Talk:PlanetPhysics/Stokes Theorem

Original TeX Content from PlanetPhysics Archive

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: Stokes' theorem %%% Primary Category Code: 02.30.-f %%% Filename: StokesTheorem.tex %%% Version: 3 %%% Owner: bloftin %%% Author(s): Wkbj79, pahio, bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}

\usepackage{html}

% 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

\begin{document}

{\bf Stokes' theorem}:\, The surface integral of the \htmladdnormallink{curl}{http://planetphysics.us/encyclopedia/Curl.html} of a \htmladdnormallink{vector function}{http://planetphysics.us/encyclopedia/VectorFunctions.html} is equal to the line integral of that vector function taken around the closed curve bounding that surface.

\begin{equation} \int \int_S \nabla \times {\bf W} \cdot d {\bf a} = \oint_O {\bf W} \cdot d {\bf r} \end{equation}

On account of its great importance in all branches of \htmladdnormallink{mathematical physics}{http://planetphysics.us/encyclopedia/PhysicalMathematics2.html}, a number of different proofs of this \htmladdnormallink{theorem}{http://planetphysics.us/encyclopedia/Formula.html} will be given.

\subsection{Proof I.}

soon to come...

\end{document}