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Regarding the note in "History": I think it would be wise to note that mathematics is a purely invented concept, and that the only way to "discover" some mathematical principle is to discover it as a facet of an invention (mathematics) rather than as a facet of nature. When it comes to calculus, this is especially true, because nowhere is nature does the concept of a perfectly curved surface exist; all things in nature are quantized down at an arbitrary level, even perfect spheres (and potentially even space itself). The notion of infinitely small changes in position to discover tangent lines, areas under curves, and lengths of curves has never been a part of reality, and only exists in the theoretical sense, so it cannot be a discovery in the traditional sense. In fact, I would suggest we change that entire sentence to something along the lines of, "Leibniz and Newton are usually designated the originators of calculus, mainly for their invention of the fundamental theorem of calculus." I understand the issue some will have with this, as they may view mathematics as a discovery not an invention, but as I said above, the things that calculus works on don't exist in nature, and cannot therefore be discovery. - Augur
I don't know how calculus is normally defined, but I prefer the definition "branch of mathematics involving the study of limits".
From what I have seen, infinite series are normally associated with calculus. This makes sense because of the summation notations ideas used while developing the concept of the definite integral, and because of the integral test.
This definition seems to include nicely differentiation, integration and infinite series.
Brianjd 07:13, Sep 12, 2004 (UTC)
'Limits' - their study is more accurately mathematical analysis. It's a bit different. Charles Matthews 08:32, 12 Sep 2004 (UTC)
I think a link to a truly functioning place to study calculus online makes a right thing to put on the calculus page. student person any ideas
---
Looking at the other languages, they look like they're a completely different encyclopedia... - User:Loisel
Old comments from calculus that I ( Gareth Owen) have tried to take on board:
First, I think a page on Calculus should reflect current word usage in Mathematics. Therefore, functions are rules that assign to each member of a specified domain a value in a specified range. We do not speak of independent and dependent variables in Math, hardly ever, any more. I am not sure this terminolgy, while easy to remember, is the what we want a learner to retain.
Second, Calculus, from the first day I opened my first book has always been both Differentiation and Integration and hopefully the relationship between them. Therefore, I see this entry as misleading.
For the above two reasons, I think it requires a major overhaul in terminology and content. This is a key entry in Math and only Math. In other areas in is ancillary. RoseParks
Well, RP, what's stopping you from rewriting it? How long can it take to rewrite two short articles about a subject you teach regularly (I'm guessing)? :-) -- LMS---- Well it is 5:39 A.M. Wednesday, March 28,2001, I think and I am still dealing with copy edit problems. Any suggestion about when I might do this, not to mention sleep, food, a shower...Not all of us have time to come and write on wikipedia every day for a number of hours...HELP...RoseParks
What can I say? Thanks! Anyway, no rush on Wikipedia. If you don't make changes, eventually, someone else will, I'm sure. -- LMS
Recently I added some other (very common?!) usage of "calculus" in mathematics, namely as a formal system of rules and axioms (which also is one general meaning of the word). This usage appears quite often in proof theory and symbolic logic. I also move the general calculi above into this section, since they are really different from the special calculus. --Markus[sorry, currently no login] 24 Jun 2003
I changed the "calculus series" table a bit. I think "topics in calculus" is more appropriate. The articles that have the old table need to be updated, of course. Thoughts? Fredrik 22:56, 27 Mar 2004 (UTC)
I would enjoy a page comparing various Calc textbooks. Personally I know Stewart's Calculus. Goodralph 02:18, 4 Apr 2004 (UTC)
Nearly 200 edits to this page so far and ... it's pretty bad. Charles Matthews 07:39, 5 Jun 2004 (UTC)
I only had time to read part of that article, but it doesn't seem to support that Seki had developed nearly as much of calculus as the two primary figures. Seki's method is referred to as a crude form of integral calculus and the article doesn't say that he even made any significant contributions to differential calculus. Newton and Leibniz had much more developed methods and notation. Just because he is referred to as Japan's Newton or Leibniz, does not mean he had the same level of contributions to the subject. The article even mentions that role is tenuous at best. I would support moving his role and citation to the lesser credit section. - Taxman 14:53, Aug 3, 2004 (UTC)
The following appeared:
An anonymous Wikipedian changed "that was the key" to "which was key". The latter seems inferior since it treats key as literally an adjective. It seems to me I've seen that a lot in the last couple of years. Has it now reached the point where, in addition to being merely acceptable, that usage is thought of as standard? Michael Hardy 22:54, 6 Dec 2004 (UTC)
Should we have a brief explanation of the formal definition of limit in terms of delta and epsilon, and the delta/epsilon proofs that have annoyed generations of math students? -- Christofurio 01:42, Feb 16, 2005 (UTC)
I went to the article to initiate my understanding of calculus. It failed completely. The article looks as if it was written by mathemeticians in order to impress other mathemiticians. The article was not written to introduce, or to instruct, the (previously uninitiated) into the idea(s).
As such, the article is worthless. Those who already have enough of an introduction to understand what the article is saying do not need to read an encyclopedia article on calculus. Those of us who need to read an article on calculus do not have the requisite understanding of what is being said to make reading the article of value. KeyStroke 20:18, 2005 Mar 17 (UTC)
Yes, the definition of calculus involving limits is a very good one. The four main principals of calculus, as far as I'm concerned, are limits, derivatives, integrals, and series (which can be argued also as limits).
Someone that speaks French: The french link from this article goes to fr:Analyse (mathématiques). The link from there to English goes to Mathematical analysis. The link from there to french also goes to Analyse (mathématiques). Then, I found fr:Calcul infinitésimal, which seems to be somewhat of a translation of this article. The MS Office dictionary says that calcul means calculus (but, interestingly, not the other way round). I just thought I'd point this out at let someone that knows this stuff sort it out. Neonumbers 11:38, 3 May 2005 (UTC)
There is a similar problem with german and I think the core of the problem is just common usage: at least in german, when you learn this at school, it is called "Analysis" and a you probably hear of "Infinitesimalrechnung" (which is the topic fitting best what is descibed as calculus here) only at university. I think in english-speaking countries this is just the other way round. So I don't really know which page should be linked from here: for use as a dictionary (for looking up the word "calculus"), de:Analysis would be preferrable but when looking for an explanation of the same topic in german de:Infinitesimalrechnung will perhaps fit better (although it is on the german page only a short text mainly linking to de:Analysis. At least I would really like to have a short description of the relation of "calculus" to "mathematical analysis" in the text.-- 84.177.245.153 10:43, 11 July 2006 (UTC)
To Oleg's Whatever he discovered was done much earlier and in isolation - Not in isolation and not much earlier to 'Indian' development of calculus . Madhava and others from the Kerala school picked up after him and developed it further. Please see [1] --Pranathi
I will agree though that I think Bhaskara being the Father of Calculus is not universally acknowledged by those familiar with Indian math history with Madhava being the other contender. But he is 'sometimes' described as the Father of calculus. --Pranathi
I'm not quite happy with the FTOC section. I would certainly like to see the FTOC reprhased physically. Something along the lines of "If we consider the net area under the velocity curve we obtain displacement".
In modern US textbooks, there is no mention of 1st and 2nd fundamental theorems. They are typically called FTOC (part 1) and FTOC (part 2). What's more unusual is the ordering given. What's called the 2nd FTOC is typically dealt with first -- the 1st FTOC presented as a consequence. I suppose this is pretty arbitrary.
Each part should be explained in plain english! For example, the 2nd FTOC says every continuous function has an antiderivate, namely that funny integral that confuses students to no end!
Comments?
I find this topic very interesting. As far as I can recall, there has always been *one* fundamental theorem of calculus (ftoc) - there is no *part 1* and no *part 2*. The version stated as the 2nd part in the article of Wikipedia is *the* theorem - it says *everything* that needs to be said. It is also accurate (just compare mathworld's and many other sites which state the theorem incorrectly) and shows immediately the connection between the integral and the derivative.
A number of things have gone into the history section that are almost right, but really wrong. I'm going to try to fix them. References would include Anton's Calculus, Rudin's Real and Complex Analysis, and various histories of mathematics. Rick Norwood 20:40, 25 September 2005 (UTC)
I would like to see the Calculus article one of the best in Wikipedia, and I do not think it is that as it stands. My major objection is that it does not give the reader any idea of the importance of calculus, and that it presents calculus as primarily a computational tool. I want to attempt a rewrite, a little at a time, and I'll begin by posting my proposed rewrite here, to see if it is acceptable, before posting it on the main page.
Rick Norwood 22:54, 26 September 2005 (UTC)
Rick, much more readable. I think though that the first parah is eurocentric. Significant advances in calculus had been made before 17th century in India (with coresponding insights into infinity etc). Also, the second parah doesn't mention Madhava [2], [3], who preceded the European mathematicians in many of their methods and results. Eudoxus, Archemedes, Bhaskara and Kowa Seki are all put on equal footing and dismissed as having done something similar to calculus - each is significant and needs to be expanded (maybe you were planning on that in detail elsewhere). I think history needs to be tied together in a better fashion - maybe mention possibility of Indian calculus influencing European ideas [4], [5]. I agree that much more has been written about the development of calculus in Europe but significant contributions of the Kerala school need to be mentioned in more detail.-- Pranathi 12:59, 27 September 2005 (UTC)
Rick, My comments can be incorporated without expanding on the history. 1. The first parah is still eurocentric. 2. Madhava, who has made significant contributions, has not been mentioned at all. 3. The 2 sentences on Exodus till Kowa Seki say the same thing, without revealing anything about their contributions.
May I propose:
If you find the second parah too detailed maybe we can do something like..
:Calculus was not discovered all at once. In the ancient world, Eudoxus and Archimedes proposed the method of exhaustion that constitutes integral calculus. In twelfth Century India, Bhaskara conceived of differential calculus and 2 centuries later, Madhava and the Kerala school invented many concepts of integral and differential calculus. In the 17th century, Kowa Seki in Japan elaborated some principles of integral calculus. In the same period, Wallis and Barrow in Europe proposed ideas that correspond to integrals, derivatives, and the Fundamental Theorem of Calculus. Newton and Leibniz brought all these ideas together, and ..of the limit. -- Pranathi 17:25, 28 September 2005 (UTC)
(Moving discussion from Rick's talk tage) Rick, In recent edits, mention of Madhava, Bhaskara and Kowa seki were removed and replaced with a generic phrase for Indian and Japanese mathematicians. For a summary they may not be important, but I see you chose to keep reference to Wallis, Barrow and James Gregory. Madhava made some of the most significant advancements in the field, some exactly the same and 300 yrs earlier than the European counterparts that remain listed. Also, all mention of period (14th century, 17th century etc) was removed, while initially your parah mentioned 17th century only. Why the bias? or am I missing something? I am open to discussion. ----
Pranathi
19:37, 28 October 2005 (UTC)
"An Indian mathematician, Bhaskara (1114-1185), developed a number of ideas that can now be seen to be forerunners of calculus, including the idea now known as "Rolle's theorem". He was the first to conceive of differential calculus. The 14th century Indian mathematician Madhava, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala school wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated in Europe only by the seventeenth century."
