Single Variable Calculus: Concepts and Contexts, 3rd Edition

  • includes Tools for Enriching Calculus, Interactive Video Skillbuilder CD-ROM, and iLrn Homework/Personal Tutor
  • James Stewart McMaster University
  • ISBN-10: 0534410227  |  ISBN-13: 9780534410223
  • 784 Pages
  • Previous Editions: 2001, 1998, 1998
  • © 2005 | Published
  • List Price = $ 337.95
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  • Newer Edition Available



Stewart's clear, direct writing style in SINGLE VARIABLE CALCULUS guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution. iLrn Homework helps you identify where you need additional help, and Personal Tutor with SMARTHINKING gives you live, one-on-one online help from an experienced calculus tutor. In addition, the Interactive Video Skillbuilder CD-ROM takes you step-by-step through examples from the book.

Features and Benefits

  • Presents a streamlined approach to calculus for instructors who want to focus on concepts, but with a balanced presentation of theory.
  • The concept of the derivative is introduced in Chapter 2, but Rules of Differentiation are not given until Chapter 3. This is intended to force students to think about the numerical and geometric meanings and consequences of derivatives before the differentiation formulas are covered.
  • Antiderivatives are introduced soon after derivatives, revisited frequently, and then summarized in section 4.10.
  • The integration chapter challenges students to understand the meaning of integrals in diverse contexts. There is no separate chapter on techniques of integration, but substitution and parts are covered here and other methods are treated briefly.
  • Parametric curves are introduced early to help students draw curves easily, with technology, whenever needed throughout the text.
  • Differential equations occur immediately after applications of integration, and stress direction fields, numerical methods, and models of population growth.
  • Margin notes clarify and expand on topics presented in the main body of the text.
  • "Principles of Problem Solving" (based on Polya's approach) is introduced at the end of Chapter One. "Focus on Problem Solving" sections then occur at the end of every chapter to reinforce this essential skill. These sections include more challenging problems.
  • Laboratory Projects, Discovery Projects, Writing Papers, and Applied Projects appear throughout the book to reinforce concepts, provide group-learning experiences, and help students understand the relevance of what they are learning.
  • Each chapter ends with a comprehensive review that includes "Concept Check Questions," a true/false quiz, and exercises for every principle covered in that chapter.

Table of Contents

Four Ways to Represent a Function. Mathematical Models. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Parametric Curves. Review. Principles of Problem Solving.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. Continuity. Limits Involving Infinity. Tangents, Velocities, and Other Rates of Change. Derivatives. The Derivative as a Function. Linear Approximations. What does f' say about f? Review. Focus on Problem Solving.
Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Rates of Change in the Natural and Social Sciences. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivatives of Logarithmic Functions. Linear Approximations and Differentials. Review. Focus on Problem Solving.
Related Rates. Maximum and Minimum Values. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Indeterminate Forms and l'Hospital's Rule. Optimization Problems. Applications to Economics. Newton's Method. Antiderivatives. Review. Focus on Problem Solving.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. Integration by Parts. Additional Techniques of Integration. Integration Using Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. Review. Focus on Problem Solving.
More about Areas. Volumes. Arc Length. Average Value of a Function. Applications to Physics and Engineering. Applications to Economics and Biology. Probability. Review. Focus on Problem Solving.
Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Exponential Growth and Decay. The Logistic Equation. Predator-Prey Systems. Review. Focus on Problem Solving.
Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representation of Functions as Power Series. Taylor and Maclaurin Series. The Binomial Series. Applications of Taylor Polynomials. Review. Focus on Problem Solving.
Appendix A: Intervals, Inequalities, And Absolute Values.
Appendix B: Coordinate Geometry.
Appendix C: Trigonometry.
Appendix D: Precise Definitions Of Limits.
Appendix E: A Few Proofs.
Appendix F: Sigma Notation.
Appendix G: Integration Of Rational Functions By Partial Fractions.
Appendix H: Polar Coordinates.
Appendix I: Complex Numbers.
Appendix J: Answers To Odd-Numbered Exercises.

What's New

  • More than 25% of the problems in each chapter are new, with additional conceptual and technology exercises and three new projects. However, the number of pages in the text remains unchanged.
  • The text contains hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and new references to the TEC CD-ROM (Tools for Enriching Calculus).
  • The only major structural change in this edition is that the two sections on linear approximations (2.9 and 3.8) have been combined as Section 3.8.
  • This text presents a more streamlined approach to calculus. For the convenience of instructors who wish to cover topics not in the book, the web site contains additional topics and expanded coverage of some topics. These are available as PDFs. These topics include: Trigonometric Integrals, Trigonometric Substitution, Strategy for Integration, Volumes by Cylindrical Shells, Area of a Surface of Revolution, Linear Differential Equations, Strategy for Testing Series, Using Series to Solve Differential Equations, Second Order Differential Equations, Nonhomogeneous Linear Equations, Applications of Second Order Differential Equations.
  • The TOOLS FOR ENRICHING CALCULUS CD-ROM has been significantly enhanced for this edition and now includes modules for multivariable calculus. This powerful CD-ROM contains visualizations, interactive modules, and homework hints that significantly enrich students' learning experience.
  • iLrn Homework allows instructors to assign machine-gradable homework problems that help students identify where they need additional help. By entering a PIN code packaged with their textbook, students gain access to both iLrn and vMentor--live, one-on-one online help from an experienced calculus tutor. If assigned by the professor, this system provides necessary problem solving practice that is automatically graded and requires very little intervention from instructors.
  • The Interactive Video Skillbuilder CD-ROM, takes students step-by-step through examples from the book, reinforcing the problem-solving skills they need to learn.
  • Preloaded with content and available free via PIN code when packaged with this text, WebTutor ToolBox pairs all the content of this text's rich Book Companion Web Site with all the sophisticated course management functionality of a WebCT or Blackboard product. It's an ideal solution for online and distance learning needs.
  • A "V" symbol has been placed beside examples (an average of three per section) for which there are videos of instructors explaining the example in more detail. These videos are free to adopters.

