Precalculus: Concepts Through Functions, A Unit Circle Approach / Edition 1

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Overview

This new text embodies Sullivan/Sullivan’s hallmarks – accuracy, precision, depth, strong student support, and abundant exercises while exposing students early (Chapter One) to the study of functions and taking a unit circle approach to trigonometry. "IT WORKS" for instructors and students because it focuses students on the fundamentals: preparing for class, practicing their homework, and reviewing. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function.

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Product Details

  • ISBN-13: 9780131874756
  • Publisher: Prentice Hall
  • Publication date: 1/11/2006
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 1100
  • Product dimensions: 9.04 (w) x 10.98 (h) x 1.76 (d)

Meet the Author

Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years. He is a native of Chicago’s South Side and currently resides in Oaklawn. Mike has four children. The two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. Mike III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Dan, the youngest, sells for Prentice Hall as a generalist.

Mike has authored or co-authored over ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oaklawn, where Mike enjoys gardening. Mike first signed this series with Deleen Publishing (Acquired by Macmillan) in 1985.

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.

Why We Wrote the Book:

Work on this series began with a unique perspective. Teaching at a large urban institution and a smaller two-year college has allowed us to see firsthand the challenges associated with teaching students with diverse backgrounds in an urban setting. Successful textbooks must be accessible to students. As lead author of this series, one of the most important things I bring to the project is my experience as author of a successful calculus text. Mike and I are both aware that students must be prepared in a Precalculus course for subsequent mathematics courses. We also realize that many College Algebra students will not be going on to take upper level math courses. In this series we resolved the seeming dilemma without sacrificing accessibility.

The books in this series are designed to be mathematically comprehensive and to provide substantial mathematical preparation for subsequent courses. At the same time, great effort has been expended to motivate the material and to make it accessible to even poorly prepared students.

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Table of Contents

FOUNDATIONS: A PRELUDE TO FUNCTIONS

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations; Intercepts; Symmetry

F.3 Lines

F.4 Circles

Chapter 1 Functions and Their Graphs

1.1 Functions

1.2 The Graph of a Function

1.3 Properties of Functions

1.4 Library of Functions; Piecewise-defined Functions

1.5 Graphing Techniques: Transformations

1.6 Mathematical Models: Constructing Functions

Chapter Review

Chapter Test

Chapter Projects

Chapter 2 Linear and Quadratic Functions

2.1 Properties of Linear Functions

2.2 Building Linear Functions from Data; Direct Variation

2.3 Quadratic Functions and Their Real Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Quadratic Models; Building Quadratic Functions From Data

2.7 Complex Zeros of a Quadratic Function

2.8 Equations and Inequalities Involving the Absolute Value Function

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 3 Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 Properties of Rational Functions

3.3 The Graph of a Rational Function; Inverse and Joint Variation

3.4 Polynomial and Rational Inequalities

3.5 The Real Zeros of a Polynomial Function

3.6 Complex Zeros: Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

Chapter 4 Exponential and Logarithmic Functions

4.1 Composite Functions

4.2 One-to-One Functions; Inverse Functions

4.3 Exponential Functions

4.4 Logarithmic Functions

4.5 Properties of Logarithms

4.6 Logarithmic and Exponential Equations

4.7 Compound Interest

4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay

4.9 Building Exponential, Logarithmic, and Logistic Functions from Data

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

Chapter 5 Trigonometric Functions

5.1 Angles and Their Measure

5.2 Trigonometric Functions: Unit Circle Approach

5.3 Properties of the Trigonometric Functions

5.4 Graphs of the Sine and Cosine Functions

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

5.6 Phase Shift; Building Sinusoidal Functions from Data

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 6 Analytic Trigonometry

6.1 The Inverse Sine, Cosine, and Tangent Functions

6.2 The Inverse Trigonometric Functions (continued)

6.3 Trigonometric Identities

6.4 Sum and Difference Formulas

6.5 Double-Angle and Half-Angle Formulas

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

6.7 Trigonometric Equations (I)

6.8 Trigonometric Equations (II)

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 7 Applications of Trigonometric Functions

7.1 Right Triangle Trigonometry; Solving Right Triangles

7.2 Law of Sines

7.3 Law of Cosines

7.4 Area of a Triangle

7.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 8 Polar Coordinates; Vectors

8.1 Polar Coordinates

8.2 Polar Equations and Graphs

8.3 The Complex Plane; DeMoivre’s Theorem

8.4 Vectors

8.5 The Dot Product

8.6 Vectors in Space

8.7 The Cross Product

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 9 Analytic Geometry

9.1 Conics

9.2 The Parabola

9.3 The Ellipse

9.4 The Hyperbola

9.5 Rotation of Axes; General Form of a Conic

9.6 Polar Equations of Conics

9.7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 10 Systems of Equations and Inequalities

10.1 Systems of Linear Equations: Substitution and Elimination

10.2 Systems of Linear Equations: Matrices

10.3 Systems of Linear Equations: Determinants

10.4 Matrix Algebra

10.5 Partial Fraction Decomposition

10.6 Systems of Nonlinear Equations

10.7 Systems of Inequalities

10.8 Linear Programming

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 11 Sequences; Induction; The Binomial Theorem

11.1 Sequences

11.2 Arithmetic Sequences

11.3 Geometric Sequences; Geometric Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

Chapter 12 Counting and Probability

12.1 Sets and Counting

12.2 Permutations and Combinations

12.3 Probability

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

Chapter 13 A Preview of Calculus: The Limit, Derivative, and Integral of a Function

13.1 Finding Limits Using Tables and Graphs

13.2 Algebra Techniques for Finding Limits

13.3 One-sided Limits; Continuous Functions

13.4 The Tangent Problem; The Derivative

13.5 The Area Problem; The Integral

Chapter Review

Chapter Test

Chapter Project

Appendix A Review

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials

A.4 Factoring Polynomials

A.5 Synthetic Division

A.6 Rational Expressions

A.7 nth Roots; Rational Exponents

A.8 Solving Equations Algebraically

A.9 Interval Notation; Solving Inequalities

A.10 Problem Solving: Applications of Linear Equations

A.11 Complex Numbers

Appendix B Graphing Utilities

B.1 The Viewing Rectangle

B.2 Graphing Equations in Two Variables

B.3 Locating Intercepts and Checking for Symmetry

B.4 Solving Equations Using a Graphing Utility

B.5 Square Screens

B.6 Graphing Inequalities in Two Variables

B.7 Solving Systems of Linear Equations

B.8 Graphing a Polar Equation

B.9 Graphing Parametric Equations

Answers

Index

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