Precalculus (with BCA/iLrn Tutorial and InfoTrac)

by Faires, J. Douglas; DeFranza, James

• ISBN13: 9780534462796
• ISBN10: 0534462790
• Format: Hardcover
• Copyright: 2003-11-05
• Publisher: Brooks Cole

Summary

Precalculus presents the course as it was intended to be taught, providing students with an integrated review of algebra and trigonometry while focusing on essential calculus concepts. Faires and DeFranza wrote this book because they believe students too often leave a precalculus class unprepared to go on to calculus. Although students who complete a precalculus course generally have had plenty of algebra and trigonometry review, they often lack the grounding in analysis and graphing necessary to make the transition to calculus. Faires and DeFranza's PRECALCULUS concentrates on teaching the essentials of what a student needs to fulfill their precalculus requirement and to fully prepare them to succeed in calculus. This streamlined text provides all the mathematics that students need--it doesn't bog them down in review, or overwhelm them with too much, too soon. And the authors have been careful to keep this book, unlike many of the precalculus books on the market, at a length that can be covered in one term.

Table of Contents

1. FUNCTIONS

Introduction

The Real Line

Inequalities

Intervals

Absolute Values

The Coordinate Plane

Distance Between Points in the Plane

Circles in the Plane

Completing the Square

Equations and Graphs

Graphs of Equations

Symmetry of a Graph

Using Technology to Graph Equations

Functions

Applications of Functions

Linear Functions

Parallel and Perpendicular Lines

Quadratic Functions

The Standard Form of a Quadratic Equation

The Quadratic Formula

2. NEW FUNCTIONS FROM OLD

Introduction

Other Common Functions

The Absolute Value Function

The Square Root Function

The Greatest Integer Function

Arithmetic Combinations of Functions

Composition of Functions

Inverse Functions

3. ALGEBRAIC FUNCTIONS

Introduction

Polynomial Functions

Finding Factors and Zeros of Polynomials

The Rational Zero Test

Rational Functions

Other Algebraic Functions

Complex Roots of Polynomials

4. TRIGONOMETRIC FUNCTIONS

Introduction

Measuring Angles

Length of a Circular Arc

Area of a Circular Sector

The Sine and Cosine Functions

Graphs of the Sine and Cosine Functions

Other Trigonometric Functions

The Graph of the Tangent Function

Trigonometric Identities

Pythagorean Identities

Sum and Difference Formulas

Double Angle Formulas

Half Angle Formulas

Products of Sines and Cosines

Right-Triangle Trigonometry

Inverse Trigonometric Functions

Applications of Trigonometric Functions

Law of Cosines

Law of Sines

Simple Harmonic Motion

Heron's Formula

5. EXPONENTIAL AND LOGARITHM FUNCTIONS

Introduction

The Natural Exponential Function

Compound Interest

Logarithm Functions

Exponential Growth and Decay

6. CONIC SECTIONS, POLAR COORDINATES, AND PARAMETRIC EQUATIONS

Introduction

Parabolas

Ellipses

Hyperbolas

Polar Coordinates

Graphs of Polar Equations

Conic Sections in Polar Coordinates

Parametric Equations