What do the subscripts in Maxwell's equations mean

[ehrenfest]

Homework Statement

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

I am confused about the subscripts next to the partial derivatives.
[tex] \left(\frac{\partial T}{\partial V}\right)_S =
-\left(\frac{\partial p}{\partial S}\right)_V\qquad=
\frac{\partial^2 U }{\partial S \partial V}[/tex]
What does the S mean after the first partial? Does it mean that this equation is only true when entropy is held constant? I thought the point of a partial derivative was to hold constant all other quantities except the one that you differentiate w.r.t?

Homework Equations

The Attempt at a Solution

 

[joelperr]

In general, the subscripts denote which parameters are held constant.

 

[ems]

You're right, it is implied that all other things are held constant when taking partial derivatives... but it's often written in out in physics whereas not so much in math. Mostly it's written down (in my opinion) in the derivations of these relations using the thermodynamic identity.