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'general Stokes theorem'
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| Title of object: |
general Stokes theorem |
| Canonical Name: |
GeneralStokesTheorem |
| Type: |
Theorem |
| Created on: |
2002-06-05 23:26:43-04 |
| Modified on: |
2002-06-08 23:39:40.317509-04 |
| Classification: |
msc:58C35 |
| Synonyms: |
general Stokes theorem=Stokes theorem |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\newcommand{\RR}{\mathbb{R}}
\newcommand{\dd}{\mathrm{d}} |
Content:
Let $M$ be an oriented $r$-dimensional differentiable manifold with boundary $\partial M$ piecewise differentiable, let the orientation
of $\partial M$ be that induced by the orientation of $M$, and let $\omega$ be an $(r-1)$-form whose components have continuous
first partial derrivatives in any coordinate chart. Then
\[ \int_M \dd \omega = \int_{\partial M} \omega.\]
Examples of familiar corrolaries and formulations to follow. |
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