StokesTheorem 2006-07-25 23:44:24 2006-07-27 18:22:13 Theorem missing comma some clarification % 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 {\bf Stokes' theorem}:\, The surface integral of the curl of a vector function 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 mathematical physics a number of different proofs will be given. \subsection{Proof I.} soon to come...