Talk:Calculus

No integral calculus page?

There is a nice article for differential calculus, which describes it as a branch of calculus and gives some history, but there is no corresponding page for integral calculus. There is only a redirect to integral. Why then is differential calculus not a redirect to derivative? 121.216.128.241 (talk) 10:59, 9 February 2018 (UTC)

Hi. Your best bet at finding editors who are interested and know enough about this subject is at Wikipedia:WikiProject Mathematics. Perhaps bring this up at their talk page (Wikipedia talk:WikiProject Mathematics). Bennv3771 (talk) 11:57, 9 February 2018 (UTC)

(edit conflict) "Integral calculus" is much less used than "differential calculus". This is probably the reason for not having Integral calculus. Also, having a separate article needs to have content that is not covered by the target of the redirect. It seems that this is not the case here. D.Lazard (talk) 12:39, 9 February 2018 (UTC)

I have started a discussion relating to this comment at Wikipedia talk:WikiProject Mathematics#Articles on "differential calculus" and "integral calculus". --Trovatore (talk) 19:11, 27 December 2021 (UTC)

Separate Section

The lead sentence does not include the alternate term infinitesimal calculus, which would help clarify. I'd change it myself, but Wikipedia... — Preceding unsigned comment added by 96.40.48.159 (talk) 23:43, 8 June 2019 (UTC)

Also this article is the target of the redirect infinitesimal calculus. I have thus exchanged the places of this term and the etymology. By the way, I have done some other modifications. D.Lazard (talk) 08:19, 9 June 2019 (UTC)

Unaware of Lazard’s edit, I also made changes! Dolphin (t) 08:21, 9 June 2019 (UTC)

I have removed the second mention of "infinitesimal calculus", as, placed there, it is unclear whether it denotes integral calculus, differential calculus, or both. By the way, it is astonishing that there was no edit conflict: I have edited all paragraphs of the lead but one, and Dolphin51 has edited the only paragraph that I have left unchanged! D.Lazard (talk) 08:45, 9 June 2019 (UTC)

D.Lazard’s changes are sound. I have no intention to meddle any further. I agree it is puzzling that I saw no alert to an Edit conflict. It seems that Edit conflicts occur when I would prefer they didn’t, and an Edit conflict doesn’t occur when it would actually be beneficial! Dolphin (t) 09:33, 9 June 2019 (UTC)

Semi-protected edit request on 12 January 2020

"developed independently in the late 17th"? How can it be? Both Leibniz and Newton died in 18th century. Datdinhquoc (talk) 23:24, 12 January 2020 (UTC)

 Not done Newton died in 1726, which is during the 18th century. His work on the calculus was done in the late 1600's, which is the 17th century. This offset of the century number is due to the fact that there is no "zero" century. --Bill Cherowitzo (talk) 23:35, 12 January 2020 (UTC)

Oh yes, 16xx is 17th century. — Preceding unsigned comment added by Datdinhquoc (talk • contribs) 22:29, 13 January 2020 (UTC)

Contested April 2020 additions

@Prototypehumanoid: WP:BRD is a very good idea to follow. The short version: there already is some material in the history section about precursors to the Calculus in South Asia. Overloading the lead with that, though, would probably lend WP:UNDUE weight to the overall importance of that with respect to the rest of the article. We also don't discuss the precursors in ancient Greece in the lead. Moreover, changing to a statement like "Modern calculus was developed in AD 1530 by Jyesthadeva of the Kerala school of mathematics ..." is simply not reflective of the mainstream view and violates WP:FRINGE. –Deacon Vorbis (carbon • videos) 14:18, 25 April 2020 (UTC)

Sorry, but you seem to be missing the point. Your edit incorrectly ascribes development of modern calculus to 17th century, which contemporary scholarship disproves. You keep stating that this is not mainstream view while providing no evidence. I have backed up my edits with reputable references including Royal Asiatic Society of Great Britain & University of St Andrews, Scotland. I wouldn't refer to them as 'fringe' views. This is the mainstream contemporary consensus. If you are reading material from the 1950s, I suggest kindly refer to the latest scholarship. Please note, I have not taken anything away from the article, simply adding the latest material. You seem to be doing the opposite. European contributions are amply provided in the page including precursors. But the chronology needs to be correct. In the absence of you providing evidence to disprove my references, I will be reincorporating the latest scholarship onto this article. May I suggest, please explain how you are arriving at the conclusion where you are dismissing the latest global scholarship on the subject. Please provide reference for such. Prototypehumanoid (talk) 14:50, 25 April 2020 (UTC)

