Precalculus

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.  

(Note: Chapters 2-12 end with Chapter Review, Chapter Projects, and Cumulative Review.)

1. Graphs.


Rectangular Coordinates. Graphs of Equations; Circles. Lines. Scatter Diagrams; Linear Curve Fitting. Chapter Review. Chapter Projects.



2. Functions and Their Graphs.


Introduction to Functions. The Graph of a Function. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Mathematical Models: Constructing Functions.



3. Polynomial and Rational Functions.


Quadratic Functions and Models. Polynomial Functions. Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomial and Rational Inequalities. The Real Zeros of a Polynomial Function. Complex Zeros; Fundamental Theorem of Algebra.



4. Exponential and Logarithmic Functions.


Composite Functions. Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Exponential Growth and Decay; Newton's Law; Logistic Models. Fitting Data to Exponential, Logarithmic, and Logistic Functions.



5. Trigonometric Functions.


Angles and Their Measure. Trigonometric Functions: Unit Circle Approach. Properties of the Trigonometric Functions. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions. Phase Shift; Sinusoidal Curve Fitting.



6. Analytic Trigonometry.


The Inverse Sine, Cosine, and Tangent Functions. The Inverse Trigonometric Functions (continued). Trigonometric Identities. Sum and Difference Formulas. Double-angle and Half-angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II.



7. Applications of Trigonometric Functions.


Right Triangle Trigonometry; Applications Involving Right Triangles. The Law of Sines. The Law of Cosines. The Area of a Triangle. Simple Harmonic Motion; Damped Motion; Combining Waves.



8. Polar Coordinates; Vectors.


Polar Coordinates. Polar Equations and Graphs. The Complex Plane; DeMoivre's Theorem. Vectors. The Dot Product. Vectors in Space. The Cross Product.



9. Analytic Geometry.


Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations.



10. Systems of Equations and Inequalities.


Systems of Linear Equations: Substitution and Elimination. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Inequalities. Linear Programming.



11. Sequences; Induction; The Binomial Theorem


Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem.



12. Counting and Probability.


Sets and Counting. Permutations and Combinations. Probability.



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


Finding Limits Using Tables and Graphs. Algebra Techniques for Finding Limits. One-sided Limits; Continuous Functions. The Tangent Problem; the Derivative. The Area Problem; the Integral. Chapter Review. Chapter Projects.



Appendix A: Review.


Algebra Review. Geometry Review. Polynomials and Rational Expressions. Polynomial Division; Synthetic Division. Solving Equations. Complex Numbers; Quadratic Equations in the Complex Number System. Applications: Interest, Mixture, Uniform Motion, Constant Rate Jobs. nth Roots; Rational Exponents.



Appendix B: Graphing Utilities.


The Viewing Rectangle. Using a Graphing Utility to Graph Equations. Using a Graphing Utility to Locate Intercepts and Check for Symmetry. Using a Graphing Utility to Solve Equations. Square Screens. Using a Graphing Utility to Graph Inequalities. Using a Graphing Utility to Solve Systems of Linear Equations. Using a Graphing Utility to Graph a Polar Equation. Using a Graphing Utility to Graph Parametric Equations.



Answers.


Index.