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## Overview

This bestselling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors' attention to detail and clarity—the same as found in James Stewart's market-leading Calculus text—is what makes this text a proven market leader.

- Early Chapter on Functions: The chapter on functions now appears earlier in the book (Chapter 2). The review material is now streamlined and rewritten in only two chapters (Chapters P and 1).
- CHAPTER 4 Exponential and Logarithmic Functions: The chapter now includes two sections on the applications of these functions. Section 4.7, "Modeling with Exponential Functions," focuses on modeling growth and decay, Newton's Law of Cooling, and other such applications. Section 4.8, "Logarithmic Scales," covers the concept of a logarithmic scale with applications involving the pH, Richter, and decibel scales.
- CHAPTER 5 Trigonometric Functions: Unit Circle Approach: This chapter includes a new subsection on the concept of phase shift as used in modeling harmonic motion.
- CHAPTER 10 Systems of Equations and Inequalities: The material on systems of inequalities has been rewritten to emphasize the steps used in graphing the solution of a system of inequalities.
- New Exercises: More than 20% of the exercises are new, and groups of exercises now have headings that identify the type of exercise. New Skills Plus exercises in most sections contain more challenging exercises that require students to extend and synthesize concepts.
- Review Material: The review material at the end of each chapter now includes a summary of properties and formulas and a new Concept Check. Each Concept Check provides a step-by-step review of all the main concepts and applications of the chapter. Answers to the Concept Check questions are on tear-out sheets at the back of the book.
- Discovery Projects: References to Discovery Projects, including brief descriptions of the content of each project, are located in boxes where appropriate in each chapter. These boxes highlight the applications of precalculus in many different real-world contexts. The projects are located at the book companion website www.stewartmath.com.
- Geometry Review: A new Appendix A contains a review of the main concepts of geometry used in this book, including similarity and the Pythagorean Theorem.
- Chapter P Preliminaries: This chapter now contains a section on basic equations, including linear equations and power equations, and a section on modeling with equations.
- CHAPTER 1 Fundamentals: This chapter now contains two new sections: Section 1.5, "Complex Numbers" (formerly in Chapter 3), and Section 1.12, "Modeling with Variation."
- CHAPTER 2 Functions: This chapter now includes the new Section 2.5, "Linear Functions and Models," which highlights the connection between the slope of a line and the rate of change of a linear function. These two interpretations of slope help prepare students for the concept of the derivative in calculus.
- CHAPTER 3 Polynomial and Rational Functions: This chapter now includes the new Section 3.7, "Solving Polynomial and Rational Inequalities Graphically." Section 3.6, "Rational Functions," has a new subsection on rational functions with "holes." The sections on complex numbers and on variation have been moved to Chapter 1.

- Focus on Modeling sections illustrate modeling techniques as well as how mathematics can be applied to model real-life situations. These sections, as well as others, are devoted to teaching students how to create their own mathematical models, rather than using prefabricated formulas.
- Real-world applications from engineering, physics, chemistry, business, biology, environmental studies, and other fields demonstrate how mathematics is used to model real-life situations.
- The chapters on trigonometry are written so professors can begin with either the right triangle approach or the unit circle approach.
- Each approach to trigonometry is accompanied by the applications appropriate for that approach, clarifying the reason for different approaches to trigonometry.
- Mathematics in the Modern World vignettes show that mathematics is a living science crucial to the scientific and technological progress of recent times, as well as to the social, behavioral, and life sciences.
- Discovery/Discussion/Writing problems at the end of every section encourage students to use and develop conceptual, critical thinking, and writing skills.
- Discovery Projects on the Book Companion Website engage students by providing a challenging but accessible set of activities that enable them (perhaps working in groups) to explore in greater depth an interesting aspect of the topic they have just learned.
- Review Sections and Chapter Tests at the end of each chapter help students gauge their learning progress. Brief answers to the odd-numbered exercises in each section and to all questions in the Chapter Tests are provided at the back of the book.

To the Student.

Prologue: Principles of Problem Solving.

P. PREREQUISITES.

P1. Modeling the Real-World with Algebra. P2. The Real Numbers. P3. Integer Exponents and Scientific Notation. P4. Rational Exponents and Radicals.

P5. Algebraic Expressions. P6. Factoring. P7. Rational Expressions. P8. Solving Basic Equations. P9. Modeling with Equations. Chapter P Review. Chapter P Test.

FOCUS ON MODELING: MAKING THE BEST DECISIONS.

1. EQUATIONS AND GRAPHS.

1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines. 1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test.

FOCUS ON MODELING: Fitting Lines to Data.

2. FUNCTIONS.

Chapter Overview.2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models. 2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test.

FOCUS ON MODELING: MODELING WITH FUNCTIONS.

3. POLYNOMIAL AND RATIONAL FUNCTIONS.

Chapter Overview. 3.1. Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test.

FOCUS ON MODELING: FITTING POLYNOMIAL CURVES TO DATA.

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Chapter Overview. 4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test.

FOCUS ON MODELING: FITTING EXPONENTIAL AND POWER CURVES TO DATA.

5. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH.

Chapter Overview.

5.1 Angle Measure.

5.2 Trigonometry of Right Triangles.

5.3 Trigonometric Functions of Angles. 5.4 Inverse Trigonometric Functions and Triangles. 5.5 The Law of Sines. 5.6 The Law of Cosines. 5.7 Chapter 5 Review. Chapter 5 Test.