Please, take your nationalist POV nonsense elsewhere. --JBL (talk) 15:05, 25 April 2020 (UTC)

(edit conflict) The mainstream view is that while there were pieces of the Calculus worked out, a full-fledged picture with the general tookit of it that resembles its modern form wasn't put together until Newton & Leibniz. One single paper (the Raju one, which has some problems, which we can discuss if needed) does not allow you to make this kind of claim in the article. Your other sources are either junk (some slides, some weird poster with a nationalist POV, etc), or are just backing up secondary stuff, like the basics of the work itself. –Deacon Vorbis (carbon • videos) 15:16, 25 April 2020 (UTC)

I think I agree with @Prototypehumanoid. Further references could be added. Including Divakarans papers. Also the original paper 'Yuktibasha'. Madhava is increasingly seen as the true inventor. Marcus du sautoy for instance has done previous studies that showcase - lack of due credit to eastern mathematicians (during 17th to 21st century Europe). Imagetoimageless (talk) 12:16, 23 August 2020 (UTC)

Evidence based change should be made welcome. There has been an increasing consensus for many elements- See Madhava series, formula for pi etc... Imagetoimageless (talk) 13:50, 23 August 2020 (UTC)

However for a point by point consensus in mathematics for the invention of calculus, please see Divakarans work. Imagetoimageless (talk) 13:53, 23 August 2020 (UTC)

Prototypehumanoid made obviously terrible edits for dumb nationalist reasons. Their edits were correctly reverted, and nothing that closely resembles them is going to come back into the article. --JBL (talk) 16:18, 23 August 2020 (UTC)

Request that this article be semi-protected to prevent vandalism. — Preceding unsigned comment added by TheMaxinumMaker (talk • contribs) 00:52, 13 November 2020 (UTC)

"continuous" versus "contiguous" in the lead

Considering the hidden comment explicitly states that the terms in the lead are not being used in mathematical senses, it would be incorrect to use "continuous" over "contiguous" to describe change. Sikonmina (talk) 16:56, 23 October 2021 (UTC)

Even for the common meanings, "continuous" and "contiguous" are not synonyms. D.Lazard (talk) 19:34, 23 October 2021 (UTC)

Agreed. "Contiguous" is simply incorrect. And the note appears to be saying that the normal links for "change" and "continuous" will not have the correct mathematical meaning, not that the terms as used in the lead do not have the mathematical meaning. We correctly link to Continuous function elsewhere in the article. Meters (talk) 00:24, 24 October 2021 (UTC)

Rigorizing the lead section

User:D.Lazard Apparently my last edit wasn't consensual, so I will explain my motivations:

• I'm against the use of "rates of changes" or even worse "instantaneous rates of change" as synonyms for "derivatives". Not only are these expressions more of a talking term for non-mathematicians than a real mathematical vocabulary (and there is no reason to invent new words for "derivative", an established expression already exists, namely "derivative"), but there is also a risk of ambiguity because "rate of change" can also refer to the rate of increase of a function between two values (ie ${\frac {f(a)-f(b)}{a-b}}$) (as shown on the distinction page), which is not a derivative.
• I'm also against the use of "accumulation of quantities" as synonyms for "integrals" for the same reasons : this is misleading non-mathematical gibberish. As the page Integral correctly reminds us, an integral is not defined as an "area between curve", but more abstractly as a number assigned to a function and expressing an idea of mass or volume. --L'âne onyme (talk) 16:55, 27 October 2021 (UTC)

I think it's important to recognize that this article is about calculus, not mathematical analysis. Calculus is not a branch of research mathematics; hasn't been for well over a century. It's a mathematical toolkit for science and engineering.

