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## Overview

Millions of students worldwide have explored calculus through James Stewart's trademark precision and accuracy, clear exposition, and outstanding examples and problem sets -- while instructors have turned to his approach time and time again. In CALCULUS: EARLY TRANSCENDENTALS, 8th Edition, Stewart continues to set the standard for the course with carefully revised content and patient explanations, superb exercises, a focus on problem solving, and graded problems. For the most unprepared students to the most mathematically gifted, Stewart's writing and presentation enhance understanding and build confidence.

## Digital Platforms

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WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

## Features & Benefits

{{collapseContainerClosed['features'] ? 'Show More' : 'Show Less'}}- The text's clean, user-friendly design provides a clear presentation of calculus. The art program, with its functional and consistent use of color, helps students identify and review mathematical concepts more easily.
- The topic of Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration.
- Stewart draws on physics, engineering, chemistry, biology, medicine, and social science to motivate students and demonstrate the power of calculus as a problem-solving tool in a wide variety of fields.
- Stewart's presentation repeatedly provides answers to the question, "When will I use this?" You'll find many examples of how calculus is used as a problem-solving tool in fields such as physics, engineering, chemistry, biology, medicine, and the social sciences.
- Stewart's text offers an extensive collection of more than 8,000 quality exercises. Each exercise set is carefully graded, progressing from skill-development problems to more challenging problems involving applications and proofs. The wide variety of types of exercises includes many technology-oriented, thought-provoking, real, and engaging problems.
- Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. These exercises stimulate critical thinking and reinforce the concepts of calculus.
- A wealth of engaging projects reinforce concepts. "Writing Projects" ask students to compare present-day methods with those of the founders of calculus. "Discovery Projects" anticipate results to be discussed later. "Applied Projects" feature content that engages student interest and demonstrates the real-world use of mathematics. "Laboratory Projects" anticipate results to be discussed later or encourage discovery through pattern recognition.
- Comprehensive review sections follow each chapter and further support conceptual understanding. A "Concept Check" and "True/False Quiz" allow students to prepare for upcoming tests through ideas and skill-building.
- "Strategies" sections (based on George Polya's problem-solving methodology) help students select what techniques they'll need to solve problems in situations where the choice is not obvious, and help them develop true problem-solving skills and intuition.
- Historical and biographical margin notes enliven the course and show students that mathematics was developed to help explain and represent natural phenomena.
- More challenging exercises called "Problems Plus" follow the end-of-chapter exercises. These sections reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem.
- Four carefully-crafted diagnostic tests in algebra, analytic geometry, functions, and trigonometry appear at the beginning of the text. These provide students with a convenient way to test their preexisting knowledge and brush up on skill techniques they need to successfully begin the course. Answers are included, and students who need to improve will be referred to points in the text or on the book's website where they can seek help.
- Stewart's writing style speaks clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus.
- Every concept is supported by thoughtfully worked examples—many with step-by-step explanations—and carefully chosen exercises. The quality of this pedagogical system is what sets Stewart's texts above others.
- Examples are not only models for problem solving or a means of demonstrating techniques; they also encourage students to develop an analytic view of the subject. To provide further insight into mathematical concepts, many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically. Margin notes expand on and clarify the steps of the solution.

### Calculus: Early Transcendentals

#### TABLE OF CONTENTS

To the Student.

Diagnostic Tests.

A Preview of Calculus.

1. FUNCTIONS AND MODELS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.

2. LIMITS AND DERIVATIVES.

The Tangent and Velocity Problems.The Limit of a Function.Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents.The Derivative as a Function. Review. Problems Plus.

3. DIFFERENTIATION RULES.

Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Laboratory Project: Families of Implicit Curves. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and l''Hospital''s Rule. Writing Project: The Origins of l''Hospital''s Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton''s Method. Antiderivatives. Review. Problems Plus.

5. INTEGRALS.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.

6. APPLICATIONS OF INTEGRATION.

Areas Between Curves. Applied Project: The Gini Index. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Applied Project: Where to Sit at the Movies. Review. Problems Plus.

7. TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations. Direction Fields and Euler''s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Linear Equations. Predator-Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bézier Curves. Polar Coordinates. Laboratory Project: Families of Polar Curves. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus.

11. INFINITE SEQUENCES AND SERIES.

Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

12. VECTORS AND THE GEOMETRY OF SPACE.

Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Review. Problems Plus.

