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Stokes-Greens-Gauss Theorems


Date: 03/25/97 at 19:37:09
From: Michael Mullen
Subject: Green's-Stokes'-Gauss' Theorems

Are the Stokes-Greens-Gauss theorems related?

Also, where can I find a brief interpretation of the significance of 
the theorems?


Date: 03/28/97 at 13:51:38
From: Doctor Ceeks
Subject: Re: Green's-Stokes'-Gauss' Theorems

Hi,

Yes, they are all generalizations of the Fundamental Theorem of
Calculus which asserts that

F(b)-F(a) = integral from a to b of F'(x) dx

where F'(x) denotes the derivative of F(x).

All of them say that some measure of the function over a regions
boundary is the same as some other measure of some appropriately
related function over the entire region.

A good place to look for the significance of these theorems is in
their use in physics: see, for instance, Edward M. Purcell,
"Electricy and Magnetism".

There is a vast generalization of even these theorems into one
single all encompassing statement, which also goes by the name
Stoke's theorem.  A treatment of this can be found in "Calculus
on Manifolds" by Michael Spivak, for instance, but this treatment
is advanced.

There's another book which I've heard of, but not looked at, but
I've been told by some that it's easy to read, and unfortunately,
I only remember the title: "Div, Grad, Curl, and all that."

-Doctor Ceeks,  The Math Forum
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