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Introduction

What is usually called Helmholtz theorem[11] is the fact that a vector field $ \vec{V}$ which vanishes at infinity is completely determined by giving, everywhere, $ div\vec{V}$ and $ curl\;\vec{V}$. Helmholtz arrived at it in his study of vortices in fluids[14]. Nowadays it is mostly used in Electrodynamics, where the very Maxwell equations express its importance by being nothing else than the specification of what the $ div$ and $ curl$ of the electric and magnetic fields are.

Henrique Fleming 2003-08-11