This sentence,
In scientific applications, the derivative is often used to find the velocity given the displacement, and the integral is often used to find the displacement given the velocity.
I don't find very clear. More specifically I don't understand what the word displacement means in its context.
What is said in the introduction is nonsense. Charles Matthews 22:49, 29 October 2005 (UTC)
In particular, calculus gave a clear and precise definition of infinity, both in the case of the infinitely large and the infinitely small.
Where does that come from? Calculus, you could say, was born around the Great Fire of London. There was nothing in the way of precision on 'infinity' until after the Battle of Waterloo. That's 150 years of history just elided. Tell me, Rick, are we selling something here? We are not, in fact. So why put such tendentious stuff in article introductions. I'm going to put back the old, informative intro from September, move this down to an overview section, and try to take out the mistakes. Charles Matthews 10:26, 30 October 2005 (UTC)
Calculus is essentially a collection of algorithmic, semi-algorithmic and heuristic techniques. It has been like that since Euler, and nothing changes. Physicists still do Euler's way. It doesn't 'define infinity'. You have that quite wrong. Modern mathematics, if the phrase means anything, was initiated by Gauss. Mathematical analysis - say with Gauss and the hypergeometric function, or Abel and convergence testing, also dates from that time. And, yes, Cauchy too. Eliding the difference between that and calculus is completely wrong and historically barbarous. Charles Matthews 21:54, 30 October 2005 (UTC)
I would have thought that a major change in the article such as moving the history section to the end would be discussed here first. Guess not. Rick Norwood 22:08, 31 October 2005 (UTC)
would you like to publish this article? -- Zondor 22:18, 27 November 2005 (UTC)
"With my support, certainly. In my behalf -- for that I need more information. I notice you have made this request on several articles. Where are you going with this? Rick Norwood 21:55, 29 November 2005 (UTC)
The intro paragraph says that differential and integral calculus are inverse operations of each other. I do not believe this is necessarily correct, or at least the wording and placement. First of all, at this stage in the article, calculus has only been described as complementary concepts, that is, the study of change and accumulation respectively. In the intro, calculus has not yet been described in terms of transformations (eg. taking a derivative) so referring to "operations" seems premature in the article. Secondly, I believe the statement itself isn't entirely correct anyway. Simply put, differentiating isn't an injective process and therefore it cannot have a clear inverse. To illustrate, consider and which are not equal functions but they both have the same derivative. I will wait a little while to see if anyone has anything else to say on the matter before I make the change. Soltras 19:20, 3 December 2005 (UTC)
No other comments. I made a wording change that functions as an agreeable solution for myself. Soltras 00:32, 15 December 2005 (UTC)
Semitrical has made major changes in the article without discussion. He has thrown away some useful formulas, and there are many errors in what he has written. My inclination is to revert his edit. Any objections? Rick Norwood 15:37, 8 December 2005 (UTC)
There seems to be a consensus that I should edit rather than revert. I'll see what I can do. I like the formulas. What they state is ... well, fundamental. Rick Norwood 21:11, 8 December 2005 (UTC)
I do agree, in retrospect, that some of my additions bloated the article, but I think my example (or at least some example) would be useful either here or at Derivative/ Integral. Good examples are important in allowing those not knowledgeable in the field to get a better understanding of the principles underlying the subject matter. Maybe my example was too convoluted or not phrased well, but surely there should be some kind of example there. (The paragraph about natural rates of change not having a true limit was stupid and pedantic, though, in retrospect—I agree it doesn't belong here, if it even belongs anywhere.)
As for the formulae of the fundamental theorem of calculus: as I see it, it's rather silly for an article explaining calculus to assume that the reader is familiar with calculus notation. Obviously if you're sufficiently familiar with calculus notation to understand the fundamental theorem of calculus, you know pretty much everything that's going to be contained within the basic Calculus article, which is only an overview. If you're going to include formulae, the definitions of derivatives and integrals should surely be added before the FToC! The latter is meaningless without the former. I say leave the FToC formulae at the FToC article, and I'd leave the definitions of derivative/integral to their respective articles as well; to explain them properly you'd need to devote a few paragraphs to each, which would bloat the article too much. Leave this article with concepts.
Two more things. First, Rick Norwood, you said what I wrote contained "many errors". What are some examples of errors that I made? I see some long-windedness and pedantry, perhaps, but no actual errors. (But incidentally, speaking of errors, odometers don't measure displacement last I checked. They measure distance traveled. If they measured displacement, they would reset to zero when driven to the place they were manufactured. :) )
Second, Taxman, what material did I provide that you think needs to be backed up by references? I would have thought that pretty much everything I added could be found in any calculus textbook. And it's not like there are any references in the article at present, or at least no specific ones (i.e., not counting Further Reading). — Simetrical ( talk) 07:17, 9 December 2005 (UTC)
Having the fundamental theorem of calculus in is good I think. Yes, this is an introductory calculus article, however, some people reading this article would have known some calculus. So, while one should not offend the newbies, one should also write important things in, like the above-mentioned theorem, as long as it is not too proeminent or not too early in the article. One may lessen the impact by carefully providing links to all concepts involved. Oleg Alexandrov ( talk) 19:26, 9 December 2005 (UTC)
"Well, first two sections are about derivatives and integrals. So, I would say that your requirement is satisfied, as the fundamental theorem of calculus is in the third section." Yes, but the notation for the FTOC isn't given in the sections on derivatives and integrals. Without being defined, the notation of the FTOC makes no sense to the readers. Explain the idea, don't use the formula. — Simetrical ( talk) 05:19, 26 December 2005 (UTC)
Spinoza defined the terms "perfection"; "sorrow-boredom-joy"; "hate-indifference-love" by their causes; not by their properties. They can be expressed using a Calculus format—precise definition, rates-of-change at any one instant.
Yesselman 23:45, 9 December 2005 (UTC)
Happy happy, joy joy! Rick Norwood 22:09, 12 December 2005 (UTC)
I don't thing we need two economic examples in the introduction, but I like the new example better than the old, which is vague. Replace? Rick Norwood 22:08, 12 December 2005 (UTC)
I like the cut to two examples of each -- don't like combining paragraphs throughout the article. I think it was easier to read with shorter paragraphs, and examples in separate sentences. Rick Norwood 14:26, 13 December 2005 (UTC)
I have clarified the nature of the dispute between Newton and Leibniz in the history section. Also, I have highlighted the key importance of the first and second fundamental theorems of calculus. Perhaps we should explain the contributions of people like Descartes and Fermat a little bit more. It was Fermat's insight into integrating functions of the form x^r that gave Newton and Leibniz a vital insight into the development of the fundamental theorems. —the preceding unsigned comment is by Grokmoo ( talk • contribs) 18:06, 16 December 2005
I previously added this example to the derivative section:
Now, this example is a bit lengthy and confusing, perhaps, but I think that something like it would be appropriate. It would allow a layman to get an idea of what exactly is happening when you take the limit of a function's rate of change, and what an instantaneous rate of change is. Currently, the reader is told things like "[d]ifferential calculus can be used to determine the instantaneous speed at any given instant"—but not told what "instantaneous speed" is. This stuff really isn't obvious. — Simetrical ( talk) 05:06, 26 December 2005 (UTC)
I'm sorry to have to say so, but I find your lengthy example confusing. I think the example of the speedometer as a measure of instantaneous speed is both shorter and easier to understand. Rick Norwood 17:35, 26 December 2005 (UTC)
A bit of history about this article. While I think the limit is the essense of calculus, a majority of the people contributing to this article take a more practical approach. I was able to get in a mention of the limit -- after having my material on the limit reverted several times -- but I doubt you will be able to go much further with the limit here. I think it is probably more practical to discuss the limit in the article of that title. Rick Norwood 15:38, 27 December 2005 (UTC)
when was calculus invented by newton,when was calculus invented by leibniz?
Here is my site with calculus example problems. Someone please put this link in the external links section if you think it's helpful and relevant. Tbsmith
http://www.exampleproblems.com/wiki/index.php/Calculus
What does this has to do with calculus? Isn't this just a fancy name for a common-sensical idea which everyone across all civilizations must have known. Most of them would have considered it too obvious to even mention. deeptrivia ( talk) 17:56, 8 January 2006 (UTC)
Just look at these two paragraphs:
An Indian mathematician, Bhaskara (1114-1185), developed a number of ideas that are foundational to the development of calculus, including the statement of the theorem now known as "Rolle's theorem", which is a special case of one of the most important theorems in analysis, the Mean Value Theorem. He was the first to conceive of the derivative. The 14th century Indian mathematician Madhava, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala school wrote the first differential calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated in Europe only in the seventeenth century.
Calculus started making great strides in Europe towards the end of the early modern period and into the first years of the eighteenth century. This was a time of major innovation in Europe, making accessible answers to old questions. Calculus provided a new method in mathematical physics. Several mathematicians contributed to this breakthrough, notably John Wallis and Isaac Barrow. James Gregory proved a special case of the Second Fundamental Theorem of Calculus in 1668. Leibniz and Newton pulled these ideas together into a coherent whole and they are usually credited with the independent and nearly simultaneous creation of calculus. Newton was the first to apply calculus to physics and Leibniz developed much of the notation used in calculus today; he often spent days determining appropriate symbols for concepts. It was generations after Newton and Leibniz that Cauchy, Riemann, and other mathematicians finally put calculus on a rigorous basis, with the definition of the limit, and the formal definition of the Riemann integral.
The first is just a bland statement of facts, desperately trying to minimise any indication of achievement. It doesn't even explicitly mention Bhaskara's work of differential calculus. The second has no limits to romaticising it's invention in Europe, "started making great strides in Europe", "This was a time of major innovation in Europe, making accessible answers to old questions", "contributed to this breakthrough". And you think you're not biased?
This article was formerly listed as a good article, but was removed from the listing because the article lists none of its references or sources -- Allen3 talk 20:38, 18 February 2006 (UTC)
I've been active in wikipedia for quite a while, now, but I still find the rules for "sources", "references", and "bibliography" confusing and inconsistent from article to article. Also, some articles seem to use footnotes, other do not. Rick Norwood 13:40, 19 February 2006 (UTC)
I followed the link you gave and it is very informative. I will try to modify the articles I work on accordingly, starting with this one. Rick Norwood 13:47, 19 February 2006 (UTC)
I trust Grokmoo will not mind my posting here his message to my mailbox:
"This is in reference to your recent revert on the history of calculus section of the calculus article. I was wondering if you read the discussion in the talk page on this topic. In any event, you reverted the article to saying Archimedes was near a breakthrough, without giving any explanation of why. As for Archimedes "contribution" to calculus, you must be aware that he did significant work developing the method of exhaustion. This method is conceptually quite similar to the modern Riemann Integral, and is also probably the first example of using a limiting process to compute area exactly, which was precisely what doing an integral was before the fundamental theorems came along. For example, this sort of process is how Fermat computed the integral of general power functions. As for a source backing this up, I don't know why you would need a reference from Barrow. As for a more contemporary reference, see any book with a little history of calculus. Here is a link with some information: [7]
For the time being, I changed the statement back to what I had before. If you would like to change the wording to something more agreeable to you, I won't mind, so long as you don't put back in the statement about Archimedes "almost making a breakthrough". Grokmoo 04:51, 20 February 2006 (UTC)"
It seems odd that Grokmoo asks if I read the discussion, since my name appears here so often, but, yes, I do read the discussion. I'm really not sure what your point is, since we both agree that Archimedes got as close to calculus as any of the ancients -- though of course the method of exhaustion was originally developed by Eudoxus.
