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More About This Textbook
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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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 coauthored 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 coauthored 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 coauthor 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 twoyear 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.
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; Piecewisedefined 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 OnetoOne 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 DoubleAngle and HalfAngle Formulas
6.6 ProducttoSum and SumtoProduct 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 Onesided 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