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Conclusion

The first Helmholtz theorem explains why the $ div$ and $ curl$ are so ubiquitous in vector fields. It also explains the structure of Maxwell equations, usually written in such a way that the first member of each is either a $ div$ or a $ curl$. The second explains the meanings, and so also the names, of those operators. Considering that Hermann von Helmholtz graduated in Medicine, not in Physics, that was not a bad job at all!

Henrique Fleming 2003-08-11