# Precalculus

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## Description

For undergraduate courses in Precalculus.A proven motivator for students of diverse mathematical backgrounds, these texts explore mathematics within the context of real life using understandable, realistic applications consistent with the abilities of any student. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. The use of a graphing calculator is optional.show more

## Product details

- Hardback | 1069 pages
- 210.8 x 254 x 40.6mm | 2,131.91g
- 23 May 2001
- Pearson Education Limited
- Prentice-Hall
- Harlow, United Kingdom
- English
- Revised
- 6th Revised edition
- 0130412147
- 9780130412140

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## 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.show more