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Multivariable Calculus 8th Edition

James Stewart

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Overview

James Stewart's CALCULUS resources are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. MULTIVARIABLE CALCULUS, 8th Edition, 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 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.

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.

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.

  • 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 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.
  • 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.

Multivariable Calculus

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. 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.

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

Complete Solutions Manual, Chapters 10-17 for Stewart's Multivariable Calculus, 8th

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.

Cengage Learning Testing, powered by Cognero Instant Access

ISBN: 9781305387096
Cengage Learning Testing Powered by Cognero is a flexible, online system that allows you to author, edit, and manage test bank content, create multiple test versions in an instant, and deliver tests from your LMS, your classroom or wherever you want. This is available online via your SSO account at login.cengage.com.

FOR STUDENTS

Study Guide

ISBN: 9781305271845
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.

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).