Archimedes was near a breakthrough in that if original Hellic mathematics had continued, the discovery of calculus would have been the natural next step. There was no breakthrough because that didn't happen.
On the other hand, to denomstrate a "contribution" by Archimedes, Wallis or Barrow or Newton or Liebniz or somebody would have had to acknowledge reading Archimedes and being inspired by what he had done. If you know of a case where that was done, please reference it. Rick Norwood 13:37, 20 February 2006 (UTC)
It is a little hard to be specific about which breakthrough did not occur. If you want to delete the part about "close to a breakthrough" I have no objection.
We, from our vantage point, can see that the Greeks were close to integral calculus. I would have no objection to a statement to that effect. There is a big difference, however, between one idea anticipating another and the earlier idea contributing to the later. Maybe it did. I'd love to see a reference. Rick Norwood 20:49, 20 February 2006 (UTC)
Looks good to me. Rick Norwood 13:50, 21 February 2006 (UTC)
"Differental and integral calculus...calculus has two basic principles: Differential... and integral calculus" This article's intro is redundent! Should we change the beginning to Calculus, instead of Differental and integral calculus?
I don't know about umbral calculus, but I do know that propositional calculus (and predicate calculus) are now most often called "propositional logic" and "predicate logic" precisely because the meaning of the word "calculus" is becoming more specialized over time. Today it usually means the mathematics that follows from the introduction of the concept of the limit. A more mathematical approach to the same subject is often called "analysis" (but Spivac's Calculus on Manifolds is an obvious exception). Rick Norwood 14:22, 9 March 2006 (UTC)
I don't think its redundant. "Calculus" like "algebra" can have many meaning, depending on the context. For exmaple, college elgebra, linear algebra, mulitlinear algebra, abstract algebra, and the calculus of variations, tensor calculus, lambda calculus, differential and integral calculus. Although today what we normally refer to as "The Calculus" is a combination of both differential and integral calculi, until Newton/Leibitz, the connecxion was not realized as such and could be seen as constututing two different branches of math. The Funadamental Theorem is what connects the two. Arundhati bakshi 13:39, 29 March 2006 (UTC)
Paul August removed some links about discoveries of calculus in India. I've put them back, at least for the time being. Throughout wikipedia there are a large numbers of claims about mathematical discoveries in India that are very general in nature and which keep being pushed further and further back in time. We need evidence for those claims, and the two links in question purport to provide evidence. This is a subject that needs to be investigated further. Rick Norwood 22:39, 16 March 2006 (UTC)
Your implication that mainstraim historians of math would "cover up" new discoveries does not jibe with my own experience, which is that math historians love new discoveries. Nobody I know doubts that India has made and is still making major contributions to mathematics. But there is a problem when one source dates a particular contribution as 200 CE and another source dates the same contribution as 600 BCE. Maybe you can suggest some reference books? Rick Norwood 02:04, 19 March 2006 (UTC)
The problem is widespread, with increasingly older (often conflicting) dates appearing in many of the math articles. I attempted to research the dates on the web, and was met with a maze of conflicting dates for ancient manuscripts. It is really beyond my expertise, but I hope someone more knowledgable than I will try to at least bring the dates of Indian mathematical discoveries in Wikipedia into agreement with one another. Rick Norwood 00:18, 18 April 2006 (UTC)
I didn't think the etymology of the word "calculus" was appropriate as the second sentence of the article's main paragraph, so I created a subsection of the History section and pasted it there. Soltras 05:07, 8 April 2006 (UTC)
Hi, I was thinking of further fleshing out the history of section, with a list of some specific contributions by Newton, Fermat, Leibniz, and others, and also information about developments after Newton (which is mysteriously absent) when I realized something. The history section is already too long. We already have an article called the history of calculus. Detailed lists of contributions by Aryabhata, Madhava, and others should probably go there, not here. If we included this much detail on every contributer, we would be duplicating the entire history of calculus page here.
To me, this situation is misrepresentative. I'd like to wait for some feedback on this before I make any changes, since my changes here have often been repeatedly reverted without explanation, and I know a lot of people feel strongly about this Indian Mathematics issue. Grokmoo 21:48, 17 April 2006 (UTC)
Calculus is a very important field and it's great to see that effort is being made to make this a great article. I think adding the following two images in their respective sections to graphically illustrate the difference between differential and integral calculus would greatly add to the strength of this article:
As a final comment, it would be great to be able to see which statements are supported by which reference. One commonly used way to do this is inline references, but I think there is some artistic freedom there. - Samsara ( talk • contribs) 13:05, 26 May 2006 (UTC)
Anybody claiming Indian priority in inventing calculus please quote the ancient sources. Don't tell me the dog ate them or the invading Turks burnt them. I want to see your proof! When I say sources I do not mean Hindutva booklets. Surely if some Indian mathematician 'long before Newton' used the notions of say derivative and integral in his work, he can be quoted directly.
By the way, I greatly appreciate Indian culture and science. Dear Indian friends, if you made me sick and tired of reading these endless passages about supposed Indian contributions to just about everything, think about disastrous impression it will make upon other readers. It's just like spam, nobody likes it. 212.199.22.126 01:12, 3 July 2006 (UTC)
These are certainly interesting references, but they do not lay all the problems to rest. The history of Indian mathematics, for example, is by a grad student, Ian G Pearce, whose specialty is the study of insects. It seems to be very well researched, but to rely almost entirely on secondary sources. It would be nice to have a reference to a scholar who had read the originals, and who comments on their provenence, the methods by which they were dated, and the relationship between the notation used in the ancient sources and modern notation. For example, Pearce reports that in the 13th century, an Indian mathematician discovered that δ sin x = cos x δx. In what notation was this discovery expressed? In short, the reference answers some questions but raises others.
I certainly don't see any effort to belittle the mathematics of India. Every respectable history of mathematics mentions the Indian discovery of the decimal number system, of negative numbers, and of zero as a place holder. Rather, I think mathematicians are cautious, and want proof. Rick Norwood 21:44, 3 July 2006 (UTC)
So far 3 days have passed since my original call for a quotation. Nothing. The only valuable piece of information is from http://en.wikipedia.org/wiki/Talk:Indian_mathematics where I have asked the same question. According to thunderboltz a.k.a.Deepu Joseph "A lot of work and ideas by Indian scientists were disregarded due to Eurocentric views of Western scientists. Yuktibhasa is the ancient text by Jyeshtadeva of Kerala School describing Calculus". I am very interested in a relevant passage from this work, so let me address myself again to any Indian who can get access to this text - please, quote it! I have no anti-Indian agenda here, so I will be glad if this is really the first calculus text in the world. But if not - the false claims have to be removed, no matter what legends say. 212.199.22.219 22:56, 6 July 2006 (UTC)
“ | The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude. | ” |
I don't want to open an ethnic editing war. The situation is unbearable. Only an Indian can check the sources. So please speak up! Do you think the quotation we got could be qualified as the first calculus text? 212.199.22.51 22:35, 8 July 2006 (UTC)
If someone wants another better info on Indian Mathematics, please have a look at this research project from Scotland University of Mathematics.
Madhava and his history
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Madhava.html
About Indian mathematics
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Indians.html
warm regards,
Source from,
School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland
Am I the only one seeing "failure to parse" messages wherever there should be a formula? -- Spangineer es (háblame) 22:46, 30 July 2006 (UTC)
Stable versioning is being tested on this article. This means that all editing will be made on Calculus/development, and on a regular basis, good edits will be moved onto the consensus page. If you disagree with the current version, please let me know. Ral315 ( talk) 05:27, 2 August 2006 (UTC)
Not really. The active editors of an article don't get to vote themselves an exemption from the m:Foundation issues, nor to decree that people shall not edit their article. The correct way to go about this is, for the umpteenth time, to go and build a workable, accepted proposal somewhere and then test to see if it works. It is wrong on many levels to take a proposal, the talk page for which is littered with objections, ruminations, alternatives, proposals and everything else and then say "right then, let's have some of that". You're doing it backwards, in the same way that these so-called 'test' earlier were backwards. Oppose, and object to the implication that only those who edit here should have anything to say. - Splash - tk 16:20, 2 August 2006 (UTC)
Oppose per WP:PROT and WP:OWN. Both of these trump a proposal that hasn't even achieved consensus support yet. Cynical 13:05, 4 August 2006 (UTC)
come out of your eurocentric point of view. Refferences are not readily available. But Lots of scholors(most of them western) have translated these texts and conclude that calculus in fact was from kerala much more than anyother place. Its easy to just deny ...when the world has just studied what you have. —The preceding unsigned comment was added by Vvn india ( talk • contribs) 21:44, 15 August 2006.
Great article, but one suggestion, shouldn't we include the power of a function rule within the differentiation category on the right hand side. Or is there even such an article on Wikipedia yet? -- Arsenous Commodore 00:15, 18 August 2006 (UTC)
i'm placing a request for references on the section in relation to india and calculus history. i've noticed a disturbing trend on a lot of history articles with a lot of POV pushing. these claims should be removed if they can not be verified because i have not read any of these supposed discoveries in any history book on mathematics. and please do not claim that the information was suppressed by the academic community... we need evidence for these claims. Truth100 01:43, 15 September 2006 (UTC)
Madhava and his history; about kerala school.
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Madhava.html
About Indian mathematics
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Indians.html
From
School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland
warm regards,
Note: This article has a small number of in-line citations for an article of its size and subject content. Currently it would not pass criteria 2b.
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05:57, 26 September 2006 (UTC)
If we want to bring this article to FA status I think that the following things should be adressed:
Feel free to add items to this list and to cross out those that have been adressed. Pascal.Tesson 18:40, 20 November 2006 (UTC)
Might I also suggest a peer review? The peer review bots might help us more on a quality scale. Tarret 22:36, 20 November 2006 (UTC)
The following suggestions were generated by a semi-automatic javascript program, and might not be applicable for the article in question.
Hope we can use it. Tarret 22:19, 21 November 2006 (UTC)
Calculus isn't really a branch of mathematics, anymore than arithmetic is. Both are pretty much used in all of mathematics and just considered basic tools.
