CALCULUS Understanding
Its Concepts and Methods
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
,
then
where
.
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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.