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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 Eighth Edition of MULTIVARIABLE CALCULUS, INTERNATIONAL METRIC EDITION, 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 Eighth Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.

Preface.

To the Student.

Diagnostic Tests.

A Preview of Calculus.

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.

F Proofs of Theorems.

G The Logarithm Defined as an Integral.

H Complex Numbers.

I Answers to Odd-Numbered Exercises.

INDEX.

- The data in examples and exercises have been updated to be more timely.
- New examples have been added (see Examples 11.2.5, and 14.3.3, for instance). And the solutions to some of the existing examples have been amplified.
- A new project has been added: In the project, The Speedo LZR Racer Suit, it is explained that this suit reduces drag in the water and, as a result, many swimming records were broken. Students are asked why a small decrease in drag can have a big effect on performance.
- More than 20% of the exercises in each chapter are new. Here are some Author favorites: 12.5.81, 12.6.29-30, 14.6.65-66.

- 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 presentation repeatedly provides answers to the question, When will I use this? Students will 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.
- Historical and biographical margin notes enliven the course and show students that mathematics was developed to help explain and represent natural phenomena.
- 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.

**James Stewart**

McMaster University

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.

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