Also, it's nice to see all the physical applications mentioned, but very little is mentioned of its ubiquity in modern mathematics in general. -- C S (Talk) 00:43, 26 November 2006 (UTC)
Hello. While I have been on Wikipedia for a while now, I am still fairly new to the mathematics areas of Wikipedia, and I would like to make some contributions. I recently added a large (and hopefully comprehensive) footer navigation box to this article, Template:Calculus footer. There are a number of reasons why I support adding this template to this and other calculus-related articles. Currently, with the exception of a rare use of Template:Calculus as a side infobox, there is no easy way to navigate between calculus articles of different subjects. I have read previous discussions regarding infoboxes vs. categorization in the Wikiproject Mathematics, and saw that calculus was listed as a possible exception to the mainly anti-infobox opinion presented. As a result, I began creating side infoboxes for each branch (differential, integral, vector, etc.) until I realized that it is simply impossible to list even just the most important topics without having too-large-and-bloated infoboxex. At this point, I was lucky enough to stumble upon the World War II article; at the footer of each page of a World War II-related article, they have a comprehensive template ( Template:World War II) that makes World War II articles, covering a vast topic in history, easy and user-friendly to navigate. Therefore, I decided to "be bold" and to do the same thing for the major topics of each branch of calculus, a vast total area in mathematics while using this World War II template as a base. While some things are probably still missing and others can be organized in a better fashion, I think this presents a much more user-friendly solution to those looking for information about calculus topics. Please let me know of any concerns you might have about this; barring any major objections, I would like to soon start putting this footer in other calculus articles. Thank you very much for your time and any feedback, Hotstreets 19:55, 8 December 2006 (UTC)
(de-indenting) Having it at the bottom goes a long way to overcoming my dislike of navigation boxes. In my opinion, the list is clearly more useful than the category. It is huge though. If it's possible to hide it by default, that would be great. Otherwise, how about shortening it to two lines and linking to a separate page with the whole list? -- Jitse Niesen ( talk) 02:40, 10 December 2006 (UTC)
Article says, "When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit." but I understand from the Wikipedia article on the controversy itself (to which this should link) that the controversy evolved many years after Leibniz published his results. Also, the slant of the story itself, as it is told here, seems to favor one side (Newton). — Preceding unsigned comment added by Rentstrike ( talk • contribs) 18:25, 28 November 2012 (UTC)
It is my understanding that the formal name for calculus is "The Calculus." While the "The" is generally dropped these days, isn't it still appropriate to capitalize the word Calculus?
"A calculus is a way of calculating, so mathematicians sometimes talk about the 'calculus of logic', the 'calculus of probability', and so on. But all are agreed there is really only one Calculus, pure and simple, and this is spelled with a capital C" (emphasis mine) (Crilly, Tony (2007). 50 Mathematical Ideas You Really Need to Know. London: Quercus Publishing Plc. p. 76, 208. ISBN 1-84724-147-6.)
Interestingly, the index of the book does not capitalize the word.
It would seem seems that we should at least mention the issue of capitalization in the article.
Billiam1185 ( talk) 01:02, 4 March 2013 (UTC)
Perhaps more examples on this matter. — Preceding unsigned comment added by Pedrovalle ( talk • contribs) 13:11, 20 May 2013 (UTC)
To be clear, most who add to the mathematical pages have probable forgotten more than I know about maths (I'm British, so I refuse to call it math). However it couldn't escape my notice that when Google put Leonhard Euler up in a Google doodle and specifically mentioned his historical significance to maths and his important work on infinitesimal calculus, that there is no mention of him whatsoever on the infinitesimal calculus page. Is Google incorrect in its highlighting the importance of Euler? Or is his work on infinitesimal calculus not as important as made out on his Wikipedia page? Either one or the other needs correction?
I think there should be something in the introduction about when it was invented and (gulp) who invented it. At the risk of being beaten over the head by all the history revisionists and refactorers out there, I think that should be the 17th century, Newton, and Leibniz. -- Chetvorno TALK 00:43, 27 July 2013 (UTC)
The Neumann quote box is hanging on Newton's image edge. Can someone fix it? Tried to, but got rolled-back. Formatting problems. -- J. D. Redding 00:11, 28 July 2013 (UTC)
Come on, people, let's hold the line for general references. We don't have to give in to the inline-cite extremists, not here. For most aspects of the topic, all our refs are going to say the same thing, probably in almost the same words. Save the inline cites for the stuff that's a little particular, and don't make the reader work through a forest of little blue numbers. -- Trovatore ( talk) 19:14, 4 December 2013 (UTC)
I check pages listed in Category:Pages with incorrect ref formatting to try to fix reference errors. One of the things I do is look for content for orphaned references in wikilinked articles. I have found content for some of Calculus's orphans, the problem is that I found more than one version. I can't determine which (if any) is correct for this article, so I am asking for a sentient editor to look it over and copy the correct ref content into this article.
Reference named "almeida":
I apologize if any of the above are effectively identical; I am just a simple computer program, so I can't determine whether minor differences are significant or not. AnomieBOT ⚡ 21:02, 11 January 2014 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
Request received to merge Infinitesimal calculus into Calculus. User:Unsigned request. Reason= unknown. Please discuss here. GenQuest "Talk to Me" 00:16, 30 March 2014 (UTC)
I have undone this edit. It is based on 4 sources, all of which i.m.o. unreliable:
Comments? - DVdm ( talk) 10:47, 22 February 2015 (UTC)
I've removed this from the article's Ancient History section since it should be dealt with here.
{{clarify|post-text=(Why mention this if not relevant? <-Perhaps it is a first/early instance of volume and area calculation, which the paragraph suggests would be the evolutionary antecedent of modern calculus, thus introducing a historical and logical progression, which would seem to be the purpose of this section.)|date=August 2015}}
Should something be added to the article in way of clarifying this point? Bill Cherowitzo ( talk) 04:37, 30 August 2015 (UTC)
A question. Mesmerate ( talk) 04:32, 22 November 2015 (UTC)
It is dx+Δx. Mesmerate ( talk) 04:36, 22 November 2015 (UTC)
Sir, the idea is you're taking the limit as it gets really close to zero, and as it gets closer, that is what it gets closer and closer to. As it gets closer and closer, infinitely, it can be considered infinitesimal. Mesmerate ( talk) 04:55, 22 November 2015 (UTC)
Please tell me HOW they saw what they were doing? Mesmerate ( talk) 05:05, 22 November 2015 (UTC)
The change in x, or Δx, can be defined to include infintely small or infinitely large numbers in its list of possible numbers. It commonly is, and that is partly why i think it is a just fine canidate for being an infinitesimal. Mesmerate ( talk) 05:08, 22 November 2015 (UTC)
So, you think infinitesimals cannot be defined using limits? Mesmerate ( talk) 05:11, 22 November 2015 (UTC)
We are talking about modern calculus, where Δx is allowed to approach zero, and where dx is defined as Δx as dx. Mesmerate ( talk) 05:25, 22 November 2015 (UTC)
Sorry. Mesmerate ( talk) 05:26, 22 November 2015 (UTC)
No it isn't, check. Mesmerate ( talk) 05:35, 22 November 2015 (UTC)
It's under "principals". Mesmerate ( talk) 05:37, 22 November 2015 (UTC)
I still argue otherwise, I argue in modern calculus dx itself can be considered as the change in x as it approaches 0. Mesmerate ( talk) 12:37, 22 November 2015 (UTC)
And I have already clarified that we are talking about modern calculus, "principals" is not a sub heading of "history". Mesmerate ( talk) 18:43, 22 November 2015 (UTC)
Sorry, nevermind. I read in a text book that the (dy/dx) could be seperated by multyplying by "dy" and as such, it had a page where it said "Who are we to throw around these numbers?" and defined dx as the change in x. I also understand that something getting infinitely cl in all the mess. I admitzero by itself. I still think that delta x equals zero, i just added a small note and got tangled up in it all. I still think something approaching zero still works like an infinitesimal, except for that one case in which it just goes to zero. Sorry i'm a little put of tune in calculus, plus, please tell me if i am right in "It acts like an infinitesimal, except for that one case.". Mesmerate ( talk) 23:44, 22 November 2015 (UTC)
Sorry, i mean you can seperate the (dy/dx) by multyplying by dx, not dy. Mesmerate ( talk) 23:46, 22 November 2015 (UTC)
Sorry my sentence 2 sentences ago was messed up. Mesmerate ( talk) 23:47, 22 November 2015 (UTC)
I meant to say i got caught in it all, and in all cases except for that case "approaching" acts like an infinitesimal. Mesmerate ( talk) 23:48, 22 November 2015 (UTC)
Sorry, by "two sentences ago" i meant two comments ago. Mesmerate ( talk) 23:50, 22 November 2015 (UTC)
Also, to clarify, i admit i was wrong. I will stop editing that part of the page, and i am sorry for disrupting wikipedia. Mesmerate ( talk) 23:53, 22 November 2015 (UTC)
The idea i had in mind was "dx=the change in x", "the change in x can act infinitesimal in most cases", "the change in x is fine, smd should be mentioned." Mesmerate ( talk) 23:57, 22 November 2015 (UTC)
Still, i believe that dx in integrals stands for "the change in x" in integrals,as the definition of the integral uses it alot. infact, it used "the change in x" an infinite number of times. and in both case, dx is short hand for "the limit of this using delta x" Mesmerate ( talk) 00:00, 23 November 2015 (UTC)
And as such i would like to start a new discussion. I would like to discuss the idea of mentioning that the meaning of "dx" is different across modern and old calculus. Mesmerate ( talk) 00:01, 23 November 2015 (UTC)
Read description. Mesmerate ( talk) 00:06, 23 November 2015 (UTC)
I believe it is important enough to be mentioned. Is there any consensus? Mesmerate ( talk) 00:07, 23 November 2015 (UTC)
On one hand, that entire section is historical - there are no infinitesimals in the real line. I would remove both the δx and the dx from that sentence, which is really only trying to say what an infinitesimal is. The symbol dx is not an infinitesimal in modern treatments of calculus. — Carl ( CBM · talk) 12:37, 23 November 2015 (UTC)
It's in "principals", not "history". If it is historical, that's a mistake. Mesmerate ( talk) 22:53, 24 November 2015 (UTC)
So we should remove the mention of "dx" meaning infinitesimal all together and only say it's just the change in x? I'm fine with that. Mesmerate ( talk) 22:56, 24 November 2015 (UTC)
What does h stand for in:
Why don't we explain it in Calculus#Differential_calculus? Warmest Regards, :)— thecurran Speak your mind my past 13:54, 6 December 2015 (UTC)
The h used to be a delta x, but at some point someone decided that a two letter symbol might confuse students, and replaced it with h. I think Thomas was the first, at least the first I saw. I think the explanation "h was free" is as good as any. Rick Norwood ( talk) 12:24, 7 December 2015 (UTC)
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Regarding the note in "History": I think it would be wise to note that mathematics is a purely invented concept, and that the only way to "discover" some mathematical principle is to discover it as a facet of an invention (mathematics) rather than as a facet of nature. When it comes to calculus, this is especially true, because nowhere is nature does the concept of a perfectly curved surface exist; all things in nature are quantized down at an arbitrary level, even perfect spheres (and potentially even space itself). The notion of infinitely small changes in position to discover tangent lines, areas under curves, and lengths of curves has never been a part of reality, and only exists in the theoretical sense, so it cannot be a discovery in the traditional sense. In fact, I would suggest we change that entire sentence to something along the lines of, "Leibniz and Newton are usually designated the originators of calculus, mainly for their invention of the fundamental theorem of calculus." I understand the issue some will have with this, as they may view mathematics as a discovery not an invention, but as I said above, the things that calculus works on don't exist in nature, and cannot therefore be discovery. - Augur
I don't know how calculus is normally defined, but I prefer the definition "branch of mathematics involving the study of limits".
