Equations in Two Variables

Systems of Linear Equations in Several Variables

Discovery Project: Best Fit versus Exact Fit

Systems of Linear Equations: Matrices

The Algebra of Matrices

Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations

Discovery Project: Computer Graphics I

Determinants and Cramer's Rule

Partial Fractions

Systems of Inequalities

Review

Test

Focus on Modeling: Linear Programming

Analytic Geometry

Parabolas

Ellipses

Hyperbolas

Discovery Project: Conics in Architecture

Shifted Conics

Rotation of Axes

Discovery Project: Computer Graphics II

Polar Equations of Conics

Plane Curves and Parametric Equations

Chapt

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