Stokes-Greens-Gauss TheoremsDate: 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 Check out our web site! http://mathforum.org/dr.math/ |
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