CALCULUS Understanding Its Concepts and Methods

Divergence theorem

Suppose is a vector field.

The divergence of is the scalar function

Divergence theoremLet be a vector field defined on a solid whose boundary is a piecewise smooth surface . Let be the outward-pointing unit normal vector at each point of . If the components of have continuous first order partial derivatives on , thenwhere .

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.