What Is the Dirac Delta Function in Electrodynamics?

[quantum123]

I often see this in electrodynamics in the form of a point charge density function. There are some rules on how to manipulate the thing in integrals.
But what is it mathematically?

 

[bomba923]

http://en.wikipedia.org/wiki/Dirac_delta_function

 

[cliowa]

arildno created a nice tutorial on this. You can find it https://www.physicsforums.com/showthread.php?t=73447".