Understanding Maxwell's Equations: Integral and Differential Forms

[girlinphysics]

I am getting really confused with the millions of different versions/forms of Maxwell's equations. I know there is differential form and integral form, but sometimes there is a B for magnetic field...other times there is an H. Sometimes there is dependence on $\rho$ or J (current density) and sometimes there isn't.

If someone could clarify those confusions and provide a concrete set of both integral and differential forms hopefully I can tackle a few homework questions I have been given on them.

 

[Fredrik]

The Wikipedia article seems to cover this really well. Link.