Talk:Leibniz's notation
Modern formalism
The modern formalism for derivative and integral is imprecise. Unless there is a reason not to do so, we should use that given in any real analysis textbook, namely the Riemann sum for an integral and the long functional forms of y(x) and x for the derivative. —Preceding unsigned comment added by SamuelRiv (talk • contribs) 04:48, 14 October 2007 (UTC)
On second thought, it can be argued that for a page dealing with notation, and not formal mathematics, a simplified, less precise form is acceptable as long as it is clear and unambiguous to someone with a semester of calculus (or limits). I guess the notation for integral is then acceptable, but I will change that for derivative. SamuelRiv 04:56, 14 October 2007 (UTC)
Needs work
This article needs a lot of work. The second paragraph (not the line, the paragraph) is nearly incoherent. The closing statement describing units merely hints at what I wanted to know. Maybe it's somewhere else; in that case, a link will be needed.
-Malakai
- Does this look better now? Fresheneesz 00:17, 11 February 2006 (UTC)
"(One mathematician, Jerome Keisler, has gone so far as to write a first-year-calculus textbook according to Robinson's point of view.)" Why don't you tell us the name of the textbook, given that you tell us it exists? GangofOne 00:22, 11 February 2006 (UTC)
Merger
In the absence of any talk here, I have implemented the proposed merger by moving the content of Leibniz's notation for differentiation into this article. A while ago, I also adapted the notation here for coherence with that article. There is now a new (not fully developed) article at Notation for differentiation: the material here should ultimately inform this new article. I have made a similar move for the Newton's notation articles, where the issues are more straightforward, because Newton's notations for integration are not developed in wikipedia. Geometry guy 19:00, 26 March 2007 (UTC)
- Good job. I have a question about this odd looking thing:
- Did Leibniz always write the function being differentiated on top of the line, instead of the nicer looking
I suspect that the notation you suggest was not current in the 17th century, since it presumes the (later) idea of d/dx as an operator, and it was probably for precisely this reason that a more concise form was needed for multiple derivatives. However, I'm not an expert of 17th century notation, and they probably had a different way to write multiple fractions. Anyway, I would be happy if you would incorporate the notation you propose as an addition (but not a replacement) to the text, since it certainly makes sense, and is certainly now used. It could comfortably be inserted into the explanation for the origin of the d^ny/dx^n notation. Geometry guy 23:21, 26 March 2007 (UTC)
To answer your question: I have had a look into the correspondence of Leibniz:
Google Books "Mathematischer, naturwissenschaftlicher und technischer Briefwechsel von Gottfried Wilhelm Leibniz" Letter No. 44, Leibniz to Bernoulli, p.121, l.17
(3)
Which would look in modern notation like
I am not sure whether Leibniz thought the derivation as a functor which would justify the notation
And here is also my problem with this notation. The modern version regards as functor applied to functions rather than to function values. Function values are considered as constants and so would evaluate to 0. I would prefer to write for the derivation of the function f and as evaluation of at x; hence .
The d debate
For those like me wondering whether the d should be upright or italic, this has been discussed at length on Wikipedia before: see Wikipedia talk:WikiProject Mathematics/Archive 20#Symbol for differential and Wikipedia talk:WikiProject Mathematics/Archive2007#Upright d in math notation, etc. In summary: italic d is usual in mathematics, though not universal; Wikipedia consensus is that each page should keep its existing usage, and one form should not be turned into the other solely for consistency. --82.36.30.34 22:34, 25 June 2007 (UTC)
- What did Leibniz himself use??? — DIV (128.250.204.118 10:10, 31 August 2007 (UTC))