Is there a convention for roman d vs italic d, e.g. as in df

[pellman]

At first I thought that roman d was reserved for the exterior derivative and italic d for scalar differentials.

That is, one would have df for the exterior derivative of function f but write dy/dx in regular calculus.

But the author of the wikipedia article http://en.wikipedia.org/wiki/Differential_(infinitesimal ) has used roman d for dy/dx. Is this just a matter of author's taste? Or am I missing a subtle distinction?

 

[I like Serena]

At first I thought that roman d was reserved for the exterior derivative and italic d for scalar differentials.

That is, one would have df for the exterior derivative of function f but write dy/dx in regular calculus.

But the author of the wikipedia article http://en.wikipedia.org/wiki/Differential_(infinitesimal ) has used roman d for dy/dx. Is this just a matter of author's taste? Or am I missing a subtle distinction?

As I've understood it:

Variables like x and y are supposed to be italic.
Operators (like sin, log, and yes, also "d") are supposed to be upright (roman).
Units (like m, s, kg) are supposed to be upright (roman).

These are the conventions that I've seen in the SI unit standard and in the LaTex reference.

However, you'll see that usually people will simply type what's easiest and brings the message across.
It's only in scientific articles that these conventions are (or should be) properly applied.

 

[Mute]

At first I thought that roman d was reserved for the exterior derivative and italic d for scalar differentials.

That is, one would have df for the exterior derivative of function f but write dy/dx in regular calculus.

But the author of the wikipedia article http://en.wikipedia.org/wiki/Differential_(infinitesimal ) has used roman d for dy/dx. Is this just a matter of author's taste? Or am I missing a subtle distinction?

If I recall correctly, if you have differential forms \mbox{d}y and \mbox{d}x, the derivative is really

\frac{\mbox{d}y}{\mbox{d}x}
a quotient of the two forms. The definitions of differential forms were pretty much defined so that this notation would make sense as a division of the two differential forms, matching the Leibniz notation. So, I guess they're kind of equivalent.

Whether or not the Liebniz notation itself should have roman d's or not, I'm not aware of any convention that anyone really follows. Using italicised d's doesn't look nearly as sloppy as sin(x) vs. \sin(x) does, and I'm not aware of a latex command for the derivative that automatically gives you roman d's, so most authors will just use italicised d's to avoid having to write \mbox{d} all over the place or try to define their own latex command to give them roman d derivatives.