From what I have seen, infinite series are normally associated with calculus. This makes sense because of the summation notations ideas used while developing the concept of the definite integral, and because of the integral test.
This definition seems to include nicely differentiation, integration and infinite series.
Brianjd 07:13, Sep 12, 2004 (UTC)
'Limits' - their study is more accurately mathematical analysis. It's a bit different. Charles Matthews 08:32, 12 Sep 2004 (UTC)
I think a link to a truly functioning place to study calculus online makes a right thing to put on the calculus page. student person any ideas
---
Looking at the other languages, they look like they're a completely different encyclopedia... - User:Loisel
Old comments from calculus that I ( Gareth Owen) have tried to take on board:
First, I think a page on Calculus should reflect current word usage in Mathematics. Therefore, functions are rules that assign to each member of a specified domain a value in a specified range. We do not speak of independent and dependent variables in Math, hardly ever, any more. I am not sure this terminolgy, while easy to remember, is the what we want a learner to retain.
Second, Calculus, from the first day I opened my first book has always been both Differentiation and Integration and hopefully the relationship between them. Therefore, I see this entry as misleading.
For the above two reasons, I think it requires a major overhaul in terminology and content. This is a key entry in Math and only Math. In other areas in is ancillary. RoseParks
Well, RP, what's stopping you from rewriting it? How long can it take to rewrite two short articles about a subject you teach regularly (I'm guessing)? :-) -- LMS---- Well it is 5:39 A.M. Wednesday, March 28,2001, I think and I am still dealing with copy edit problems. Any suggestion about when I might do this, not to mention sleep, food, a shower...Not all of us have time to come and write on wikipedia every day for a number of hours...HELP...RoseParks
What can I say? Thanks! Anyway, no rush on Wikipedia. If you don't make changes, eventually, someone else will, I'm sure. -- LMS
Recently I added some other (very common?!) usage of "calculus" in mathematics, namely as a formal system of rules and axioms (which also is one general meaning of the word). This usage appears quite often in proof theory and symbolic logic. I also move the general calculi above into this section, since they are really different from the special calculus. --Markus[sorry, currently no login] 24 Jun 2003
I changed the "calculus series" table a bit. I think "topics in calculus" is more appropriate. The articles that have the old table need to be updated, of course. Thoughts? Fredrik 22:56, 27 Mar 2004 (UTC)
I would enjoy a page comparing various Calc textbooks. Personally I know Stewart's Calculus. Goodralph 02:18, 4 Apr 2004 (UTC)
Nearly 200 edits to this page so far and ... it's pretty bad. Charles Matthews 07:39, 5 Jun 2004 (UTC)
I only had time to read part of that article, but it doesn't seem to support that Seki had developed nearly as much of calculus as the two primary figures. Seki's method is referred to as a crude form of integral calculus and the article doesn't say that he even made any significant contributions to differential calculus. Newton and Leibniz had much more developed methods and notation. Just because he is referred to as Japan's Newton or Leibniz, does not mean he had the same level of contributions to the subject. The article even mentions that role is tenuous at best. I would support moving his role and citation to the lesser credit section. - Taxman 14:53, Aug 3, 2004 (UTC)
The following appeared:
An anonymous Wikipedian changed "that was the key" to "which was key". The latter seems inferior since it treats key as literally an adjective. It seems to me I've seen that a lot in the last couple of years. Has it now reached the point where, in addition to being merely acceptable, that usage is thought of as standard? Michael Hardy 22:54, 6 Dec 2004 (UTC)
Should we have a brief explanation of the formal definition of limit in terms of delta and epsilon, and the delta/epsilon proofs that have annoyed generations of math students? -- Christofurio 01:42, Feb 16, 2005 (UTC)
I went to the article to initiate my understanding of calculus. It failed completely. The article looks as if it was written by mathemeticians in order to impress other mathemiticians. The article was not written to introduce, or to instruct, the (previously uninitiated) into the idea(s).
As such, the article is worthless. Those who already have enough of an introduction to understand what the article is saying do not need to read an encyclopedia article on calculus. Those of us who need to read an article on calculus do not have the requisite understanding of what is being said to make reading the article of value. KeyStroke 20:18, 2005 Mar 17 (UTC)
Yes, the definition of calculus involving limits is a very good one. The four main principals of calculus, as far as I'm concerned, are limits, derivatives, integrals, and series (which can be argued also as limits).
Someone that speaks French: The french link from this article goes to fr:Analyse (mathématiques). The link from there to English goes to Mathematical analysis. The link from there to french also goes to Analyse (mathématiques). Then, I found fr:Calcul infinitésimal, which seems to be somewhat of a translation of this article. The MS Office dictionary says that calcul means calculus (but, interestingly, not the other way round). I just thought I'd point this out at let someone that knows this stuff sort it out. Neonumbers 11:38, 3 May 2005 (UTC)
There is a similar problem with german and I think the core of the problem is just common usage: at least in german, when you learn this at school, it is called "Analysis" and a you probably hear of "Infinitesimalrechnung" (which is the topic fitting best what is descibed as calculus here) only at university. I think in english-speaking countries this is just the other way round. So I don't really know which page should be linked from here: for use as a dictionary (for looking up the word "calculus"), de:Analysis would be preferrable but when looking for an explanation of the same topic in german de:Infinitesimalrechnung will perhaps fit better (although it is on the german page only a short text mainly linking to de:Analysis. At least I would really like to have a short description of the relation of "calculus" to "mathematical analysis" in the text.-- 84.177.245.153 10:43, 11 July 2006 (UTC)
To Oleg's Whatever he discovered was done much earlier and in isolation - Not in isolation and not much earlier to 'Indian' development of calculus . Madhava and others from the Kerala school picked up after him and developed it further. Please see [1] --Pranathi
I will agree though that I think Bhaskara being the Father of Calculus is not universally acknowledged by those familiar with Indian math history with Madhava being the other contender. But he is 'sometimes' described as the Father of calculus. --Pranathi
I'm not quite happy with the FTOC section. I would certainly like to see the FTOC reprhased physically. Something along the lines of "If we consider the net area under the velocity curve we obtain displacement".
In modern US textbooks, there is no mention of 1st and 2nd fundamental theorems. They are typically called FTOC (part 1) and FTOC (part 2). What's more unusual is the ordering given. What's called the 2nd FTOC is typically dealt with first -- the 1st FTOC presented as a consequence. I suppose this is pretty arbitrary.
Each part should be explained in plain english! For example, the 2nd FTOC says every continuous function has an antiderivate, namely that funny integral that confuses students to no end!
Comments?
I find this topic very interesting. As far as I can recall, there has always been *one* fundamental theorem of calculus (ftoc) - there is no *part 1* and no *part 2*. The version stated as the 2nd part in the article of Wikipedia is *the* theorem - it says *everything* that needs to be said. It is also accurate (just compare mathworld's and many other sites which state the theorem incorrectly) and shows immediately the connection between the integral and the derivative.
A number of things have gone into the history section that are almost right, but really wrong. I'm going to try to fix them. References would include Anton's Calculus, Rudin's Real and Complex Analysis, and various histories of mathematics. Rick Norwood 20:40, 25 September 2005 (UTC)
I would like to see the Calculus article one of the best in Wikipedia, and I do not think it is that as it stands. My major objection is that it does not give the reader any idea of the importance of calculus, and that it presents calculus as primarily a computational tool. I want to attempt a rewrite, a little at a time, and I'll begin by posting my proposed rewrite here, to see if it is acceptable, before posting it on the main page.
Rick Norwood 22:54, 26 September 2005 (UTC)
Rick, much more readable. I think though that the first parah is eurocentric. Significant advances in calculus had been made before 17th century in India (with coresponding insights into infinity etc). Also, the second parah doesn't mention Madhava [2], [3], who preceded the European mathematicians in many of their methods and results. Eudoxus, Archemedes, Bhaskara and Kowa Seki are all put on equal footing and dismissed as having done something similar to calculus - each is significant and needs to be expanded (maybe you were planning on that in detail elsewhere). I think history needs to be tied together in a better fashion - maybe mention possibility of Indian calculus influencing European ideas [4], [5]. I agree that much more has been written about the development of calculus in Europe but significant contributions of the Kerala school need to be mentioned in more detail.-- Pranathi 12:59, 27 September 2005 (UTC)
Rick, My comments can be incorporated without expanding on the history. 1. The first parah is still eurocentric. 2. Madhava, who has made significant contributions, has not been mentioned at all. 3. The 2 sentences on Exodus till Kowa Seki say the same thing, without revealing anything about their contributions.
May I propose:
If you find the second parah too detailed maybe we can do something like..
:Calculus was not discovered all at once. In the ancient world, Eudoxus and Archimedes proposed the method of exhaustion that constitutes integral calculus. In twelfth Century India, Bhaskara conceived of differential calculus and 2 centuries later, Madhava and the Kerala school invented many concepts of integral and differential calculus. In the 17th century, Kowa Seki in Japan elaborated some principles of integral calculus. In the same period, Wallis and Barrow in Europe proposed ideas that correspond to integrals, derivatives, and the Fundamental Theorem of Calculus. Newton and Leibniz brought all these ideas together, and ..of the limit. -- Pranathi 17:25, 28 September 2005 (UTC)
(Moving discussion from Rick's talk tage) Rick, In recent edits, mention of Madhava, Bhaskara and Kowa seki were removed and replaced with a generic phrase for Indian and Japanese mathematicians. For a summary they may not be important, but I see you chose to keep reference to Wallis, Barrow and James Gregory. Madhava made some of the most significant advancements in the field, some exactly the same and 300 yrs earlier than the European counterparts that remain listed. Also, all mention of period (14th century, 17th century etc) was removed, while initially your parah mentioned 17th century only. Why the bias? or am I missing something? I am open to discussion. ----
Pranathi
19:37, 28 October 2005 (UTC)
"An Indian mathematician, Bhaskara (1114-1185), developed a number of ideas that can now be seen to be forerunners of calculus, including the idea now known as "Rolle's theorem". He was the first to conceive of differential calculus. The 14th century Indian mathematician Madhava, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala school wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated in Europe only by the seventeenth century."
