## Table of Contents

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.

## Products Included

## Instructor Supplements

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Instructor's Guide
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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.

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

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

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Study Guide, MV
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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.

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Multivariable Calculus
(ISBN-10: 0538497874 | ISBN-13: 9780538497879)

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.

## Student Supplements

# Student Supplements

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.**

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Enhanced WebAssign Homework and eBook One-Term Printed Access Card for Multiple-Term Math and Science
(ISBN-10: 0538738081 | ISBN-13: 9780538738088)

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.

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Study Guide, MV
(ISBN-10: 0840054106 | ISBN-13: 9780840054104)

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.

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CourseMate Instant Access
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Multivariable Calculus
(ISBN-10: 0538497874 | ISBN-13: 9780538497879)

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