Alternate Formats

Choose the format that best fits your student's budget and course goals

To customize your learning solution, contact your Learning Consultant for more information.

  • Non-Media Version

    ISBN-10: 0534410014 | ISBN-13: 9780534410018

    List Price = $287.95

Efficacy and Outcomes


"I have appreciated two main things from this textbook. The first is the concise language that Stewart uses. It makes my job much easier. I can embellish, add, emphasize or not easily. The second item is the paring down of the calculus material to an amount that…allows me enough room to add the various exploratory activities that I have my classes use."

— Laura Moore-Mueller, Green River Community College

"The single feature of this book that I like the most is the breadth in the exercises."

— Carrie Kyser, Clackamas Community College

"Stewart does a good job in extracting the best parts from calculus reform efforts and traditional approaches. The book is well organized, the material is clearly presented, and there is an abundance of problems of varying levels. The problems are the right type to engage students in thinking about the concepts and to develop skills and ability to apply the calculus. . . . The organization and presentation is designed to develop perspective, conceptual understanding and ability to use the concepts and methods to actually solve problems." "I like the author’s approach very much…it combines the best features of both [the traditional and the reform approaches], making it possible to present a better course. Stewart’s approach contains the most important aspects of that [reform] approach—rule of four, use of projects, use of technology, focus on topics of value to clients, development of conceptual understanding over formalism, writing." "The text is well-informed about the use of calculus and makes good use of realistic settings, not just artificially manufactured information."

— John Hagood, Northern Arizona University

"I want a text that stresses the numerical and graphical as well as the algebraic approach to calculus. But I also want a calculus text that still has a solid rigorous foundation, and the Stewart book provides both."

— William Ardis, Collin County Community College

"Among the strengths of this text are the clear writing styles of the author, the use of color and diagrams throughout the book, the excellent organization of the book, the superb set of ancillaries both for the student and the instructor, and the excellent homework exercises."

— Gary S. Itzkowitz, Rowan University

"In a majority of the sections, this text includes more examples than other texts in the market. The examples are well chosen and explain the ideas well." "I sampled a rather large number of sections of this book with the corresponding sections of other successful texts in the market, and I again arrived at a firm conclusion that Stewart’s text is simply a better text. It includes more [and interesting] examples and applications in each section than other texts. The text strikes the right balance between mathematical accuracy and clarity. It also provides an effective learning and problem-solving experience for students going into engineering, mathematical and physical sciences."

— Mohammed Kazemi, University of North Carolina, Charlotte

"I think the book is excellent. We had used the Hughes-Hallet, Gleason Calculus text for several years prior to changing to Stewart—and [his] book is such a refreshing change. I have not received a single complaint from a faculty member or student about your text. That is amazing when you consider how many students have used your text at our university."

— John Richard Griggs, North Carolina State University

"I think that the book is perfect. The topics are well introduced and, in many cases, anticipated, so that the book seems to flow. The amount of rigor in the text is perfect."

— Judy Broadwin, Jericho High School (retired)


All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Complete Solutions Manual (SV)  (ISBN-10: 0534410251 | ISBN-13: 9780534410254)

The complete solutions manual provides worked out solutions to all of the problems in Chapters 1-8.

Test Bank  (ISBN-10: 0534410316 | ISBN-13: 9780534410315)

Contains multiple-choice and short-answer items that key directly to the text.

AP* Calculus Instructor's Guide  (ISBN-10: 0534410324 | ISBN-13: 9780534410322)

Taking the perspective of optimizing preparation for the AP exam, each section of the main text is discussed from several viewpoints and contains suggested time to allot, points to stress, daily quizzes, core materials for lecture, workshop/discussion suggestions, group work exercises in a form suitable for handout, tips for the AP exam, and suggested homework problems.

Student Solutions Manual (SV)  (ISBN-10: 0534410235 | ISBN-13: 9780534410230)

This Student Solutions Manual, written by Jeffery A. Cole, contains detailed solutions to the odd-numbered exercises in each chapter section, review section, True-False Quiz, and Focus on Problem Solving section. Also included are solutions to all Concept Check questions. Use of the solutions manual ensures that students learn the correct steps to arrive at an answer. This solutions manual covers chapters 1-8.

List Price = $169.95  | CengageBrain Price = $169.95  | College Bookstore Wholesale Price = $127.50

Student Supplements

WebTutor™ Advantage on WebCT™ Printed Access Card  (ISBN-10: 0534410286 | ISBN-13: 9780534410285)

Includes lecture notes, discussion threads, and quizzes.

List Price = $43.00  | College Bookstore Wholesale Price = $32.25

Student Solutions Manual (SV)  (ISBN-10: 0534410235 | ISBN-13: 9780534410230)

This Student Solutions Manual, written by Jeffery A. Cole, contains detailed solutions to the odd-numbered exercises in each chapter section, review section, True-False Quiz, and Focus on Problem Solving section. Also included are solutions to all Concept Check questions. Use of the solutions manual ensures that students learn the correct steps to arrive at an answer. This solutions manual covers chapters 1-8.

List Price = $169.95  | CengageBrain Price = $169.95  | College Bookstore Wholesale Price = $127.50

Meet the Author

Author Bio

James Stewart

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.