13. VECTOR FUNCTIONS.

Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler''s Laws. Review. Problems Plus.

14. PARTIAL DERIVATIVES.

Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximation. Applied Project: The Speedo LZR Race Suit. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. Problems Plus.

15. MULTIPLE INTEGRALS.

Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical Coordinates. Discovery Project: The Intersection of Three Cylinders. Triple Integrals in Spherical Coordinates. Applied Project: Roller Derby. Change of Variables in Multiple Integrals. Review. Problems Plus.

16. VECTOR CALCULUS.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green''s Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes'' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus.

17. SECOND-ORDER DIFFERENTIAL EQUATIONS.

Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus.

APPENDIXES.

A Numbers, Inequalities, and Absolute Values. B Coordinate Geometry and Lines. C Graphs of Second-Degree Equations. D Trigonometry. E Sigma Notation. F Proofs of Theorems. G The Logarithm Defined as an Integral. H Complex Numbers. I Answers to Odd-Numbered Exercises.

INDEX.

### Single Variable Calculus: Early Transcendentals

#### TABLE OF CONTENTS

To the Student.

Diagnostic Tests.

A Preview of Calculus.

1. FUNCTIONS AND MODELS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.

2. LIMITS AND DERIVATIVES.

The Tangent and Velocity Problems.The Limit of a Function.Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents.The Derivative as a Function. Review. Problems Plus.

3. DIFFERENTIATION RULES.

Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Laboratory Project: Families of Implicit Curves. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and l''Hospital''s Rule. Writing Project: The Origins of l''Hospital''s Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton''s Method. Antiderivatives. Review. Problems Plus.

5. INTEGRALS.

Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.

6. APPLICATIONS OF INTEGRATION.

Areas Between Curves. Applied Project: The Gini Index. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Applied Project: Where to Sit at the Movies. Review. Problems Plus.

7. TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations. Direction Fields and Euler''s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Linear Equations. Predator-Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bézier Curves. Polar Coordinates. Laboratory Project: Families of Polar Curves. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus.

11. INFINITE SEQUENCES AND SERIES.

Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

APPENDIXES.

A Numbers, Inequalities, and Absolute Values. B Coordinate Geometry and Lines. C Graphs of Second-Degree Equations. D Trigonometry. E Sigma Notation. F Proofs of Theorems. G The Logarithm Defined as an Integral. H Complex Numbers. I Answers to Odd-Numbered Exercises.

INDEX.

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

#### Test Bank

ISBN: 9781305387225

Contains text-specific multiple-choice and free response test items

#### Online Instructor's Guide

ISBN: 9781305393714

Each section of the text is discussed from several viewpoints. The Instructor’s Guide contains suggested time to allot, points to stress, text discussion topics, core materials for lecture, workshop/discussion suggestions, group work exercises in a form suitable for handout, and suggested homework assignments.

#### Complete Solutions Manual, Chapters 10-17

ISBN: 9781305276116

This manual includes worked-out solutions to every exercise in Multivariable Calculus, 8e (Chapters 10-17 of Calculus, 8e). This manual can be found on the Instructors Companion Site.

#### Student Solutions Manual

ISBN: 9781305272422

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.

#### Student Solutions Manual, Chs. 10-17

ISBN: 9781305271821

This manual includes worked-out solutions to every odd-numbered exercise in Multivariable Calculus, 8e (Chapters 1-11 of Calculus, 8e).

#### CourseMate Instant Access

ISBN: 9781305394926

Complement your text and course content with study and practice materials. Cengage Learning Calculus CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Watch student comprehension soar as your class works with the printed textbook and the textbook specific website. Calculus goes beyond the book to deliver what you need!

#### Complete Solutions Manual, Chapters 1-22 (SV: ET)

ISBN: 9781305272392

This manual contains solutions to all exercises from the text. This manual can be found on the Instructors Companion Site.

### FOR STUDENTS

#### Student Solutions Manual

ISBN: 9781305272422

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.

#### Student Solutions Manual, Chs. 10-17

ISBN: 9781305271821

This manual includes worked-out solutions to every odd-numbered exercise in Multivariable Calculus, 8e (Chapters 1-11 of Calculus, 8e).

#### CourseMate Instant Access

ISBN: 9781305394926

The more you study, the greater your success. You can make the most of your study time by accessing everything you need to succeed in one place—online with CourseMate. You can use CourseMate to read the textbook, take notes, watch videos and take practice quizzes.