Multivariable Calculus,
4th Edition

9. 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. Laboratory Project: Putting 3D in Perspective. Functions and Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Focus on Problem Solving.
10. 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. Parametric Surfaces. Review. Focus on Problem Solving.
11. PARTIAL DERIVATIVES.
Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. 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. Focus on Problem Solving.
12. MULTIPLE INTEGRALS.
Double Integrals over Rectangles. Iterated Integrals. 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 and Spherical Coordinates. Applied Project: Roller Derby. Discovery Project: The Intersection of Three Cylinders. Change of Variables in Multiple Integrals. Review. Focus on Problem Solving.
13. VECTOR CALCULUS.
Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Surface Integrals. Stokes' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Focus on Problem Solving.
APPENDIXES.
A. Intervals, Inequalities, and Absolute Values.
B. Coordinate Geometry.
C. Trigonometry.
D. Precise Definitions of Limits.
E. A Few Proofs.
F. Sigma Notation.
G. Integration of Rational Functions by Partial Fractions.
H. Polar Coordinates.
I. Complex Numbers.
J. Answers to Odd-Numbered Exercises.

• James Stewart

  The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He conducted research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Dr. Stewart most recently served as a professor of mathematics at McMaster University, and his research focused on harmonic analysis. Dr. Stewart authored a best-selling calculus textbook series, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS and CALCULUS: CONCEPTS AND CONTEXTS as well as a series of successful precalculus texts.

• Four new diagnostic tests in the beginning of the book gauge students’ proficiency in Basic Algebra, Analytic Geometry, Functions, and Trigonometry. Answers are provided, and students who don't do well are referred to where they should seek help.

• Some material has been rewritten for greater clarity or for better motivation. See, for example, the introduction to maximum and minimum values on pages 262-263 and the introduction to series on page 565.

• Examples are now titled for easier reference, and some new examples have been added. In some cases, solutions given have been amplified, and data has been thoroughly revised and reviewed to reflect current values.

• In response to user feedback, specific areas of content have been condensed, moved, or expanded upon, including: the material motivating the derivative is briefer and is now a single section called Derivatives and Rates of Change. Rates of Change in the Natural and Social Sciences has been moved later in Ch. 3, to incorporate more differentiation rules. Coverage of inverse trigonometric functions has been consolidated in a single section (3.6). The former sections 4.6 and 4.7 have been merged into one section, with a briefer treatment of optimization problems in business and economics. There is now a full section on volumes by cylindrical shells (6.3).

• CONCEPTUAL EXERCISES. The most important way to foster conceptual understanding is through assigned problems. Stewart Concepts offers various types of problems, including explanations/mathematical writing problems, use of graphs and tables, Concept Checks, and True/False quizzes in the review sections.

• GRADED HOMEWORK EXERCISES. Each exercise set is carefully graded, progressing from basic conceptual exercises and skill-development problems to more challenging problems involving applications and proofs.

• REAL-WORLD DATA. Interesting real-world data gathered from a variety of contemporary sources introduces, motivates, and illustrates the concepts of calculus.

• INSTRUCTOR RESOURCE GUIDE WITH SOLUTIONS. The instructor's resource guide contains an abundance of resources keyed to the textbook by chapter and section, including diagnostic tests, chapter summaries, teaching strategies, chapter tests and final exams, and more.

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.

Cengage eBook: Multivariable Calculus 12 Months
9788000029443