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Precalculus, 9th Edition

By Michael Sullivan

Published by Pearson

Published Date: Feb 15, 2011

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Description

Mike Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. In the Ninth Edition, Precalculus has evolved to meet today’s course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online.

Table of Contents

1. Graphs

1.1 The Distance and Midpoint Formulas

1.2 Graphs of Equations in Two Variables: Intercepts; Symmetry

1.3 Lines

1.4 Circles

            Chapter Review

            Chapter Test

            Chapter Projects

 

2. Functions and Their Graphs

2.1 Functions

2.2 The Graph of a Function

2.3 Properties of Functions

2.4 Library of Functions; Piecewise-defined Functions

2.5 Graphing Techniques: Transformations

2.6 Mathematical Models: Building Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

 

3. Linear and Quadratic Functions

3.1 Linear Functions and Their Properties

3.2 Linear Models: Building Linear Functions from Data

3.3 Quadratic Functions and Their Properties

3.4 Build Quadratic models from Verbal Descriptions and from Data

3.5 Inequalities Involving Quadratic Functions

Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

4. Polynomial and Rational Functions

4.1 Polynomial Functions and Models

4.2 Properties of Rational Functions

4.3 The Graph of a Rational Function

4.4 Polynomial and Rational Inequalities

4.5 The Real Zeros of a Polynomial Function

4.6 Complex Zeros: Fundamental Theorem of Algebra

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

5. Exponential and Logarithmic Functions

5.1 Composite Functions

5.2 One-to-One Functions; Inverse Functions

5.3 Exponential Functions

5.4 Logarithmic Functions

5.5 Properties of Logarithms

5.6 Logarithmic and Exponential Equations

5.7 Financial Models

5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models

5.9 Building Exponential, Logarithmic, and Logistic Functions from Data

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Trigonometric Functions: Unit Circle Approach

6.3 Properties of the Trigonometric Functions

6.4 Graphs of the Sine and Cosine Functions

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

6.6 Phase Shift; Sinusoidal Curve Fitting

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

7. Analytic Trigonometry

7.1 The Inverse Sine, Cosine, and Tangent Functions

7.2 The Inverse Trigonometric Functions (continued)

7.3 Trigonometric Equations

7.4 Trigonometric Identities

7.5 Sum and Difference Formulas

7.6 Double-angle and Half-angle Formulas

7.7 Product-to-Sum and Sum-to-Product Formulas

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

8. Applications of Trigonometric Functions

8.1 Applications Involving Right Triangles

8.2 Law of Sines

8.3 Law of Cosines

8.4 Area of a Triangle

8.5 Simple Harmonic Motion; Damped Motion; Combining Waves

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

9. Polar Coordinates; Vectors

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 The Complex Plane; DeMoivre's Theorem

9.4 Vectors

9.5 The Dot Product

9.6 Vectors in Space

9.7 The Cross Product

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

10. Analytic Geometry

10.1 Conics

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

10.5 Rotation of Axes; General Form of a Conic

10.6 Polar Equations of Conics

10.7 Plane Curves and Parametric Equations

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

11. Systems of Equations and Inequalities

11.1 Systems of Linear Equations: Substitution and Elimination

11.2 Systems of Linear Equations: Matrices

11.3 Systems of Linear Equations: Determinants

11.4 Matrix Algebra

11.5 Partial Fraction Decomposition

11.6 Systems of Nonlinear Equations

11.7 Systems of Inequalities

11.8 Linear Programming

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

12. Sequences; Induction; The Binomial Theorem

12.1 Sequences

12.2 Arithmetic Sequences

12.3 Geometric Sequences; Geometric Series

12.4 Mathematical Induction

12.5 The Binomial Theorem

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

13. Counting and Probability

13.1 Counting

13.2 Permutations and Combinations

13.3 Probability

            Chapter Review

            Chapter Test

            Cumulative Review

            Chapter Projects

 

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

14.1 Finding Limits Using Tables and Graphs

14.2 Algebra Techniques for Finding Limits

14.3 One-sided Limits; Continuous Functions

14.4 The Tangent Problem; The Derivative

14.5 The Area Problem; The Integral

            Chapter Review

            Chapter Test

            Chapter Projects

 

Appendix A. Review

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials

A.4 Synthetic Division

A.5 Rational Expressions

A.6 Solving Equations

A.7 Complex Numbers; Quadratic Equations in the Complex Number System

A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications

A.9 Interval Notation; Solving Inequalities

A.10 nth Roots; Rational Exponents

 

Appendix B. Graphing Utilities

B.1 The Viewing Rectangle

B.2 Using a Graphing Utility to Graph Equations

B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry

B.4 Using a Graphing Utility to Solve Equations

B.5 Square Screens

B.6 Using a Graphing Utility to Graph Inequalities

B.7 Using a Graphing Utility to Solve Systems of Linear Equations

B.8 Using a Graphing Utility to Graph a Polar Equation

B.9 Using a Graphing Utility to Graph Parametric Equations

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