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leaves to be desired

The following section has room for improvement if anyone would like to take a look at it: "Limits and infinitesimals Main articles: Limit (mathematics) and Infinitesimal Calculus is usually developed by manipulating very small quantities. Historically, the first method of doing so was by infinitesimals. These are objects which can be treated like numbers but which are, in some sense, "infinitely small". On a number line, these would be locations which are not zero, but which have zero distance from zero. No non-zero number is an infinitesimal, because its distance from zero is positive. Any multiple of an infinitesimal is still infinitely small, in other words, infinitesimals do not satisfy the Archimedean property. From this viewpoint, calculus is a collection of techniques for manipulating infinitesimals. This viewpoint fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals.

In the 19th century, infinitesimals were replaced by limits. Limits describe the value of a function at a certain input in terms of its values at nearby input. They capture small-scale behavior, just like infinitesimals, but use ordinary numbers. From this viewpoint, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits are easy to put on rigorous foundations, and for this reason they are usually considered to be the standard approach to calculus." Katzmik (talk) 16:03, 15 January 2009 (UTC)

It doesn't look bad to me. What is it that you don't like about it? The only minor quibble I'd have is that it jumps back and forth a little chronologically.--76.167.77.165 (talk) 17:56, 7 March 2009 (UTC)

errors in section on Limits and infinitesimals

The section "Limits and infinitesimals" had some problems, in my opinion, which I've tried to fix. It stated "On a number line, these would be locations which are not zero, but which have zero distance from zero." This was incorrect. In nonstandard analysis, for example, an infinitesimal does not have zero distance from zero; the uniqueness of zero is a fact that can be expressed in first-order logic, so the transfer principle says that zero is unique on the hyperreals as well. This statement was also sort of a muddle: "No non-zero number is an infinitesimal, because its distance from zero is positive." The mistake is similar to the mistake in the first statement. It seems as though the person who wrote these statements was trying to give clear distinction between reals and infinitesimals, and was also trying to explain why reals can't be infinitesimals. The first question boils down to the Archimedean principle. The second one depends on the foundational framework you're using for the reals, e.g., an axiomatic one that includes an axiom of completeness, or a constructive one such as Dedekind cuts. I've made some edits to try to make this section correct, without making it too technical.--76.167.77.165 (talk) 18:18, 7 March 2009 (UTC)

Hmm. But when one is talking about distance, it sounds like the right framework is a more geometric and intuitive setting; like what one would get if one updated Euclid. I like your edits, though. They're definite improvements. (Though I'd like to point out that it's "Leibniz" not "Liebniz".) Ozob (talk) 18:29, 9 March 2009 (UTC)

Liebniz notation

The article conspicuously avoids the Liebniz notation when it introduces the derivative, and that's a perfectly reasonable choice to make. However, it then uses the Liebniz notation in other places, without explanation. I think the Liebniz notation is so widespread and useful that it really needs to be explained in the article. I'm going to add a little discussion of it.--76.167.77.165 (talk) 18:23, 7 March 2009 (UTC)

Rigorization

I disagree with the quote; "Calculus is a ubiquitous topic in most modern high schools and universities, and mathematicians around the world continue to contribute to its development.[11]" Calculus was rigourized by Baron Augustin-Louis Cauchy by 1828. No history of calculus I can find indicates any further work on calculus. The reference given to Unesco has no info on calculus or its continued development. 70.31.100.40 (talk) 01:29, 2 November 2009 (UTC)

The problem arises because the study of the derivative and integral and their properties, called "calculus" at the undergraduate level, is called "analysis" at the research level. Rick Norwood (talk) 13:08, 25 August 2010 (UTC)

Misuse of sources

This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.

Please help by viewing the entry for this article shown at the cleanup page, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed. Tobby72 (talk) 21:42, 24 August 2010 (UTC)

This goes all the way back to 2007, and there are a large number of edits to check. I checked the last one, and it seems to accurately reflect a reliable source. Rick Norwood (talk) 13:10, 25 August 2010 (UTC)

Here is a typical misuse of sources: In this edit Jagged introduced the text which now reads "the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus" with this source. But the source merely mentions that Egyptians knew a certain formula, and it speculates (in a student exercise) that dividing a volume into small blocks might have led to the formula. The statement in the article should be removed. I sampled Jagged's edits and they appear to be connected with Calculus#Ancient and Calculus#Medieval where Jagged introduced the text on Ibn al-Haytham ("was the first to derive the formula") and much more. To fix the mess, we need to read the sources with a skeptical eye while checking each claim in the Ancient/Medieval sections (there is no need to check each of Jagged's edits). I would remove anything that looks somewhat dubious in those sections (if really unsure, the removed text could be copied to here). In particular, when Jagged used the word "first", it is usually wrong (or fails verification). Johnuniq (talk) 00:49, 26 August 2010 (UTC)

Everything under the Medieval section appears to check out. If anyone would like a copy of the unlinked sources, contact me. Anyone that finds other discrepancies should post them here. Hexagon70 (talk) 00:29, 10 October 2010 (UTC)

In Our Time

The BBC programme In Our Time presented by Melvyn Bragg has an episode which may be about this subject (if not moving this note to the appropriate talk page earns cookies). You can add it to "External links" by pasting * {{In Our Time|Calculus|b00mrfwq}}. Rich Farmbrough, 03:01, 16 September 2010 (UTC).

