Calculus Multivariable, 9th Edition

by Anton, Howard; Bivens, Irl C.; Davis, Stephen

• ISBN13: 9780470183465
• ISBN10: 0470183462
• Edition: 9th
• Format: Hardcover
• Copyright: 2009-03-01
• Publisher: Wiley

Summary

The ninth edition continues to provide engineers with an accessible resource for learning calculus. The book includes carefully worked examples and special problem types that help improve comprehension. New applied exercises demonstrate the usefulness of the mathematics. Additional summary tables with step-by-step details are also incorporated into the chapters to make the concepts easier to understand. The Quick Check and Focus on Concepts exercises have been updated as well. Engineers become engaged in the material because of the easy-to-read style and real-world examples.

Table of Contents

Three-Dimensional Space; Vectors

Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

Vectors

Dot Product; Projections

Cross Product

Parametric Equations of Lines

Planes in 3-Space

Quadric Surfaces

Cylindrical and Spherical Coordinates

Vector-Valued Functions

Introduction to Vector-Valued Functions

Calculus of Vector-Valued Functions

Change of Parameter; Arc Length

Unit Tangent, Normal, and Binormal Vectors

Curvature

Motion Along a Curve

Kepler's Laws of Planetary Motion

Partial Derivatives

Functions of Two or More Variables

Limits and Continuity

Partial Derivatives

Differentiability, Differentials, and Local Linearity

The Chain Rule

Directional Derivatives and Gradients

Tangent Planes and Normal Vectors

Maxima and Minima of Functions of Two Variables

Lagrange Multipliers

Multiple Integrals

Double Integrals

Double Integrals over Nonrectangular Regions

Double Integrals in Polar Coordinates

Surface Area; Parametric Surfaces}

Triple Integrals

Triple Integrals in Cylindrical and Spherical Coordinates

Change of Variable in Multiple Integrals; Jacobians

Centers of Gravity Using Multiple Integrals

Topics in Vector Calculus

Vector Fields

Line Integrals

Independence of Path; Conservative Vector Fields

Green's Theorem

Surface Integrals

Applications of Surface Integrals; Flux

The Divergence Theorem

Stokes' Theorem

Appendix [order of sections TBD]

Graphing Functions Using Calculators and Computer Algebra Systems

Trigonometry Review

Solving Polynomial Equations

Mathematical Models

Selected Proofs

Web Appendices

amp;#160; Real Numbers, Intervals, and Inequalities

Absolute Value

Coordinate Planes, Lines, and Linear Functions

Distance, Circles, and Quadratic Functions

Second-Order Linear Homogeneous Differential Equations; The Vibrating String

The Discriminant

Answers

Photocredits

Index

Table of Contents provided by Publisher. All Rights Reserved.