> (A) Why do you insist on d(V) and not just dV -
> what is the distinction?
I don't insist on it. Sometimes I write dV, and
sometimes I write d(V) to emphasize that dV always
represents the operator (d) applied to the
function-of-state (V). In particular, dV is not
just some two-letter name. Consider the difference:
Darlene is a seven-letter name.
d(Arlene) is (d) applied to a six-letter name.
To repeat: dV is always the (d) operator applied to
a one-letter name. It is always equivalent to d(V).
> (B) Have you blurred the distinction between a differential and a
> derivative? Is not dV a differential and not a derivative
> (consider its units!)? A derivative is a RATE of change.
I recognize the distinction.
But I also recognize a correspondence, which means
that many things that can be said about one can be
said about the other.
By way of analogy, I recognize that force is distinct
from momentum. But every balance-of-forces equation
has a corresponding conservation-of-momentum equation.
They're not the same, but they're not unrelated.
> 2) The second issue shows in John's wish to obliterate inexact
> differentials:
I'm not trying to obliterate anything. I'm
perfectly happy with non-exact objects such as
P dV. I just don't recommend writing them in
a form that implies that they are exact. When
people see dW, they quite naturally think it
refers to the differential of W ... but if it
were the differential of W it would be exact.
(That's the _definition_ of exact.)