College Algebra Enhanced with Graphing Utilities

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.

Chapter R            Review

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 nth Roots; Rational Exponents

 

Chapter 1            Graphs, Equations, and Inequalities

1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations

1.2 Solving Equations Using Graphing Utility; Linear and Rational Equations

1.3 Quadratic Equations

1.4 Complex Numbers; Quadratic Equations in the Complex Number System

1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations

1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

1.7 Solving Inequalities

 

Chapter 2            Graphs

2.1 Intercepts and Symmetry; Graphing Key Equations

2.2 Lines

2.3 Circles

2.4 Variation

 

Chapter 3        Functions and Graphs

3.1 Functions

3.2 The Graph of a Function

3.3 Properties of Functions

3.4 Library of Functions; Piecewise-Defined Functions

3.5 Graphing Techniques: Transformations

3.6 Mathematical Models: Building Functions

 

Chapter 4        Linear and Quadratic Functions

4.1 Linear Functions,Their Properties, and Linear Models

4.2 Building Linear Models from Data

4.3 Quadratic Functions and Their Properties

4.4 Building Quadratic Models from Verbal Descriptions and from Data

4.5 Inequalities Involving Quadratic Functions

 

Chapter 5            Polynomial and Rational Functions

5.1 Polynomial Functions and Models

5.2 Properties of Rational Functions

5.3 The Graph of a Rational Function

5.4 Polynomial and Rational Inequalities

5.5 The Real Zeros of a Polynomial Function

5.6 Complex Zeros: Fundamental Theorem of Algebra

 

Chapter 6            Exponential and Logarithmic Functions

6.1 Composite Functions

6.2 One-to-One Functions; Inverse Functions

6.3 Exponential Functions

6.4 Logarithmic Functions

6.5 Properties of Logarithms

6.6 Logarithmic and Exponential Equations

6.7 Financial Models

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

6.9 Building Exponential, Logarithmic, and Logistic Models from Data

 

Chapter 7            Analytic Geometry

7.1 Conics

7.2 The Parabola

7.3 The Ellipse

7.4 The Hyperbola

 

Chapter 8            Systems of Equations and Inequalities

8.1 Systems of Linear Equations: Substitution and Elimination

8.2 Systems of Linear Equations: Matrices

8.3 Systems of Linear Equations: Determinants

8.4 Matrix Algebra

8.5 Partial Fraction Decomposition

8.6 Systems of Nonlinear Equations

8.7 Systems of Inequalities

8.8 Linear Programming

 

Chapter 9            Sequences; Induction; The Binomial Theorem

9.1 Sequences

9.2 Arithmetic Sequences

9.3 Geometric Sequences; Geometric Series

9.4 Mathematical Induction

9.5 The Binomial Theorem

 

Chapter 10            Counting and Probability

10.1 Counting

10.2 Permutations and Combinations

10.3 Probability

 

Answers

Index