This sentence,
In scientific applications, the derivative is often used to find the velocity given the displacement, and the integral is often used to find the displacement given the velocity.
I don't find very clear. More specifically I don't understand what the word displacement means in its context.
What is said in the introduction is nonsense. Charles Matthews 22:49, 29 October 2005 (UTC)
In particular, calculus gave a clear and precise definition of infinity, both in the case of the infinitely large and the infinitely small.
Where does that come from? Calculus, you could say, was born around the Great Fire of London. There was nothing in the way of precision on 'infinity' until after the Battle of Waterloo. That's 150 years of history just elided. Tell me, Rick, are we selling something here? We are not, in fact. So why put such tendentious stuff in article introductions. I'm going to put back the old, informative intro from September, move this down to an overview section, and try to take out the mistakes. Charles Matthews 10:26, 30 October 2005 (UTC)
Calculus is essentially a collection of algorithmic, semi-algorithmic and heuristic techniques. It has been like that since Euler, and nothing changes. Physicists still do Euler's way. It doesn't 'define infinity'. You have that quite wrong. Modern mathematics, if the phrase means anything, was initiated by Gauss. Mathematical analysis - say with Gauss and the hypergeometric function, or Abel and convergence testing, also dates from that time. And, yes, Cauchy too. Eliding the difference between that and calculus is completely wrong and historically barbarous. Charles Matthews 21:54, 30 October 2005 (UTC)
I would have thought that a major change in the article such as moving the history section to the end would be discussed here first. Guess not. Rick Norwood 22:08, 31 October 2005 (UTC)
would you like to publish this article? -- Zondor 22:18, 27 November 2005 (UTC)
"With my support, certainly. In my behalf -- for that I need more information. I notice you have made this request on several articles. Where are you going with this? Rick Norwood 21:55, 29 November 2005 (UTC)
The intro paragraph says that differential and integral calculus are inverse operations of each other. I do not believe this is necessarily correct, or at least the wording and placement. First of all, at this stage in the article, calculus has only been described as complementary concepts, that is, the study of change and accumulation respectively. In the intro, calculus has not yet been described in terms of transformations (eg. taking a derivative) so referring to "operations" seems premature in the article. Secondly, I believe the statement itself isn't entirely correct anyway. Simply put, differentiating isn't an injective process and therefore it cannot have a clear inverse. To illustrate, consider and which are not equal functions but they both have the same derivative. I will wait a little while to see if anyone has anything else to say on the matter before I make the change. Soltras 19:20, 3 December 2005 (UTC)
No other comments. I made a wording change that functions as an agreeable solution for myself. Soltras 00:32, 15 December 2005 (UTC)
Semitrical has made major changes in the article without discussion. He has thrown away some useful formulas, and there are many errors in what he has written. My inclination is to revert his edit. Any objections? Rick Norwood 15:37, 8 December 2005 (UTC)
There seems to be a consensus that I should edit rather than revert. I'll see what I can do. I like the formulas. What they state is ... well, fundamental. Rick Norwood 21:11, 8 December 2005 (UTC)
I do agree, in retrospect, that some of my additions bloated the article, but I think my example (or at least some example) would be useful either here or at Derivative/ Integral. Good examples are important in allowing those not knowledgeable in the field to get a better understanding of the principles underlying the subject matter. Maybe my example was too convoluted or not phrased well, but surely there should be some kind of example there. (The paragraph about natural rates of change not having a true limit was stupid and pedantic, though, in retrospect—I agree it doesn't belong here, if it even belongs anywhere.)
As for the formulae of the fundamental theorem of calculus: as I see it, it's rather silly for an article explaining calculus to assume that the reader is familiar with calculus notation. Obviously if you're sufficiently familiar with calculus notation to understand the fundamental theorem of calculus, you know pretty much everything that's going to be contained within the basic Calculus article, which is only an overview. If you're going to include formulae, the definitions of derivatives and integrals should surely be added before the FToC! The latter is meaningless without the former. I say leave the FToC formulae at the FToC article, and I'd leave the definitions of derivative/integral to their respective articles as well; to explain them properly you'd need to devote a few paragraphs to each, which would bloat the article too much. Leave this article with concepts.
Two more things. First, Rick Norwood, you said what I wrote contained "many errors". What are some examples of errors that I made? I see some long-windedness and pedantry, perhaps, but no actual errors. (But incidentally, speaking of errors, odometers don't measure displacement last I checked. They measure distance traveled. If they measured displacement, they would reset to zero when driven to the place they were manufactured. :) )
Second, Taxman, what material did I provide that you think needs to be backed up by references? I would have thought that pretty much everything I added could be found in any calculus textbook. And it's not like there are any references in the article at present, or at least no specific ones (i.e., not counting Further Reading). — Simetrical ( talk) 07:17, 9 December 2005 (UTC)
Having the fundamental theorem of calculus in is good I think. Yes, this is an introductory calculus article, however, some people reading this article would have known some calculus. So, while one should not offend the newbies, one should also write important things in, like the above-mentioned theorem, as long as it is not too proeminent or not too early in the article. One may lessen the impact by carefully providing links to all concepts involved. Oleg Alexandrov ( talk) 19:26, 9 December 2005 (UTC)
"Well, first two sections are about derivatives and integrals. So, I would say that your requirement is satisfied, as the fundamental theorem of calculus is in the third section." Yes, but the notation for the FTOC isn't given in the sections on derivatives and integrals. Without being defined, the notation of the FTOC makes no sense to the readers. Explain the idea, don't use the formula. — Simetrical ( talk) 05:19, 26 December 2005 (UTC)
Spinoza defined the terms "perfection"; "sorrow-boredom-joy"; "hate-indifference-love" by their causes; not by their properties. They can be expressed using a Calculus format—precise definition, rates-of-change at any one instant.
Yesselman 23:45, 9 December 2005 (UTC)
Happy happy, joy joy! Rick Norwood 22:09, 12 December 2005 (UTC)
I don't thing we need two economic examples in the introduction, but I like the new example better than the old, which is vague. Replace? Rick Norwood 22:08, 12 December 2005 (UTC)
I like the cut to two examples of each -- don't like combining paragraphs throughout the article. I think it was easier to read with shorter paragraphs, and examples in separate sentences. Rick Norwood 14:26, 13 December 2005 (UTC)
I have clarified the nature of the dispute between Newton and Leibniz in the history section. Also, I have highlighted the key importance of the first and second fundamental theorems of calculus. Perhaps we should explain the contributions of people like Descartes and Fermat a little bit more. It was Fermat's insight into integrating functions of the form x^r that gave Newton and Leibniz a vital insight into the development of the fundamental theorems. —the preceding unsigned comment is by Grokmoo ( talk • contribs) 18:06, 16 December 2005
I previously added this example to the derivative section:
Now, this example is a bit lengthy and confusing, perhaps, but I think that something like it would be appropriate. It would allow a layman to get an idea of what exactly is happening when you take the limit of a function's rate of change, and what an instantaneous rate of change is. Currently, the reader is told things like "[d]ifferential calculus can be used to determine the instantaneous speed at any given instant"—but not told what "instantaneous speed" is. This stuff really isn't obvious. — Simetrical ( talk) 05:06, 26 December 2005 (UTC)
I'm sorry to have to say so, but I find your lengthy example confusing. I think the example of the speedometer as a measure of instantaneous speed is both shorter and easier to understand. Rick Norwood 17:35, 26 December 2005 (UTC)
A bit of history about this article. While I think the limit is the essense of calculus, a majority of the people contributing to this article take a more practical approach. I was able to get in a mention of the limit -- after having my material on the limit reverted several times -- but I doubt you will be able to go much further with the limit here. I think it is probably more practical to discuss the limit in the article of that title. Rick Norwood 15:38, 27 December 2005 (UTC)
when was calculus invented by newton,when was calculus invented by leibniz?
Here is my site with calculus example problems. Someone please put this link in the external links section if you think it's helpful and relevant. Tbsmith
http://www.exampleproblems.com/wiki/index.php/Calculus
What does this has to do with calculus? Isn't this just a fancy name for a common-sensical idea which everyone across all civilizations must have known. Most of them would have considered it too obvious to even mention. deeptrivia ( talk) 17:56, 8 January 2006 (UTC)
Just look at these two paragraphs:
An Indian mathematician, Bhaskara (1114-1185), developed a number of ideas that are foundational to the development of calculus, including the statement of the theorem now known as "Rolle's theorem", which is a special case of one of the most important theorems in analysis, the Mean Value Theorem. He was the first to conceive of the derivative. The 14th century Indian mathematician Madhava, along with other mathematicians of the Kerala school, studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala school wrote the first differential calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated in Europe only in the seventeenth century.
Calculus started making great strides in Europe towards the end of the early modern period and into the first years of the eighteenth century. This was a time of major innovation in Europe, making accessible answers to old questions. Calculus provided a new method in mathematical physics. Several mathematicians contributed to this breakthrough, notably John Wallis and Isaac Barrow. James Gregory proved a special case of the Second Fundamental Theorem of Calculus in 1668. Leibniz and Newton pulled these ideas together into a coherent whole and they are usually credited with the independent and nearly simultaneous creation of calculus. Newton was the first to apply calculus to physics and Leibniz developed much of the notation used in calculus today; he often spent days determining appropriate symbols for concepts. It was generations after Newton and Leibniz that Cauchy, Riemann, and other mathematicians finally put calculus on a rigorous basis, with the definition of the limit, and the formal definition of the Riemann integral.
The first is just a bland statement of facts, desperately trying to minimise any indication of achievement. It doesn't even explicitly mention Bhaskara's work of differential calculus. The second has no limits to romaticising it's invention in Europe, "started making great strides in Europe", "This was a time of major innovation in Europe, making accessible answers to old questions", "contributed to this breakthrough". And you think you're not biased?
This article was formerly listed as a good article, but was removed from the listing because the article lists none of its references or sources -- Allen3 talk 20:38, 18 February 2006 (UTC)
I've been active in wikipedia for quite a while, now, but I still find the rules for "sources", "references", and "bibliography" confusing and inconsistent from article to article. Also, some articles seem to use footnotes, other do not. Rick Norwood 13:40, 19 February 2006 (UTC)
I followed the link you gave and it is very informative. I will try to modify the articles I work on accordingly, starting with this one. Rick Norwood 13:47, 19 February 2006 (UTC)
I trust Grokmoo will not mind my posting here his message to my mailbox:
"This is in reference to your recent revert on the history of calculus section of the calculus article. I was wondering if you read the discussion in the talk page on this topic. In any event, you reverted the article to saying Archimedes was near a breakthrough, without giving any explanation of why. As for Archimedes "contribution" to calculus, you must be aware that he did significant work developing the method of exhaustion. This method is conceptually quite similar to the modern Riemann Integral, and is also probably the first example of using a limiting process to compute area exactly, which was precisely what doing an integral was before the fundamental theorems came along. For example, this sort of process is how Fermat computed the integral of general power functions. As for a source backing this up, I don't know why you would need a reference from Barrow. As for a more contemporary reference, see any book with a little history of calculus. Here is a link with some information: [7]
For the time being, I changed the statement back to what I had before. If you would like to change the wording to something more agreeable to you, I won't mind, so long as you don't put back in the statement about Archimedes "almost making a breakthrough". Grokmoo 04:51, 20 February 2006 (UTC)"
It seems odd that Grokmoo asks if I read the discussion, since my name appears here so often, but, yes, I do read the discussion. I'm really not sure what your point is, since we both agree that Archimedes got as close to calculus as any of the ancients -- though of course the method of exhaustion was originally developed by Eudoxus.
