I take it, nobody wants to touch inexact differentials. Here is my 
interpretation:
A potter is in the process of forming a vase. His vase contains a volume of:
Integral from 0 to X c dX
where c is the internal crossectional area and X is the height.
He wants to increase the contained volume V of the vase. He can use two 
methods to do that. He can add to the height of the vase by putting a ring 
of clay on top.This hight change causes the volume to change:
dV(height change) = c dX
He can also change the shape of the vase:
dV(shape change)  = integral(0 to X) dc dX
The total volume change is:
dV = dV(height change)  + dV(shape change)
     = c dX + integral(0 to X) dc dX
Finally one can not tell which of the two methods he used. He can decrease 
the volume by either height change or sape change, no matter how he had 
added the volume. dV(height change) and dV(height change)
are inexact differentials, but dV (total) is an exact differential.
Any comment?   Rudy
"Rudy von Massow" <massow@mts.net> wrote in message 
news:hde57g$qn1$1@news.eternal-september.org...
> The first law of thermodynamics is stated as: dU =DQ + DW, where capital 
> D's are inexact differentials.How does mathematics interpret and treat 
> these. I will later suggest an interpretation.  Rudy
>