from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun arithmetic differentiation with respect to x
- noun A
Roman numeralrepresenting five hundred and ten (510).
Sorry, no etymologies found.
The integral in equation 6 uses dx, which is clearly an area here, because x is a location on a surface.
But we still speak of a small increment or patch of solid angle, just like in the vector case the dx is a small increment of the vector x, in two parts.
What is confusing and perhaps I am simply misinterpreting what Arthur Smith says above, is that he seems to indicate that his dx is a vector: "Perhaps my vector dx notation for a surface element isn't the usual convention"
Seems having a dx is a good thing, even if there is no known treatment or cure.
Certain pairs of letters, such as "dx," don't exist in English, while some letters almost always appear next to a certain other letter, such as "u" after "q".
One has to be careful in drawing a direct analogy between what Wolfram shows and what Arthur Smith has done, given that Smith's "dx" is a vector, according to Smith's own words above: "Perhaps my vector dx notation for a surface element isn't the usual convention"
That is, for a surface integral you can think of "dx" as two vectors... just like the Wolfram page uses two tangent vectors to represent the patch of surface.
The wording "my vector dx notation" refers to the use of a vector x as the integration variable, and of course the "dx" in integration represents a small increment in the integration variable.
For concreteness, consider a differential equation system, such as dx dt = Fx for a set of variables x = x1, x2, ¦, xn.
(Recall that "dx" means, in an informal way, "infinitesimal bit of length".)