Maria Gaetana Agnesi

I just reverted this edit by Lorynote which added:

File:Maria Gaetana Agnesi.jpg

Maria Gaetana Agnesi' was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. The plane curve, known as versiera, is also called the "Witch of Agnesi" [ref]Agnesi Witch Agne Scot, Agnesi.

My edit summary mention "unsourced". I see that is not correct since the refs do offer some support for the statement (since the refs were on the second sentence I jumped to the conclusion that the only support was Maria Gaetana Agnesi). However, the material definitely should not be in the "Significance" section, and there needs to be consideration of whether the material is WP:DUE (did the book describe as in a text book, or did it develop?). Johnuniq (talk) 00:29, 4 December 2010 (UTC)

The fact is that she is a pioneer, a major figure for the history of maths and calculus. It answer the question "who wrote th first book on calculus?". I see this as a fundamental information. Lorynote (talk) 10:35, 4 December 2010 (UTC)

From About.com: Women History, Agnesi; And: Belle vue college, Agnesi. Lorynote (talk) 11:00, 4 December 2010 (UTC)

This source says that "her two volume textbook was the first comprehensive textbook on the calculus after L'Hopital's earlier book", so L'Hopital would be more fundamental, yet is not mentioned in the article. The other source says that "it was one of the first and most complete works on finite and infinitesimal analysis.". So there is no support for "Agnesi is credited with writing the first book...", and neither here, whereas this source is "Condensed from "The Pioneering Women Mathematicians" by G.J. Tee in The Mathematical Intelligencer", so not really a reliabe source. The sources do mention the Witch of Agnesi, but that is more on-topic in analytic geometry, not in calculus. DVdm (talk) 11:10, 4 December 2010 (UTC)

Ok, so one can say she wrote first comprehensive book. Lorynote (talk) 12:07, 4 December 2010 (UTC)

No, we can not say that. She wrote the first comprehensive book after L'Hopital's earlier book, and there is no reason to mention that, since L'Hopital is not mentioned in the article either. DVdm (talk) 12:49, 4 December 2010 (UTC)

Although there are two sources to support that she was the pioneer and only one to support the after someone else we can keep the second; mentioning she wrote one of the first books. Besides, the source clearly cites his book and her compreheensive book. The fact L´Hopital is not mentioned here it´s not relevant; once his name is on WP anyway and the link will not be red. Lorynote (talk) 13:15, 4 December 2010 (UTC)

Also note that the first source says in its disclaimer on http://jwilson.coe.uga.edu/ : "The content and opinions expressed on this Web page do not necessarily reflect the views or nor they endorsed by the University of Georgia or the University System of Georgia.". This is someone's personal web site, so It cannot be taken as a wp:reliable source either.

I think it would be okay to use the second source to write this short statement in the article:

One of the first and most complete works on finite and infinitesimal analysis was written In 1748 by Maria Gaetana Agnesi. Unlu, Elif (1995). "Maria Gaetana Agnesi". Agnes Scott College. {{cite web}}: Unknown parameter |month= ignored (help)</ref>

No details about or picture of Agnesi are needed here. Readers who click the link get all they want. What do the other contributors think about this? DVdm (talk) 13:42, 4 December 2010 (UTC)

You can guess my opinion; I vote for a picture and more details about her (just the very short 'she was italian, mathematician, philosopher'). My very honest opinion is that she has a brilliant work and she was recognized as such. Lorynote (talk) 14:13, 4 December 2010 (UTC)

I agree it needs to be short, no bio needed (no-one else has one), but a mention needs to be there. The Agnes Scott College source is adequate - there are several mathematical sources on the Witch of Agnesi curve - I think as well as your sentence, one sentence on the Witch (which is very well known and has its own article, and there's no contention that it was studied by and named after Agnesi) would be adequate. People can read both articles for more info, but if we don't put a mention in, people won't know to look. This is always the challenge of an article like this.

