Multivariable Calculus

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618503025
• ISBN10: 0618503021
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-01-24
• Publisher: Brooks Cole

Summary

Designed specifically for the Calculus III course, Multivariable Calculus, 8/e, contains chapters 10 through 14 of the full Calculus, 8/e, text. The text continues to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer a two-semester Calculus I with Precalculus text. Every edition of the series has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best.

Table of Contents

Vectors and the Geometry of Space

Vectors in the Plane

Space Coordinates and Vectors in Space

The Dot Product of Two Vectors

The Cross Product of Two Vectors in Space

Lines and Planes in Space Section Project: Distances in Space

Surfaces in Space

Cylindrical and Spherical Coordinates

Vector-Valued Functions

Vector-Valued Functions Section Project: Witch of Agnesi

Differentiation and Integration of Vector-Valued Functions

Velocity and Acceleration

Tangent Vectors and Normal Vectors

Arc Length and Curvature

Functions of Several Variables

Introduction to Functions of Several Variables

Limits and Continuity

Partial Derivatives Section Project: Moireacute; Fringes

Differentials

Chain Rules for Functions of Several Variables

Directional Derivatives and Gradients

Tangent Planes and Normal Lines Section Project: Wildflowers

Extrema of Functions of Two Variables

Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline

Lagrange Multipliers

Multiple Integration

Iterated Integrals and Area in the Plane

Double Integrals and Volume

Change of Variables: Polar Coordinates

Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail

Surface Area Section Project: Capillary Action

Triple Integrals and Applications

Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres

Change of Variables: Jacobians

Vector Analysis

Vector Fields

Line Integrals

Conservative Vector Fields and Independence of Path

Green's Theorem Section Project: Hyperbolic and Trigonometric Functions

Parametric Surfaces

Surface Integrals Section Project: Hyperboloid of One Sheet

Divergence Theorem

Stokes's Theorem Section Project: The Planimeter

Appendices

Proofs of Selected Theorems

Integration Tables

Additional Topics in Differential Equations (Web only)

Precalculus Review (Web only)

Rotation and the General Second-Degree Equation (Web only)

Complex Numbers (Web only)

Business and Economic Applications (Web only)

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