Precalculus : Enhanced with Graphing Utilities

by Sullivan, Michael; Sullivan, Michael III

• ISBN13: 9780136015789
• ISBN10: 0136015786
• Edition: 5th
• Format: Hardcover
• Copyright: 2008-02-04
• Publisher: Pearson

Summary

These authors understand what it takes to be successful in mathematics, the skills that students bring to this course, and the way that technology can be used to enhance learning without sacrificing math skills. As a result, they have created a textbook with an overall learning system involving preparation, practice, and review to help students get the most out of the time they put into studying. In sum, Sullivan and Sullivan's Precalculus:Enhanced with Graphing Utilitiesgives students a model for success in mathematics.

Author Biography

Mike Sullivan is a Professor of Mathematics at Chicago State University and received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years and has authored or co-authored over fifty books. Mike has four children, all of whom are involved with mathematics or publishing: Kathleen, who teaches college mathematics; Mike III, who co-authors this series and  teaches college mathematics; Dan, who is a Pearson Education sales representative; and Colleen, who teaches middle-school mathematics. When he's not writing, Mike enjoys gardening or spending time with his family, including nine grandchildren.  

 

Mike Sullivan III is a professor of mathematics at Joliet Junior College.  He holds graduate degrees from DePaul University in both mathematics and economics.  Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

Table of Contents

Graphs

Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations

Intercepts; Symmetry; Graphing Key Equations

Solving Equations Using a Graphing Utility

Lines

Circles

Functions and Their Graphs

Functions

The Graph of a Function

Properties of Functions

Library of Functions; Piecewise-defined Functions

Graphing Techniques: Transformations

Mathematical Models: Building Functions

Linear and Quadratic Functions

Linear Functions, Their Properties, and Linear Models

Building Linear Models from Data; Direct Variation

Quadratic Functions and Their Properties

Building Quadratic Models from Verbal Descriptions and Data

Inequalities Involving Quadratic Functions

Polynomial and Rational Functions

Polynomial Functions and Models

Properties of Rational Functions

The Graph of a Rational Function

Polynomial and Rational Inequalities

The Real Zeros of a Polynomial Function

Complex Zeros; Fundamental Theorem of Algebra

Exponential and Logarithmic Functions

Composite Functions

One-to-One Functions; Inverse Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Logarithmic and Exponential Equations

Financial Models

Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models

Building Exponential, Logarithmic, and Logistic Models from Data

Trigonometric Functions

Angles and Their Measure

Trigonometric Functions: Unit Circle Approach

Properties of the Trigonometric Functions

Graphs of the Sine and Cosine Functions

Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

Phase Shift; Building Sinusoidal Models

Analytic Trigonometry

The Inverse Sine, Cosine, and Tangent Functions

The Inverse Trigonometric Functions (Continued)

Trigonometric Identities

Sum and Difference Formulas

Double-angle and Half-angle Formulas

Product-to-Sum and Sum-to-Product Formulas

Trigonometric Equations (I)

Trigonometric Equations (II)

Applications of Trigonometric Functions

Applications Involving Right Triangles

The Law of Sines

The Law of Cosines

Area of a Triangle

Simple Harmonic Motion; Damped Motion; Combining Waves

Polar Coordinates; Vectors

Polar Coordinates

Polar Equations and Graphs

The Complex Plane; DeMoivre's Theorem

Vectors

The Dot Product

Vectors in Space

The Cross Product

Analytic Geometry

Conics

The Parabola

The Ellipse

The Hyperbola

Rotation of Axes; General Form of a Conic

Polar Equations of Conics

Plane Curves and Parametric Equations

Systems of Equations and Inequalities

Systems of Linear Equations: Substitution and Elimination

Systems of Linear Equations: Matrices

Systems of Linear Equations: Determinants

Matrix Algebra

Partial Fraction Decomposition

Systems of Nonlinear Equations

Systems of Inequalities

Linear Programming

Sequences; Induction; the Binomial Theorem

Sequences

Arithmetic Sequences

Geometric Sequences; Geometric Series

Mathematical Ind<$$$>

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