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## Overview

This best selling 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 the market leader.

- Approximately 20% of the exercises in the text are new. In addition, each exercise set has been restructured to begin with new concept exercises, and reorganized to more closely follow the exposition in the corresponding section.
- Chapter 9 is completely revised, and now features a sharper focus on the concept of coordinate systems and a new section on parametric equations.
- The addition of a new Chapter 10, "Vectors in Two and Three Dimensions," allowed the authors to reorganize the related topics in the book around more cohesive themes.
- Chapter 12 is now more sharply focused on the topic of analytic geometry; the section on parametric equations has been moved to Chapter 9.
- The section entitled "Principles of Problem Solving" is now a Prologue to the book. Problem Solving sections, each highlighting a particular problem solving principle, are now posted on the Book Companion Website.
- Discovery Projects, which encourage and motivate students to further explore chapter topics, are now available on the Book Companion Website.
- All examples in the book are now paired with a new Now Try Exercise XX, allowing students to reinforce their understanding of a concept by practicing the technique that is involved. This integration also teaches and encourages students to solve rather than just memorize.
- Chapter 3 has been completely rewritten to focus more sharply on the fundamental and crucial concept of function. The material on quadratic functions, formerly in this chapter, is now part of the chapter on polynomial functions.
- Chapter 4 now begins with a section on quadratic functions, leading to higher degree polynomial functions. (Section 4.1).
- Chapter 6 includes a new section on inverse trigonometric functions and right triangles (Section 6.4), which is needed in applying the Laws of Sines and Cosines in the following section, as well as for solving trigonometric equations in Chapter 8.
- Chapter 7 includes a new section on inverse trigonometric functions (Section 7.5) to better segue into the section on harmonic motion that follows.
- Chapter 8 has been completely revised, including two new sections on trigonometric equations (Sections 8.4 and 8.5) that expand coverage of this topic.

- 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 formerly in the text are now on the Book Companion Website. These projects 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.

P. PREREQUISITES.

Modeling the Real World. Real Numbers and Their Properties. The Real Number Line and Order. Integer Exponents. Rational Exponents and Radicals. Algebraic Expressions.

Factoring Algebraic Expressions. Rational Expressions. Chapter P Review. Chapter P Test. Focus on Problem Solving: General Principles.

1. EQUATIONS AND INEQUALITIES.

Chapter Overview. Basic Equations. Modeling with Equations. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. Absolute Value Equations and Inequalities. Chapter 1 Review. Chapter 1 Test. Focus on Modeling: Making the Best Decisions.

2. COORDINATES AND GRAPHS.

Chapter Overview. The Coordinate Plane. Graphs of Equations in Two Variables. Graphing Calculators: Solving Equations Graphically. Lines. Modeling: Variation.

Chapter 2 Review. Chapter 2 Test. Focus on Modeling: Fitting Lines to Data.

Cumulative Review Test: Chapters 1 and 2.

3. FUNCTIONS.

Chapter Overview.

What Is a Function?. Graphs of Functions. Getting Information from the Graph of a Function. Average Rate of Change of a Function. Transformations of Functions. Combining Functions. One-to-One Functions and Their Inverses. Chapter 3 Review.

Chapter 3 Test. Focus on Modeling: Functions as Models.

4. POLYNOMIAL AND RATIONAL FUNCTIONS.

Chapter Overview. Quadratic Functions and Models. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Complex Numbers. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Chapter 4 Review. Chapter 4 Test. Focus on Modeling: Fitting Polynomial Curves to Data.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Chapter Overview. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Chapter 5 Review. Chapter 5 Test. Focus on Modeling: Fitting Exponential and Power Curves to Data. Cumulative Review Test: Chapters 3, 4, and 5.

6. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH.

Chapter Overview. Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angles. Inverse Trigonometric Functions and Triangles. The Law of Sines. The Law of Cosines. Chapter 6 Review. Chapter 6 Test. Focus on Modeling: Surveying.

7. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH.

Chapter Overview. The Unit Circle. Trigonometric Functions of Real Numbers. Trigonometric Graphs. More Trigonometric Graphs. Inverse Trigonometric Functions and Their Graphs. Modeling Harmonic Motion. Chapter 7 Review. Chapter 7 Test.

Focus on Modeling: Fitting Sinusoidal Curves to Data.

8. ANALYTIC TRIGONOMETRY.

Chapter Overview. Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half-Angle, and Sum-Product Identities. Basic Trigonometric Equations. More Trigonometric Equations. Chapter 8 Review. Chapter 8 Test. Focus on Modeling: Traveling and Standing Waves. Cumulative Review Test: Chapters 6, 7, and 8.

9. POLAR COORDINATES AND PARAMETRIC EQUATIONS.

Chapter Overview. Polar Coordinates. Graphs of Polar Equations. Polar Form of Complex Numbers; DeMoivre''s Theorem. Plane Curves and Parametric Equations.

Chapter 9 Review. Chapter 9 Test. Focus on Modeling: The Path of a Projectile.

10. VECTORS IN TWO AND THREE DIMENSIONS.

Chapter Overview. Vectors in Two Dimensions. The Dot Product. Three –Dimensional Coordinate Geometry. Vectors in Three Dimensions. The Cross Product. Equations of Lines and Planes. Chapter 10 Review. Chapter 10 Test. Focus on Modeling: Vector Fields. Cumulative Review Test: Chapters 9 and 10.

11. SYSTEMS OF EQUATIONS AND INEQUALITIES.

Chapter Overview. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Systems of Linear Equations: Matrices. The Algebra of Matrices. Inverses of Matrices and Matrix Equations. Determinants and Cramer''s Rule. Partial Fractions. Systems of Non-Linear Equations. Systems of Inequalities. Chapter 11 Review. Chapter 11 Test. Focus on Modeling: Linear Programming.

12. ANALYTIC GEOMETRY.

Overview. Parabolas. Ellipses. Hyperbolas. Shifted Conics. Rotation of Axes. Polar Equations of Conics. Chapter 12 Review. Chapter 12 Test. Focus on Modeling: Conics in Architecture. Cumulative Review Test: Chapters 11 and 12.

13. SEQUENCES AND SERIES.

Chapter Overview. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Chapter 13 Review. Chapter 13 Test. Focus on Modeling: Difference Equations.

14. COUNTING AND PROBABILITY.

Chapter Overview. Counting Principles. Permutations and Combinations. Probability. Binomial Probability. Expected Value. Chapter 14 Review. Chapter 14 Test. Focus on Modeling: The Monte Carlo Method. Cumulative Review Test: Chapters 11 and 12.

APPENDIX Calculators and Calculations.

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.