Precalculus

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 a home in Oak Lawn IL and a condo in Naples FL.  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.  Mike has been writing textbooks for more than 35 years and currently has 15 books in print, twelve 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 coauthor on two precalculus series; Dan works in publishing; and Colleen teaches middle-school and secondary school mathematics. Twelve grandchildren round out the family.

• 1. Graphs1.1 The Distance and Midpoint Formulas1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry1.3 Lines1.4 Circles  2. Functions and Their Graphs2.1 Functions2.2 The Graph of a Function2.3 Properties of Functions2.4 Library of Functions; Piecewise-defined Functions2.5 Graphing Techniques: Transformations2.6 Mathematical Models: Building Functions  3. Linear and Quadratic Functions3.1 Properties of Linear Functions and Linear Models3.2 Building Linear Models from Data3.3 Quadratic Functions and Their Properties3.4 Build Quadratic Models from Verbal Descriptions and from Data3.5 Inequalities Involving Quadratic Functions  4. Polynomial and Rational Functions4.1 Polynomial Functions and Models4.2 Properties of Rational Functions4.3 The Graph of a Rational Function4.4 Polynomial and Rational Inequalities4.5 The Real Zeros of a Polynomial Function4.6 Complex Zeros; Fundamental Theorem of Algebra  5. Exponential and Logarithmic Functions5.1 Composite Functions5.2 One-to-One Functions; Inverse Functions5.3 Exponential Functions5.4 Logarithmic Functions5.5 Properties of Logarithms5.6 Logarithmic and Exponential Equations5.7 Financial Models5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models5.9 Building Exponential, Logarithmic, and Logistic Models from Data  6. Trigonometric Functions6.1 Angles and Their Measure6.2 Trigonometric Functions: Unit Circle Approach6.3 Properties of the Trigonometric Functions6.4 Graphs of the Sine and Cosine Functions6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions6.6 Phase Shift; Sinusoidal Curve Fitting  7. Analytic Trigonometry7.1 The Inverse Sine, Cosine, and Tangent Functions7.2 The Inverse Trigonometric Functions (Continued)7.3 Trigonometric Equations7.4 Trigonometric Identities7.5 Sum and Difference Formulas7.6 Double-angle and Half-angle Formulas7.7 Product-to-Sum and Sum-to-Product Formulas  8. Applications of Trigonometric Functions8.1 Right Triangle Trigonometry; Applications8.2 The Law of Sines8.3 The Law of Cosines8.4 Area of a Triangle8.5 Simple Harmonic Motion; Damped Motion; Combining Waves  9. Polar Coordinates; Vectors9.1 Polar Coordinates9.2 Polar Equations and Graphs9.3 The Complex Plane; DeMoivre’s Theorem9.4 Vectors9.5 The Dot Product9.6 Vectors in Space9.7 The Cross Product  10. Analytic Geometry10.1 Conics10.2 The Parabola10.3 The Ellipse10.4 The Hyperbola10.5 Rotation of Axes; General Form of a Conic10.6 Polar Equations of Conics10.7 Plane Curves and Parametric Equations  11. Systems of Equations and Inequalities11.1 Systems of Linear Equations: Substitution and Elimination11.2 Systems of Linear Equations: Matrices11.3 Systems of Linear Equations: Determinants11.4 Matrix Algebra11.5 Partial Fraction Decomposition11.6 Systems of Nonlinear Equations11.7 Systems of Inequalities11.8 Linear Programming  12. Sequences; Induction; the Binomial Theorem12.1 Sequences12.2 Arithmetic Sequences12.3 Geometric Sequences; Geometric Series12.4 Mathematical Induction12.5 The Binomial Theorem  13. Counting and Probability13.1 Counting13.2 Permutations and Combinations13.3 Probability  14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function14.1 Finding Limits Using Tables and Graphs14.2 Algebra Techniques for Finding Limits14.3 One-sided Limits; Continuous Functions14.4 The Tangent Problem; The Derivative14.5 The Area Problem; The Integral  Appendix A: ReviewA.1 Algebra EssentialsA.2 Geometry EssentialsA.3 PolynomialsA.4 Synthetic DivisionA.5 Rational ExpressionsA.6 Solving EquationsA.7 Complex Numbers; Quadratic Equations in the Complex Number SystemA.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job ApplicationsA.9 Interval Notation; Solving InequalitiesA.10 nth Roots; Rational Exponents  Appendix B: Graphing UtilitiesB.1 The Viewing RectangleB.2 Using a Graphing Utility to Graph EquationsB.3 Using a Graphing Utility to Locate Intercepts and Check for SymmetryB.4 Using a Graphing Utility to Solve EquationsB.5 Square ScreensB.6 Using a Graphing Utility to Graph InequalitiesB.7 Using a Graphing Utility to Solve Systems of Linear EquationsB.8 Using a Graphing Utility to Graph a Polar EquationB.9 Using a Graphing Utility to Graph Parametric Equations