# Multivariable Calculus, Hybrid, 7th Edition

- includes Enhanced WebAssign 1-Semester Printed Access Card
**James Stewart**McMaster University**ISBN-10:**1133110835**ISBN-13:**9781133110835- 480 Pages Paperback
- Previous Editions: 2012
- © 2012 | Published

- includes Enhanced WebAssign 1-Semester Printed Access Card
**James Stewart**McMaster University**ISBN-10:**1133110835**ISBN-13:**9781133110835- 480 Pages Paperback
- Previous Editions: 2012
- © 2012 | Published

Reflecting Cengage Learning’s commitment to offering flexible teaching solutions and value for students and instructors, these new hybrid versions feature the instructional presentation found in the printed text while delivering end-of-section and/or end-of chapter exercises online in Enhanced WebAssign. The result—a briefer printed text that engages students online! James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of MULTIVARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence. CourseSmart goes beyond traditional expectations–providing instant, online access to the textbooks and course materials you need and at a lower cost to your students. To request an electronic sample of this Cengage Learning title, go to: www.coursesmart.com/instructors.

- 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 pre-existing 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.
- 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.
- Additional exercises have been added to the existing end-of-chapter collections of more challenging exercises called “Problems Plus”. 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.

- TOC change: Chapters 1 and 2 have been combined – and some material has been moved to an appendix—to streamline the presentation of these early topics.
- Throughout the text, the author has revised the narrative as necessary to improve clarity and aid in student comprehension.
- NEW examples, margin notes, applications, and projects have been added. In addition, new collections of more challenging exercises called "Problems Plus" have been added, reinforcing concepts by requiring students to apply techniques from more than one chapter of the text. "Problems Plus" sections patiently show students how to approach a challenging problem.
- NEW! This edition has been updated with approximately 25% more exercises than the previous edition, giving students more opportunities to practice concepts they have learned.
- NEW “PS” icons denoting problem-solving margin notes are aimed at increasing instructors' awareness of this important aspect of Stewart's approach.
- UPDATED! Tools for Enriching Calculus—a free, online, interactive resource that allows Calculus students to work with animations that deepen their understanding of key concepts by helping them visualize the concepts they are learning—has been updated with new problems and a new Flash design that is more visually appealing and engaging to students.
- NEW-AND-IMPROVED! Exclusively from Cengage Learning, Enhanced WebAssign® offers an extensive online program for Stewart's Calculus, 7e, to encourage the practice that's so critical for concept mastery. The meticulously crafted pedagogy and exercises in our proven texts become even more effective in Enhanced WebAssign, supplemented by multimedia tutorial support and immediate feedback as students complete their assignments. Enhanced WebAssign for Stewart now includes opportunities for students to review prerequisite skills and content both at the start of the course (in conjunction with four diagnostic tests) and at the beginning of each section. In addition, at the problem-level, student can get extra help in the form of “math mentor” feedback and video solutions.
- NEW! Cengage YouBook is a Flash-based eBook that is interactive and customizable! Containing all the content from Stewart's Calculus, 7e, YouBook features a text edit tool that allows you to rewrite, delete, modify, or add to the textbook narrative as needed. With YouBook, you can quickly re-order entire chapters and sections or hide any content you don't teach to create an eBook that perfectly matches your syllabus. Additional media assets include interactive simulations, animations, and video clips that complement the traditional text presentation. The YouBook also lets you embed videos of your own or from YouTube directly into eBook pages.
- NEW! Interested in a simple way to complement your text and course content with study and practice materials? Cengage Learning's 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. CourseMate goes beyond the book to deliver what you need!
- NEW! Hybrid versions of the text provide a less-expensive, shorter option for students using EWA. End-of-section problems are omitted from the text and appear online only.

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.

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.

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.

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.

14. PARTIAL DERIVATIVES.

Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximation. 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.

15. MULTIPLE INTEGRALS.

Double Integrals over Rectangles. Iterated Integrals. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. 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.