One of the first and most complete works on finite and infinitesimal analysis was written in 1748 by Maria Gaetana Agnesi (Unlu, Elif (1995). "Maria Gaetana Agnesi". Agnes Scott College. {{cite web}}: Unknown parameter |month= ignored (help)). The Witch of Agnesi curve is named after Agnesi, who wrote about it in 1748 in her book Istituzioni Analitiche. (Mac Curves. "Witch of Agnesi". MacTutor's Famous Curves Index. University of St Andrew. Retrieved 4 December 2010., this citation taken from the Witch article)

Picture I'm in favour of. We have Newton and Leibzitz - the fathers of calculus (that sounds odd I know). Agnesi I agree is probably not more notable as a mathematician (as opposed to a female mathematician) than several others who advanced one area of calculus or other, but I think the addition of her picture would possibly attract the interest of more readers, because she is a woman. It's a bit tokenistic I know, but pictures should mho pique the interest, not just decorate the page. Elen of the Roads (talk) 16:27, 4 December 2010 (UTC)

Elen, I would sign next to your words as if they were mine. Lorynote (talk) 16:34, 4 December 2010 (UTC)

I have no problem with Agnesi being mentioned, but shouldn't there be a sentence about l'Hôpital as well, since he actually produced the first textbook (plus l'Hôpital's rule of course)? Favonian (talk) 16:43, 4 December 2010 (UTC)

I´m for L´Hôpital as well! Sure, he´s welcome! Lorynote (talk) 17:15, 4 December 2010 (UTC)

@Favonian, could do. That entire modern section is pretty unsourced at the moment, except for the rather random closing sentence about calculus being taught in schools (I'm sure that's wandered in from somewhere else) so I'm not averse to anything with sources. That last paragraph could be a little enlarged without any ill effects as well I feel.Elen of the Roads (talk) 17:26, 4 December 2010 (UTC)

But let's make sure we have a proper source for l'Hôpital's first textbook -- note that the Wilson source cannot be taken as a wp:RS (see disclaimer, cited above). DVdm (talk) 17:30, 4 December 2010 (UTC)

It appears that L'Hospital's claim is somewhat dubious [1] - his book was actually written by Bernoulli. Havent seen anything yet - article on the book is sourced to a book I don't have Elen of the Roads (talk) 18:32, 4 December 2010 (UTC)

FYI, there might be no further comments from Lorynote again on this. - DVdm (talk) 22:55, 4 December 2010 (UTC)

So she did turn out to be Jackiestud. Figures. Still, I'd rather AGF a bit than bite the heads off newbies (I'll leave that to Darwinbish). I would still support putting my two penn'orth above about Agnesi into the article. Your thoughts?Elen of the Roads (talk) 02:21, 5 December 2010 (UTC)

Did you notice that there is currently something in the article? I would prefer someone with knowledge of the area to comment on the DUEness of the wording, and the sentence on the curve should be removed since it is not relevant here, and is in the linked article. Until we encounter someone with relevant knowledge (so they can find the refs), I am happy with the current image and wording if the curve sentence is removed. Johnuniq (talk) 03:23, 5 December 2010 (UTC)

I've removed the section entirely, since it's not clear how notable Agnesi and her book are. If this is in fact a notable event in the history of calculus then it could come back. Ozob (talk) 04:26, 5 December 2010 (UTC)

Agree with Johnuniq. The one-of-the-firstness of the book seems to be sufficiently sourced and (thus) notable. The curve is indeed off-topic. Don't care about the pic: afaiac it can stay. DVdm (talk) 10:22, 5 December 2010 (UTC)

@Johnuniq - wording and pic fine by me - I'll defer to others on the curve. I will however revert Ozob's deletionadd back DVdm's contribution. It was already agreed it was sufficiently notable to put in the article, but should be limited to one sentence. I've also put the picture back, per discussion above.Elen of the Roads (talk) 10:52, 5 December 2010 (UTC)

Looks good to me! Ozob (talk) 12:20, 5 December 2010 (UTC)

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Assessment comment

The comment(s) below were originally left at Talk:Calculus/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Need to address the issues of clarity and stability raised in the latest GA review. Geometry guy 23:03, 21 April 2007 (UTC) Uprated to B+, but some of the exposition is still too advanced, and the recent changes need to be integrated more smoothly. Geometry guy 22:05, 28 May 2007 (UTC) == Benchmark of technical writing == I have been reading math and engineering material on Wikipedia for about five years. This is the first time that I have felt I needed to make a comment on an article: This is the best-written article I have ever read, without contest. The pace and rigor of the article is ideal for a person who has some general inclination in mathematics but who may not be authoritative on the subject. In my opinion, this is exactly the scope at which technical material needs to be written. Very well done. Excellent work. Daniel.sparks (talk) 23:50, 29 April 2012 (UTC)

Last edited at 23:50, 29 April 2012 (UTC). Substituted at 20:17, 2 May 2016 (UTC)