Precalculus

by Sullivan, Michael

• ISBN13: 9780130412140
• ISBN10: 0130412147
• Edition: 6th
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Pearson College Div

Summary

The Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Counting and Probability; A Preview of Calculus; and more. For individuals with an interest in learning Precalculus as it applies to their everyday lives.

Table of Contents

(All chapters end with a Chapter Review and a Project at Motorola).
Preface.
List of Applications.
1. Graphs.

Rectangular Coordinates. Graphs of Equations. Lines. Scatter Diagrams: Linear Curve Fitting.

2. Functions and Their Graphs.

Functions. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. 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.

One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms; Exponential and Logarithmic Models. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay; Newton's Law; Logistic Models. Logarithmic Scales.

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. 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; De Moivre'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: Two Equations Containing Two Variables. Systems of Linear Equations: Three Equations Containing Three Variables. 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.

Appendix A. Review.

Algebra Review. Geometry Review. Polynomials and Rational Expressions. Polynomial Division; Synthetic Division. Solving Equations. Complex Numbers; Quadratic Equations with a Negative Discriminant. Setting Up Equations; Applications. Inequalities. 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.

Photo and Illustration Credits.
Answers.
Index.