Archimedes was near a breakthrough in that if original Hellic mathematics had continued, the discovery of calculus would have been the natural next step. There was no breakthrough because that didn't happen.
On the other hand, to denomstrate a "contribution" by Archimedes, Wallis or Barrow or Newton or Liebniz or somebody would have had to acknowledge reading Archimedes and being inspired by what he had done. If you know of a case where that was done, please reference it. Rick Norwood 13:37, 20 February 2006 (UTC)
It is a little hard to be specific about which breakthrough did not occur. If you want to delete the part about "close to a breakthrough" I have no objection.
We, from our vantage point, can see that the Greeks were close to integral calculus. I would have no objection to a statement to that effect. There is a big difference, however, between one idea anticipating another and the earlier idea contributing to the later. Maybe it did. I'd love to see a reference. Rick Norwood 20:49, 20 February 2006 (UTC)
Looks good to me. Rick Norwood 13:50, 21 February 2006 (UTC)
"Differental and integral calculus...calculus has two basic principles: Differential... and integral calculus" This article's intro is redundent! Should we change the beginning to Calculus, instead of Differental and integral calculus?
I don't know about umbral calculus, but I do know that propositional calculus (and predicate calculus) are now most often called "propositional logic" and "predicate logic" precisely because the meaning of the word "calculus" is becoming more specialized over time. Today it usually means the mathematics that follows from the introduction of the concept of the limit. A more mathematical approach to the same subject is often called "analysis" (but Spivac's Calculus on Manifolds is an obvious exception). Rick Norwood 14:22, 9 March 2006 (UTC)
I don't think its redundant. "Calculus" like "algebra" can have many meaning, depending on the context. For exmaple, college elgebra, linear algebra, mulitlinear algebra, abstract algebra, and the calculus of variations, tensor calculus, lambda calculus, differential and integral calculus. Although today what we normally refer to as "The Calculus" is a combination of both differential and integral calculi, until Newton/Leibitz, the connecxion was not realized as such and could be seen as constututing two different branches of math. The Funadamental Theorem is what connects the two. Arundhati bakshi 13:39, 29 March 2006 (UTC)
Paul August removed some links about discoveries of calculus in India. I've put them back, at least for the time being. Throughout wikipedia there are a large numbers of claims about mathematical discoveries in India that are very general in nature and which keep being pushed further and further back in time. We need evidence for those claims, and the two links in question purport to provide evidence. This is a subject that needs to be investigated further. Rick Norwood 22:39, 16 March 2006 (UTC)
Your implication that mainstraim historians of math would "cover up" new discoveries does not jibe with my own experience, which is that math historians love new discoveries. Nobody I know doubts that India has made and is still making major contributions to mathematics. But there is a problem when one source dates a particular contribution as 200 CE and another source dates the same contribution as 600 BCE. Maybe you can suggest some reference books? Rick Norwood 02:04, 19 March 2006 (UTC)
The problem is widespread, with increasingly older (often conflicting) dates appearing in many of the math articles. I attempted to research the dates on the web, and was met with a maze of conflicting dates for ancient manuscripts. It is really beyond my expertise, but I hope someone more knowledgable than I will try to at least bring the dates of Indian mathematical discoveries in Wikipedia into agreement with one another. Rick Norwood 00:18, 18 April 2006 (UTC)
I didn't think the etymology of the word "calculus" was appropriate as the second sentence of the article's main paragraph, so I created a subsection of the History section and pasted it there. Soltras 05:07, 8 April 2006 (UTC)
Hi, I was thinking of further fleshing out the history of section, with a list of some specific contributions by Newton, Fermat, Leibniz, and others, and also information about developments after Newton (which is mysteriously absent) when I realized something. The history section is already too long. We already have an article called the history of calculus. Detailed lists of contributions by Aryabhata, Madhava, and others should probably go there, not here. If we included this much detail on every contributer, we would be duplicating the entire history of calculus page here.
To me, this situation is misrepresentative. I'd like to wait for some feedback on this before I make any changes, since my changes here have often been repeatedly reverted without explanation, and I know a lot of people feel strongly about this Indian Mathematics issue. Grokmoo 21:48, 17 April 2006 (UTC)
Calculus is a very important field and it's great to see that effort is being made to make this a great article. I think adding the following two images in their respective sections to graphically illustrate the difference between differential and integral calculus would greatly add to the strength of this article:
As a final comment, it would be great to be able to see which statements are supported by which reference. One commonly used way to do this is inline references, but I think there is some artistic freedom there. - Samsara ( talk • contribs) 13:05, 26 May 2006 (UTC)
Anybody claiming Indian priority in inventing calculus please quote the ancient sources. Don't tell me the dog ate them or the invading Turks burnt them. I want to see your proof! When I say sources I do not mean Hindutva booklets. Surely if some Indian mathematician 'long before Newton' used the notions of say derivative and integral in his work, he can be quoted directly.
By the way, I greatly appreciate Indian culture and science. Dear Indian friends, if you made me sick and tired of reading these endless passages about supposed Indian contributions to just about everything, think about disastrous impression it will make upon other readers. It's just like spam, nobody likes it. 212.199.22.126 01:12, 3 July 2006 (UTC)
These are certainly interesting references, but they do not lay all the problems to rest. The history of Indian mathematics, for example, is by a grad student, Ian G Pearce, whose specialty is the study of insects. It seems to be very well researched, but to rely almost entirely on secondary sources. It would be nice to have a reference to a scholar who had read the originals, and who comments on their provenence, the methods by which they were dated, and the relationship between the notation used in the ancient sources and modern notation. For example, Pearce reports that in the 13th century, an Indian mathematician discovered that δ sin x = cos x δx. In what notation was this discovery expressed? In short, the reference answers some questions but raises others.
I certainly don't see any effort to belittle the mathematics of India. Every respectable history of mathematics mentions the Indian discovery of the decimal number system, of negative numbers, and of zero as a place holder. Rather, I think mathematicians are cautious, and want proof. Rick Norwood 21:44, 3 July 2006 (UTC)
So far 3 days have passed since my original call for a quotation. Nothing. The only valuable piece of information is from http://en.wikipedia.org/wiki/Talk:Indian_mathematics where I have asked the same question. According to thunderboltz a.k.a.Deepu Joseph "A lot of work and ideas by Indian scientists were disregarded due to Eurocentric views of Western scientists. Yuktibhasa is the ancient text by Jyeshtadeva of Kerala School describing Calculus". I am very interested in a relevant passage from this work, so let me address myself again to any Indian who can get access to this text - please, quote it! I have no anti-Indian agenda here, so I will be glad if this is really the first calculus text in the world. But if not - the false claims have to be removed, no matter what legends say. 212.199.22.219 22:56, 6 July 2006 (UTC)
“ | The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude. | ” |
I don't want to open an ethnic editing war. The situation is unbearable. Only an Indian can check the sources. So please speak up! Do you think the quotation we got could be qualified as the first calculus text? 212.199.22.51 22:35, 8 July 2006 (UTC)
If someone wants another better info on Indian Mathematics, please have a look at this research project from Scotland University of Mathematics.
Madhava and his history
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Madhava.html
About Indian mathematics
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Indians.html
warm regards,
Source from,
School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland
Am I the only one seeing "failure to parse" messages wherever there should be a formula? -- Spangineer es (háblame) 22:46, 30 July 2006 (UTC)
Stable versioning is being tested on this article. This means that all editing will be made on Calculus/development, and on a regular basis, good edits will be moved onto the consensus page. If you disagree with the current version, please let me know. Ral315 ( talk) 05:27, 2 August 2006 (UTC)
Not really. The active editors of an article don't get to vote themselves an exemption from the m:Foundation issues, nor to decree that people shall not edit their article. The correct way to go about this is, for the umpteenth time, to go and build a workable, accepted proposal somewhere and then test to see if it works. It is wrong on many levels to take a proposal, the talk page for which is littered with objections, ruminations, alternatives, proposals and everything else and then say "right then, let's have some of that". You're doing it backwards, in the same way that these so-called 'test' earlier were backwards. Oppose, and object to the implication that only those who edit here should have anything to say. - Splash - tk 16:20, 2 August 2006 (UTC)
Oppose per WP:PROT and WP:OWN. Both of these trump a proposal that hasn't even achieved consensus support yet. Cynical 13:05, 4 August 2006 (UTC)
come out of your eurocentric point of view. Refferences are not readily available. But Lots of scholors(most of them western) have translated these texts and conclude that calculus in fact was from kerala much more than anyother place. Its easy to just deny ...when the world has just studied what you have. —The preceding unsigned comment was added by Vvn india ( talk • contribs) 21:44, 15 August 2006.
Great article, but one suggestion, shouldn't we include the power of a function rule within the differentiation category on the right hand side. Or is there even such an article on Wikipedia yet? -- Arsenous Commodore 00:15, 18 August 2006 (UTC)
i'm placing a request for references on the section in relation to india and calculus history. i've noticed a disturbing trend on a lot of history articles with a lot of POV pushing. these claims should be removed if they can not be verified because i have not read any of these supposed discoveries in any history book on mathematics. and please do not claim that the information was suppressed by the academic community... we need evidence for these claims. Truth100 01:43, 15 September 2006 (UTC)
Madhava and his history; about kerala school.
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Madhava.html
About Indian mathematics
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Indians.html
From
School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland
warm regards,
Note: This article has a small number of in-line citations for an article of its size and subject content. Currently it would not pass criteria 2b.
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05:57, 26 September 2006 (UTC)
If we want to bring this article to FA status I think that the following things should be adressed:
Feel free to add items to this list and to cross out those that have been adressed. Pascal.Tesson 18:40, 20 November 2006 (UTC)
Might I also suggest a peer review? The peer review bots might help us more on a quality scale. Tarret 22:36, 20 November 2006 (UTC)
The following suggestions were generated by a semi-automatic javascript program, and might not be applicable for the article in question.
Hope we can use it. Tarret 22:19, 21 November 2006 (UTC)
Calculus isn't really a branch of mathematics, anymore than arithmetic is. Both are pretty much used in all of mathematics and just considered basic tools.