With that in mind, I think it's important to reference the intuitive meaning of the terms early and often, rather than shoving the formalism down the readers' throats. The formalism should certainly be available for the interested reader, but the motivations are of utmost importance. --Trovatore (talk) 17:51, 27 October 2021 (UTC)

I don't understand why anyone would have a problem with the phrase "rate of change." A derivative is an instantaneous rate of change in that it is the infinitesimal limit of how one variable changes with respect to another. This is how "derivative" is defined in every calculus textbook I have ever seen.—Anita5192 (talk) 18:55, 27 October 2021 (UTC)

User:Anita5192 I explained why I have a problem with this phrase: firstly because there is no need for another synonym since the word "derivative" already exists (which pertains to the principle of least astonishment), and secondly because it is an ambiguous phrase that can also mean other things than derivatives. L'âne onyme (talk) 19:38, 27 October 2021 (UTC)

Your personal moral qualms about a phrase that is used in essentially every textbook on the subject are interesting but certainly cannot be used to determine article content. Wikipedia is guided by reliable sources, not by the most idiosyncratic views of its editors. (Though I must say that I think the substance of your edit is surprisingly good given the total absurdity of your defense for it -- I would not personally have reverted it.) (I don't watch this page, if you want my attention here please ping me.) --JBL (talk) 20:21, 27 October 2021 (UTC)

Semi-protected edit request on 6 December 2021

The last sentence under History > Ancient, and second sentence under Principles > Fundamental Theorem use the word "Formulas" as opposed to the preferred "Formulae" in academic writing, used in History > Medieval. I suggest only one to be used throughout the article (preferably "Formulae") to avoid confusion.

Change from "Calculations of volume and area, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (13th dynasty, c. 1820 BC); but the formulas are simple instructions, with no indication as to method, and some of them lack major components." to "Calculations of volume and area, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (13th dynasty, c. 1820 BC); but the formulae are simple instructions, with no indication as to method, and some of them lack major components."

Change from "The fundamental theorem provides an algebraic method of computing many definite integrals—without performing limit processes—by finding formulas for antiderivatives." to "The fundamental theorem provides an algebraic method of computing many definite integrals—without performing limit processes—by finding formulae for antiderivatives." Atrochez42 (talk) 22:30, 6 December 2021 (UTC)

 Done. See [1], per

Google	Scholar
formulas	3.640.000
formulae	2.170.000
"mathematical formulas"	65.800
"mathematical formulae"	101.000

and since this is a mathematics article. But as far as I'm concerned, we could do it just as well the other way around . - DVdm (talk) 00:34, 7 December 2021 (UTC)

"More citation needed" rationale

User:XOR'easter, I disagree with your revert. If the content is "general expositions of standard material that's in a zillion books", why don't we cite the material from the book itself? That's far better than no citations. I do agree though that me drive-by tagging isn't gonna help the article that much, so I'm gonna dig up math textbooks and cite the article with them. Hopefully that would make the article much better in quality. CactiStaccingCrane (talk) 02:50, 26 July 2022 (UTC)

I simply don't think that slapping a banner on top of a page that reads basically fine for the first several sections is helpful guidance. XOR'easter (talk) 02:52, 26 July 2022 (UTC)

I've gone through and added several footnotes. A little more could be done in that vein, perhaps, though at the moment I'm wondering if portions of the as-yet-unfootnoted text are actually too detailed for this article and should be cut instead. I expect that bits and pieces were added along the way by people who wanted to say everything they knew about integrals, without stopping to think if those remarks belonged in an overview like this article. XOR'easter (talk) 03:32, 26 July 2022 (UTC)

Agreed, we should cut down on irrelevant details. CactiStaccingCrane (talk) 03:33, 26 July 2022 (UTC)

General notes for possible improvements

I've been aiming for at least one citation per paragraph; even though this is all standard material and the guideline for routine calculations probably applies to some of it, it can't hurt to have pointers to good books. The last paragraph of the introduction doesn't really follow the Manual of Style, since it talks about things that the rest of the article doesn't go into more depth about. The "Applications" section is still not great; some of it, like the planimeter business, looks like random trivia that got shoved in without regard for whether or not it's significant enough to belong in a survey article like this one. XOR'easter (talk) 21:42, 14 August 2022 (UTC)

Reduce size of history section

I'm updating History of calculus from the history section of this article and hope to eventually remove most of the history from this article. Parts of the history will have to remain of course but they should point to relevant other articles for more details. The parts on foundations and Significance have a place as well but should be more directed towards the modern day and they can be copied to the history article where they can dwell more on the past.

I hope this will leave the article freer to include more about modern day developments and uses. NadVolum (talk) 21:57, 20 August 2022 (UTC)