Ok. I am used to see written everywhere the following Cauchy-Rieamman equations for complex functions:

http://upload.wikimedia.org/math/c/2...ead3bdf686.png

and

http://upload.wikimedia.org/math/5/b...1e868c24ae.png

Now, today I saw this other notation

http://upload.wikimedia.org/math/0/9...98334feee9.png and I'd like to understand how it maps to the first. It must be pretty simple, I guess?

Thanks