16. ECTOR 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.

17. SECOND-ORDER DIFFERENTIAL EQUATIONS.

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

APPENDIXES.

F. Proofs of Theorems.

G. Graphing Calculators and Computers .

H. Complex Numbers.

I. Answers to Odd-Numbered Exercises.

All supplements have been updated in coordination with the main title. Select the main title’s "About the Solution" 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.**

Cengage Learning’s Enhanced WebAssign allows you to create online homework assignments that draw from thousands of end of chapter questions that match your adopted textbook. Problems are enhanced with rich tutorial content like Watch It Videos and Animations, Practice It and Master it Tutorials and access to the relevant textbook sections. Flexible assignment options allow you to choose how feedback and tutorial content is released to students as well as the ability to conditionally release assignments based on your student’s prerequisite assignment scores. This access card also provides students access to an interactive Premium eBook, which offers search, highlighting, and note-taking functionality, as well as links to multimedia resources. Increase student engagement, improve course outcomes and experience the superior service offered through CourseCare. Visit us at http://webassign.net/cengage to learn more.

Enrich the way you teach the course with the Instructor's Guide for Stewart's Calculus, 7E. Each section of the main text is discussed from several viewpoints and 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 problems. The guide includes single variable and multivariable content. An electronic version is available on PowerLecture.

Equip yourself with the dynamic teaching tools available with PowerLecture CD-ROM. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Enhance your lectures with Microsoft® PowerPoint® lecture slides and figures from the book.

Includes multiple-choice and short-answer test items that key directly to the text. (Includes single variable and multivariable content).

This manual includes worked-out solutions to every exercise in Single Variable Calculus, 7e (Chapters 1-11 of Calculus, 7e).

Includes worked-out solutions to all exercises in the multivariable text (Chapters 10-17 of the complete text).

For each section of Stewart's Multivariable text, the Study Guide provides students with a brief introduction, a short list of concepts to master, as well as summary and focus questions with explained answers. The study guide also contains "Technology Plus" questions, and multiple-choice "On Your Own" exam-style questions.

Interested in a simple way to complement your text and course content with study and practice materials? Stewart's Calculus CourseMate from Cengage Learning 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. Stewart's Calculus CourseMate goes beyond the book to deliver what you need! Key features include interactive eBook, quizzes, flashcards, videos, Tools for Enriching Calculus, and Engagement tracker.

Available on the PowerLecture™ CD and featuring automatic grading, ExamView® testing software allows instructors to quickly create, deliver, and customize tests for class in print and online formats. The program includes a test bank with hundreds of questions customized directly to the text, with all questions also provided in PDF and Microsoft® Word formats for instructors who opt not to use the software component.

James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of MULTIVARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.

All supplements have been updated in coordination with the main title. Select the main title’s "About the Solution" 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.**

Exclusively from Cengage Learning, Enhanced WebAssign helps students develop a deeper conceptual understanding of their subject matter and complete required online homework assignments. With Enhanced WebAssign, students receive access to a Premium eBook along with immediate feedback and tutorial content, which may include Watch It Videos, Animations, Practice It Questions, Master It Tutorials, Read It Text passages, Chat About It Tutor services, and a Personal Study Plan to aid in the mastery of their course materials. The printed access card features single semester access to an Enhanced WebAssign course with an interactive eBook and is suitable for a one term course in the Calculus, Physics, Chemistry course sequence.

Study smarter with the Study Guide for Stewart's Multivariable Calculus, 7E. For each section of the text, the Study Guide provides a brief introduction, a short list of concepts to master, and summary and focus questions with explained answers. "Technology Plus" questions and multiple-choice "On Your Own" exam-style questions help you prepare for exams.

The more you study, the better the results. Make the most of your study time by accessing everything you need to succeed in one place. Stewart's Calculus CourseMate includes an interactive eBook with highlighting, note-taking, and glossary, quizzes, flashcards, videos, Tools for Enriching Calculus, and more!

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With MULTIVARIABLE CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course.