Do these symbols:∇, ħ, ∂ (del/nabla, h-bar, the partial differentiation sign) have any meaning outside maths? i.e. are they characters in any language?
My guess is that del is just an upside down delta (due to it’s relationship with ‘change’ and it’s mathematical symbol delta).I’m sure I’ve seen h-bar in Eastern European languages like Polish and Esperanto. As for the partial differenation sign I’ve not got a clue.
So what’s the Straight Dope?
Before Uno Mundo tells me off, yes I know Esperanto’s a world language but it does borrow from Eastern European languages in many ways and I think I’ve seen it use a h-bar 
It seems like whenever there’s a differentiation operator, it has to be some stylized “d”. Nabla is an upside-down Greek D, and the partial differentiation operator is sort of a squiggly d. uppercase and lowercase D and Delta were all already used for other kinds of differentiation things. I’ve also seen a script D and partial-symbol-with-a-bar. This brings the total number of these to eight (!). I’m guessing that eventually they just started making up D-like things when they ran out of real ones.
I don’t think Esperanto uses h-bar (ħ). Instead they use h with a caret (ĥ). I couldn’t tell you about Polish.
I can’t see your symbols, and you probably can’t see mine. Here they are anyway.
∇ ħ ∂
^ <— Used in Portuguese and French above some vowels to denote pronunciation/inflection.
Achenar, I can see your characater set, I just pasted mine off google by typing there names into search. I should learn the correct code for them.
I’ve used the other types of differentiation symbols, never seen a d/partial with a bar though, what does it signify?
Some information about nabla and the partial differentiation symbols can be found on Jeff Miller’s Earliest Uses of Symbols of Calculus. If you’re interested in that sort of thing, the best book about the history of mathematical notation is, well, A History of Mathematical Notations, by Florian Cajori. Unless you’re interested in mathematical notations introduced after 1923.
I haven’t encountered h-bar in mathematics. I believe Paul Dirac was the first to use it in physics in the late 1920s or early 30s. Whether it was used for anything else before that, I don’t know.
Mathematical/physical there’s not much difference, I’m sure you’d find h-bar in a decent sized maths dictionary.
Anyway if anyones interested, I found that h-bar is a maltese symbol.
You know, I can’t find it, so it’s possible I misremembered it. It was in a thermodynamics book, discussing the First Law of Thermodynamics, and it said (very briefly in a footnote) that
dU = dQ - dW
should actually be written with these unique differential signs, because these weren’t true differentials or something like that. It struck me as being like the angular momentum pseudovector - something the book notes but then ignores unless it becomes important.
There’s also the partial sign with a slash through it used fairly extensively (albeit as a time-saving measure) in field theory. Look at the bottom of page 5 of this PDF for an example.
As for the d-bar symbol that Achernar remembered, the description he gave is correct; it’s called an “inexact differential.” Look here for an example (around Equation 141.)