FOCUS ON MODELING: SURVEYING.

1. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH.

Chapter Overview.

6.1 The Unit Circle. 6.2 Trigonometric Functions of Real Numbers. 6.3 Trigonometric Graphs. 6.4 More Trigonometric Graphs. 6.5 Inverse Trigonometric Functions and Their Graphs. 6.6 Modeling Harmonic Motion. Chapter 6 Review. Chapter 6 Test.

FOCUS ON MODELING: FITTING SINUSOIDAL CURVES TO DATA.

7. CONIC SECTIONS.

Chapter Overview.

7.1 Trigonometric Identities. 7.2 Addition and Subtraction Formulas. 7.3 Double-Angle, Half-Angle, and Sum-Product Formulas. 7.4 Basic Trigonometric Equations. 7.5 More Trigonometric Equations. Chapter 7 Review. Chapter 7 Test.

FOCUS ON MODELING: TRAVELING AND STANDING WAVES.

8. POLAR COORDINATES AND PARAMETRIC EQUATIONS.

Chapter Overview. 8.1 Polar Coordinates. 8.2 Graphs of Polar Equations. 8.3 Polar Form of Complex Numbers; De Moivre''s Theorem. 8.4 Plane Curves and Parametric Equations. Chapter 8 Review. Chapter 8 Test.

FOCUS ON MODELING: THE PATH OF A PROJECTILE.

9. VECTORS IN TWO AND THREE DIMENSIONS.

Chapter Overview. 9.1 Vectors in Two Dimensions. 9.2 The Dot Product. 9.3 Three–Dimensional Coordinate Geometry. 9.4 Vectors in Three Dimensions. 9.5 The Cross Product. 9.6 Equations of Lines and Planes. Chapter 9 Review. Chapter 9 Test.

FOCUS ON MODELING: VECTOR FIELDS.

10. SYSTEMS OF EQUATIONS AND INEQUALITIES.

10.1 Systems of Linear Equations in Two Variables. 10.2 Systems of Linear Equations in Several Variables. 10.3 Partial Fractions. 10.4 Systems of Nonlinear Equations. 10.5 Systems of Inequalities. Chapter 10 Review. Chapter 10 Test.

FOCUS ON MODELING: LINEAR PROGRAMMING.

11. MATRICES AND DETERMINANTS.

11.1 Matrices and Systems of Linear Equations. 11.2 The Algebra of Matrices. 11.3 Inverses of Matrices and Matrix Equations. 11.4 Determinants and Cramer''s Rule. Chapter 11 Review. Chapter 11 Test.

FOCUS ON MODELING: COMPUTER GRAPHICS.

12. CONIC SECTIONS.

Chapter Overview. 12.1 Parabolas. 12.2 Ellipses. 12.3 Hyperbolas. 12.4 Shifted Conics. 12.5 Rotation of Axes. 12.6 Polar Equations of Conics. Chapter 12 Review. Chapter 12 Test.

FOCUS ON MODELING: CONICS IN ARCHITECTURE.

13. SEQUENCES AND SERIES.

Chapter Overview. 13.1 Sequences and Summation Notation. 13.2 Arithmetic Sequences. 13.3 Geometric Sequences. 13.4 Mathematics of Finance. 13.5 Mathematical Induction. 13.6 The Binomial Theorem. Chapter 13 Review. Chapter 13 Test.

FOCUS ON MODELING: MODELING WITH RECURSIVE SEQUENCES.

14. COUNTING AND PROBABILITY.

14.1 Counting. 14.2 Probability. 14.3 Binomial Probability. 14.4 Expected Value. Chapter 14 Review. Chapter 14 Test.

FOCUS ON MODELING: THE MONTE CARLO METHOD.

APPENDIX A: Geometry Review.

APPENDIX B: Calculations and Significant Figures.

APPENDIX C: Graphing with a Graphing Calculator.

APPENDIX D: Using the TI-83/84 Graphing Calculator.

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

### FOR INSTRUCTORS

#### Online Instructor's Companion Web Site with Instructor's Guide

ISBN: 9781305118249

This helpful teaching companion contains points to stress, suggested time to allot, text discussion topics, core materials for lectures, workshop/discussion suggestions, group work exercises in a form suitable for handout, solutions to group work exercises, and suggested homework problems.

#### Online Test Bank

ISBN: 9781305118256

This supplement includes test forms for every chapter of the text, and can be found on the instructor companion site.

#### Cengage Learning Testing, powered by Cognero Instant Access

ISBN: 9781305251113

Cengage Learning Testing Powered by Cognero is a flexible, online system that allows you to author, edit, and manage test bank content; create multiple test versions in an instant; and deliver tests from your LMS, your classroom or wherever you want. This is available online via the Instructor Companion Site at www.cengage.com/login

#### Study Guide

ISBN: 9781305118164

This carefully crafted guide helps students develop problem-solving skills while reinforcing their understanding with detailed explanations, worked-out examples, lists of key concepts to master, and practice problems. Each section of the main text has a corresponding section in the Study Guide.

#### Student Solutions Manual

ISBN: 9781305118157

### FOR STUDENTS

#### Study Guide

ISBN: 9781305118164

This carefully crafted guide helps you develop problem-solving skills while reinforcing your understanding with detailed explanations, worked-out examples, lists of key concepts to master, and practice problems. Each section of the main text has a corresponding section in the Study Guide.

#### Student Solutions Manual

ISBN: 9781305118157

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.