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Divergence theorem

Suppose MATH is a vector field.

The divergence of $\QTR{bf}{F}$ is the scalar functionMATH

Divergence theoremLet MATHbe a vector field defined on a solid $E$ whose boundary is a piecewise smooth surface $S$. Let $\QTR{bf}{n}$ be the outward-pointing unit normal vector at each point of $S$. If the components of $\QTR{bf}{F}$ have continuous first order partial derivatives on $E$, thenMATHwhere $d\QTR{bf}{S=n\,}dS$.


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


Green's theorem

Stokes' theorem


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.

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