Talk:Leibniz's notation

message: 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)
thread_title: Modern formalism

message: 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)
replies: text: GIYF: http://www.math.wisc.edu/~keisler/calc.html TomJF 00:37, 21 April 2006 (UTC)
thread_title: Needs work

message: 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)
replies: text: What did Leibniz himself use??? — DIV (128.250.204.118 10:10, 31 August 2007 (UTC)

text: Roger Penrose used upright "d" --zzo38(✉) 06:24, 23 May 2010 (UTC)
replies: text: For Leibniz's own usage, the best place to check would be the book by Margaret Baron on calculus.  Tkuvho (talk) 07:41, 23 May 2010 (UTC)
thread_title:  The d debate 

message: The following material was recently deleted from the lede: In the 1960s, building upon earlier work by Edwin Hewitt and Jerzy Łoś, Abraham Robinson developed rigorous mathematical explanations for Leibniz' intuitive notion of the "infinitesimal," and developed non-standard analysis based on these ideas. Robinson's methods are used by only a minority of mathematicians. Jerome Keisler wrote a first-year-calculus textbook based to Robinson's approach.  What is the reason for the deletion?  Tkuvho (talk) 10:06, 4 January 2012 (UTC)
thread_title:  unexplained deletion of material 

message: Notation for integration is mentioned at the very end of the article, but it wasn't introduced anywhere. We should add details with examples, as Leibniz notation is also used to describe integration along a path. 
:\int_\gamma f d\gamma = \int_a^b f'(\gamma(t))\gamma'(t) dt
Logical Gentleman (talk) 21:25, 7 October 2016 (UTC)
thread_title:  Needs detail on Leibniz's notation for integration 

message: The year is wrong, it must be fixed but I'm not allowed to do so, can someone else look into the year issue? Vyvek (talk) 11:52, 6 February 2017 (UTC)
replies: text: Regarding  and : the cited source seems to support 1684. And in 1884 Leibniz was long dead. Comments from others? - DVdm (talk) 11:57, 6 February 2017 (UTC)
thread_title:  Fix the year 

message: I have recently been cleaning up this page and adding new material and references. As I look at the structure of the page, however, I am a bit concerned by the amount of material on non-standard analysis that appears in the lead. I am considering the following changes:
# Put into the lead the simple statement that non-standard analysis can be used to legitimize Leibniz's original conception of differentials.
# Pull all the rest of the non-standard analysis out of the lead and the history section and create a new section with that material and place it before the last section on other notations. 
I think that these changes might restore some balance to this article. Whether or not I do this, I do plan on expanding the history section to include some of the alternative notations that Leibniz played around with (based on Cajori's treatment). Comments? --Bill Cherowitzo  (talk) 05:26, 10 February 2017 (UTC)
thread_title:  Non-standard analysis 

message: I really don't get why the derivative is supposedly not a fraction since it is said to be the limit of a fraction. Non standard analysis is interesting but it seems it allows to precise the meaning of the derivative, not contradicting its "nature". Several times in the article, it's repeated a derivative is not a fraction without any counter example, and then it's explained it's the limit of a fraction.I have nothing against subtlety, but I would be grateful if the subtleties were clearly exposed, and not let "as a trivial exercice for the reader" Klinfran (talk) 23:21, 28 March 2019 (UTC)
thread_title:  clarification 

message: I removed the statement that nonstandard analysis gives a new ratio interpretation or justification of dy/dx.  What it provides are infinitesimal numbers, and thus infinitesimal increments (differentials) of functions, but the derivative does not become more of a ratio than it was using limits.   You can argue that it is the ratio "up to infinitesimal error", but justifications in that weaker sense were well known and widely taught before nonstandard analysis (e.g., as "up to an error tending to 0", up to o(1) error, up to higher-order terms in a series, up to a 1+o(1) factor, equal to leading asymptotic order, ...).   The formalism where dy/dx is, exactly and not up to small error, the derivative, is differential forms, though there it is done by definition.
Added also that Leibniz notation is used in integrals, which is where it is rather important. 73.89.25.252 (talk) 04:20, 13 June 2020 (UTC)
thread_title:  Changes to lede