Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between Oak Lawn, Illinois, and Naples, Florida.

Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows, and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America. He has been writing textbooks for more than 35 years and currently has 15 books in print, 12 with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.

Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his co-author on two precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. Twelve grandchildren round out the family.

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.

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 n th Roots; Rational Exponents 

1. Graphs, Equations, and Inequalities 

1.1 Graphing Utilities; Introduction to Graphing Equations 

1.2 Solving Equations Using a 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 Job Applications 

1.7 Solving Inequalities 

2. Graphs 

2.1 The Distance and Midpoint Formulas 

2.2 Intercepts: Symmetry; Graphing Key Equations 

2.3 Lines 

2.4 Circles 

2.5 Variation 

3. Functions and Their 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 

4. Linear and Quadratic Functions 

4.1 Properties of Linear Functions and Linear Models 

4.2 Building Linear Models from Data 

4.3 Quadratic Functions and Their Properties 

4.4 Build Quadratic Models from Verbal Descriptions and from Data 

4.5 Inequalities Involving Quadratic Functions 

5. Polynomial and Rational Functions 

5.1 Polynomial Functions 

5.2 The Graph of a Polynomial Function; Models 

5.3 The Real Zeroes of a Polynomial Function 

5.4 Complex Zeroes: Fundamental Theorem of Algebra 

5.5 Properties of Rational Functions 

5.6 The Graph of a Rational Function 

5.7 Polynomial and Rational Inequalities 

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 Models; Newton’s Law; Logistic Growth and Decay Models 

6.9 Building Exponential, Logarithmic, and Logistic Models from Data 

7. Trigonometric Functions 

7.1 Angles and Their Measure 

7.2 Right Triangle Trigonometry 

7.3 Computing the Values of Trigonometric Functions of Acute Angles 

7.4 Trigonometric Functions of Any Angle 

7.5 Unit Circle Approach; Properties of the Trigonometric Functions 

7.6 Graphs of the Sine and Cosine Functions 

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

7.8 Phase Shift; Sinusoidal Curve Fitting 

8. Analytic Trigonometry 

8.1 The Inverse Sine, Cosine, and Tangent Functions 

8.2 The Inverse Trigonometric Functions (Continued) 

8.3 Trigonometric Equations 

8.4 Trigonometric Identities 

8.5 Sum and Difference Formulas 

8.6 Double-angle and Half-angle Formulas 

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

9. Applications of Trigonometric Functions 

9.1 Applications Involving Right Triangles 

9.2 The Law of Sines 

9.3 The Law of Cosines 

9.4 Area of a Triangle 

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves 

10. Polar Coordinates; Vectors 

10.1 Polar Coordinates 

10.2 Polar Equations and Graphs 

10.3 The Complex Plane; De Moivre’s Theorem 

10.4 Vectors 

10.5 The Dot Product 

11. Analytic Geometry 

11.1 Conics 

11.2 The Parabola 

11.3 The Ellipse 

11.4 The Hyperbola 

11.5 Rotation of Axes; General Form of a Conic 

11.6 Polar Equations of Conics 

11.7 Plane Curves and Parametric Equations 

12. Systems of Equations and Inequalities 

12.1 Systems of Linear Equations: Substitution and Elimination 

12.2 Systems of Linear Equations: Matrices 

12.3 Systems of Linear Equations: Determinants 

12.4 Matrix Algebra 

12.5 Partial Fraction Decomposition 

12.6 Systems of Nonlinear Equations 

12.7 Systems of Inequalities 

12.8 Linear Programming 

13. Sequences; Induction; the Binomial Theorem 

13.1 Sequences 

13.2 Arithmetic Sequences 

13.3 Geometric Sequences; Geometric Series 

13.4 Mathematical Induction 

13.5 The Binomial Theorem 

14. Counting and Probability 

14.1 Counting 

14.2 Permutations and Combinations 

14.3 Probability

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