Also, it's nice to see all the physical applications mentioned, but very little is mentioned of its ubiquity in modern mathematics in general. -- C S (Talk) 00:43, 26 November 2006 (UTC)
Hello. While I have been on Wikipedia for a while now, I am still fairly new to the mathematics areas of Wikipedia, and I would like to make some contributions. I recently added a large (and hopefully comprehensive) footer navigation box to this article, Template:Calculus footer. There are a number of reasons why I support adding this template to this and other calculus-related articles. Currently, with the exception of a rare use of Template:Calculus as a side infobox, there is no easy way to navigate between calculus articles of different subjects. I have read previous discussions regarding infoboxes vs. categorization in the Wikiproject Mathematics, and saw that calculus was listed as a possible exception to the mainly anti-infobox opinion presented. As a result, I began creating side infoboxes for each branch (differential, integral, vector, etc.) until I realized that it is simply impossible to list even just the most important topics without having too-large-and-bloated infoboxex. At this point, I was lucky enough to stumble upon the World War II article; at the footer of each page of a World War II-related article, they have a comprehensive template ( Template:World War II) that makes World War II articles, covering a vast topic in history, easy and user-friendly to navigate. Therefore, I decided to "be bold" and to do the same thing for the major topics of each branch of calculus, a vast total area in mathematics while using this World War II template as a base. While some things are probably still missing and others can be organized in a better fashion, I think this presents a much more user-friendly solution to those looking for information about calculus topics. Please let me know of any concerns you might have about this; barring any major objections, I would like to soon start putting this footer in other calculus articles. Thank you very much for your time and any feedback, Hotstreets 19:55, 8 December 2006 (UTC)
(de-indenting) Having it at the bottom goes a long way to overcoming my dislike of navigation boxes. In my opinion, the list is clearly more useful than the category. It is huge though. If it's possible to hide it by default, that would be great. Otherwise, how about shortening it to two lines and linking to a separate page with the whole list? -- Jitse Niesen ( talk) 02:40, 10 December 2006 (UTC)
Article says, "When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit." but I understand from the Wikipedia article on the controversy itself (to which this should link) that the controversy evolved many years after Leibniz published his results. Also, the slant of the story itself, as it is told here, seems to favor one side (Newton). — Preceding unsigned comment added by Rentstrike ( talk • contribs) 18:25, 28 November 2012 (UTC)
It is my understanding that the formal name for calculus is "The Calculus." While the "The" is generally dropped these days, isn't it still appropriate to capitalize the word Calculus?
"A calculus is a way of calculating, so mathematicians sometimes talk about the 'calculus of logic', the 'calculus of probability', and so on. But all are agreed there is really only one Calculus, pure and simple, and this is spelled with a capital C" (emphasis mine) (Crilly, Tony (2007). 50 Mathematical Ideas You Really Need to Know. London: Quercus Publishing Plc. p. 76, 208. ISBN 1-84724-147-6.)
Interestingly, the index of the book does not capitalize the word.
It would seem seems that we should at least mention the issue of capitalization in the article.
Billiam1185 ( talk) 01:02, 4 March 2013 (UTC)
Perhaps more examples on this matter. — Preceding unsigned comment added by Pedrovalle ( talk • contribs) 13:11, 20 May 2013 (UTC)
To be clear, most who add to the mathematical pages have probable forgotten more than I know about maths (I'm British, so I refuse to call it math). However it couldn't escape my notice that when Google put Leonhard Euler up in a Google doodle and specifically mentioned his historical significance to maths and his important work on infinitesimal calculus, that there is no mention of him whatsoever on the infinitesimal calculus page. Is Google incorrect in its highlighting the importance of Euler? Or is his work on infinitesimal calculus not as important as made out on his Wikipedia page? Either one or the other needs correction?
I think there should be something in the introduction about when it was invented and (gulp) who invented it. At the risk of being beaten over the head by all the history revisionists and refactorers out there, I think that should be the 17th century, Newton, and Leibniz. -- Chetvorno TALK 00:43, 27 July 2013 (UTC)
The Neumann quote box is hanging on Newton's image edge. Can someone fix it? Tried to, but got rolled-back. Formatting problems. -- J. D. Redding 00:11, 28 July 2013 (UTC)
Come on, people, let's hold the line for general references. We don't have to give in to the inline-cite extremists, not here. For most aspects of the topic, all our refs are going to say the same thing, probably in almost the same words. Save the inline cites for the stuff that's a little particular, and don't make the reader work through a forest of little blue numbers. -- Trovatore ( talk) 19:14, 4 December 2013 (UTC)
I check pages listed in Category:Pages with incorrect ref formatting to try to fix reference errors. One of the things I do is look for content for orphaned references in wikilinked articles. I have found content for some of Calculus's orphans, the problem is that I found more than one version. I can't determine which (if any) is correct for this article, so I am asking for a sentient editor to look it over and copy the correct ref content into this article.
Reference named "almeida":
I apologize if any of the above are effectively identical; I am just a simple computer program, so I can't determine whether minor differences are significant or not. AnomieBOT ⚡ 21:02, 11 January 2014 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
Request received to merge Infinitesimal calculus into Calculus. User:Unsigned request. Reason= unknown. Please discuss here. GenQuest "Talk to Me" 00:16, 30 March 2014 (UTC)
I have undone this edit. It is based on 4 sources, all of which i.m.o. unreliable:
Comments? - DVdm ( talk) 10:47, 22 February 2015 (UTC)
I've removed this from the article's Ancient History section since it should be dealt with here.
{{clarify|post-text=(Why mention this if not relevant? <-Perhaps it is a first/early instance of volume and area calculation, which the paragraph suggests would be the evolutionary antecedent of modern calculus, thus introducing a historical and logical progression, which would seem to be the purpose of this section.)|date=August 2015}}
Should something be added to the article in way of clarifying this point? Bill Cherowitzo ( talk) 04:37, 30 August 2015 (UTC)
A question. Mesmerate ( talk) 04:32, 22 November 2015 (UTC)
It is dx+Δx. Mesmerate ( talk) 04:36, 22 November 2015 (UTC)
Sir, the idea is you're taking the limit as it gets really close to zero, and as it gets closer, that is what it gets closer and closer to. As it gets closer and closer, infinitely, it can be considered infinitesimal. Mesmerate ( talk) 04:55, 22 November 2015 (UTC)
Please tell me HOW they saw what they were doing? Mesmerate ( talk) 05:05, 22 November 2015 (UTC)
The change in x, or Δx, can be defined to include infintely small or infinitely large numbers in its list of possible numbers. It commonly is, and that is partly why i think it is a just fine canidate for being an infinitesimal. Mesmerate ( talk) 05:08, 22 November 2015 (UTC)
So, you think infinitesimals cannot be defined using limits? Mesmerate ( talk) 05:11, 22 November 2015 (UTC)
We are talking about modern calculus, where Δx is allowed to approach zero, and where dx is defined as Δx as dx. Mesmerate ( talk) 05:25, 22 November 2015 (UTC)
Sorry. Mesmerate ( talk) 05:26, 22 November 2015 (UTC)
No it isn't, check. Mesmerate ( talk) 05:35, 22 November 2015 (UTC)
It's under "principals". Mesmerate ( talk) 05:37, 22 November 2015 (UTC)
I still argue otherwise, I argue in modern calculus dx itself can be considered as the change in x as it approaches 0. Mesmerate ( talk) 12:37, 22 November 2015 (UTC)
And I have already clarified that we are talking about modern calculus, "principals" is not a sub heading of "history". Mesmerate ( talk) 18:43, 22 November 2015 (UTC)
Sorry, nevermind. I read in a text book that the (dy/dx) could be seperated by multyplying by "dy" and as such, it had a page where it said "Who are we to throw around these numbers?" and defined dx as the change in x. I also understand that something getting infinitely cl in all the mess. I admitzero by itself. I still think that delta x equals zero, i just added a small note and got tangled up in it all. I still think something approaching zero still works like an infinitesimal, except for that one case in which it just goes to zero. Sorry i'm a little put of tune in calculus, plus, please tell me if i am right in "It acts like an infinitesimal, except for that one case.". Mesmerate ( talk) 23:44, 22 November 2015 (UTC)
Sorry, i mean you can seperate the (dy/dx) by multyplying by dx, not dy. Mesmerate ( talk) 23:46, 22 November 2015 (UTC)
Sorry my sentence 2 sentences ago was messed up. Mesmerate ( talk) 23:47, 22 November 2015 (UTC)
I meant to say i got caught in it all, and in all cases except for that case "approaching" acts like an infinitesimal. Mesmerate ( talk) 23:48, 22 November 2015 (UTC)
Sorry, by "two sentences ago" i meant two comments ago. Mesmerate ( talk) 23:50, 22 November 2015 (UTC)
Also, to clarify, i admit i was wrong. I will stop editing that part of the page, and i am sorry for disrupting wikipedia. Mesmerate ( talk) 23:53, 22 November 2015 (UTC)
The idea i had in mind was "dx=the change in x", "the change in x can act infinitesimal in most cases", "the change in x is fine, smd should be mentioned." Mesmerate ( talk) 23:57, 22 November 2015 (UTC)
Still, i believe that dx in integrals stands for "the change in x" in integrals,as the definition of the integral uses it alot. infact, it used "the change in x" an infinite number of times. and in both case, dx is short hand for "the limit of this using delta x" Mesmerate ( talk) 00:00, 23 November 2015 (UTC)
And as such i would like to start a new discussion. I would like to discuss the idea of mentioning that the meaning of "dx" is different across modern and old calculus. Mesmerate ( talk) 00:01, 23 November 2015 (UTC)
Read description. Mesmerate ( talk) 00:06, 23 November 2015 (UTC)
I believe it is important enough to be mentioned. Is there any consensus? Mesmerate ( talk) 00:07, 23 November 2015 (UTC)
On one hand, that entire section is historical - there are no infinitesimals in the real line. I would remove both the δx and the dx from that sentence, which is really only trying to say what an infinitesimal is. The symbol dx is not an infinitesimal in modern treatments of calculus. — Carl ( CBM · talk) 12:37, 23 November 2015 (UTC)
It's in "principals", not "history". If it is historical, that's a mistake. Mesmerate ( talk) 22:53, 24 November 2015 (UTC)
So we should remove the mention of "dx" meaning infinitesimal all together and only say it's just the change in x? I'm fine with that. Mesmerate ( talk) 22:56, 24 November 2015 (UTC)
What does h stand for in:
Why don't we explain it in Calculus#Differential_calculus? Warmest Regards, :)— thecurran Speak your mind my past 13:54, 6 December 2015 (UTC)
The h used to be a delta x, but at some point someone decided that a two letter symbol might confuse students, and replaced it with h. I think Thomas was the first, at least the first I saw. I think the explanation "h was free" is as good as any. Rick Norwood ( talk) 12:24, 7 December 2015 (UTC)