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only part of a wider definition) and then giving a graphical representation of a different object is surely going to confuse. Though someone like yourself would probably see what is going on straight away, I'd imagine that people like you rarely use this article, but rather people like me, who aren't so great at multivariable calculus and are trying to get a clue what is going on. You say that because the article didn't help my problem specifically, that doesn't mean that it's confusing. That's totally true, but I expect many of the people who use it are trying to solve a problem similar to mine.
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personally - it's very admirable in my view to contribute an animation. However, I would like to take the current one down, as I worry about it causing people the same problem that it caused me. I will do this if there is no reply or change in the article. I believe ds is the unit normal vector to the path at the point of integration - I hope this is helpful in making a new animation, I am afriad that I don't know how to myself.
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people to do stuff I want changed, and it is really I guess. However, I'm happy to change the article, but I'd just rather someone with the credentials (and knowledge) do it instead, as I don't want any changes just being undone by someone thinking I'm editing for no reason; I genuinely think that this article (specifically the animation) will mislead many of it's viewers (or at least those who are going to use it).
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that the animation isn't pretty - people have suggested both that the animation is vector valued and this is fine, and that it is scalar valued (as it should be). To me it clearly shows a vector valued operation, but would be more helpful (and in agreement with the article) if it showed a scalar valued one. Even removing the red pluses would be better as then the animation would just show the integrand.
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The sentence "Line integrals of scalar fields do not depend on the chosen parametrization r." is either totally incorrect or very misleading. Who inserted this sentence? Was it supposed to say "Line integrals of gradients of scalar fields do not depend ..."? If so, then it is in the wrong section and
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have vector values. That the particular line integral the previous editor was calculating did not immediately lend itself to assistance from the supplied animation does not make the animation misleading. As such, I don't think that there is that serious a problem with the image to warrant removing it
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I'm still fuzzy myself on how a line integral works, but its my understanding that a line, and a vector field is needed for the line integral to work. Is the line integral supposed to return a scaler, or is it supposed to return a vector? It would make sense to me if it returned a vector, tho i don't
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I have never heard of line integrals having vector values, though anything is possible. (Well, the complex integral is a kind of line integral, and it can be regarded as vector-valued, since complex numbers can be represented as vectors, but it's not common to speak this way.) But I hope you haven't
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Just a question, why not put this under the title of "contour integral". I have a B.S. in physics and am currently working on my Ph.D., and in all my Math and
Physics courses I have never heard this sort of integration refered to as a path integral, always as a contour integral. "path integral" is
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Hi
Xantharius. Whether line integrals can have vector values is a matter of definition, so I guess the issue is what is the most commonly accepted usage by the mathematics community. The article itself doesn't support your statement or the animation, but from your user page it looks like you'd know
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I have also tried to start a discussion (or at least explain) what could be done to improve the animation; specifically answering
Fresheneesz question about what ds is, before removing the animation (I suppose I didn't wait long enough). This post probably looks like a lot of suggestions for other
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So yea, I like doing pictures to make people understand the concept, but since I don't even understand it very well, I can't make a very good pic. If you want me to make the picture better, i'll make the vector field version better, and I can make a scaler field version. But I need to know what ds
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The animation represents an operation, and would be vector valued (if performed as in the animation). It clearly shows the vectors being added without any suggestion of another operation, which would give a vector valued result. I am not confused about the operation or terminology nor am I saying
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What I'm saying I think is that it would be better to address the issue explicitly and say that vector field path integrals are a broader class of operations, but usually refer to this specific type of operation (involving the dot product). Giving an algebraic definition (and not suggesting it is
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I have a BS in math and am working on a PhD in math. The way I just learned it is that a contour is just a collection of smooth curves linked together. So I could have a path integral along the path which is a bottom half circle from 0 to 1 and then the line from 1 to i. Or I could call the whole
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I'd be happy to change the animation myself, even put in little dot product diagrams for each pair of vectors if someone could recommend a suitable free application. I've looked at a few, but all the animation programs I've seen aren't the right sort of thing. Just something that lets you put in
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There seems to be confusion over whether the second operation above is a line integral - it seems to be similar to the one in the animation on the article. Could someone who knows for certain please state whether there are several definitions of line integrals on vector fields, or just the 'dot
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I was rather taken back by your statement about your textbook. I thought it was fairly universal that calculus textbooks like the term "line integral", e.g. Thomas' calculus or
Stewart. Anyway, I checked the book you cite and it uses line integrals. In fact, the chapter on it is called "Line
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I don't agree with the claim in that link that all integrals are line integrals. On the other hand, the caveat "should not be confused with arc length" is probably misguided. If I'm not mistaken, arc length is a special case of the line integral. You get arc length when the integrand in a line
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Hi
Freshneesz. I unfortunately found you image really misleading - I am a second year degree student, and I used this page, and your animation, to try to answer a set problem; I don't think it is correct though, and had a *lot* of trouble as a result! Please note that I'm not criticising you
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completely, without providing a replacement animation which addresses the issues that the previous editor raised. (Besides, I thought the animation was really good. Removing it wholesale without discussing what has to be done to improve it does not seem like a good policy.)
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so I'm guessing that it's the article that isn't as general as it could be. However, all the textbooks I've read (admitting I'm primarily a physicist) define a vector field line integral as it is currently defined in the article; as returning a scalar.
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I'd appreciate if you could give a hint in the definition about the sense of the absoulute value notation use here. Just for all people not common with this but common with the 2-norm notation. Btw, the german article uses the 2-norn notation :-)
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Now that I think of it, I'm not sure my suggestions are even correct. But I still think the current left hand side of the definition is bad for understanding the subject, and differential forms need to be used a little bit more explicitly —
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You don't agree with the claim? Well, please tell what you don't agree with. I am not a mathematician, but think the link would add to this article. Do you know what caveat means? I think you may have used the word incorrectly.
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Additionally, in my experience, mathematicians do not use "path integral" for this concept, but prefer "contour integral" or "line integral". I've almost always heard "path integral" refer to integration in the
Feynman
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You're very welcome to modify the picture yourself (i'd suggest editing the higher quality, and firstly uploaded picture). Do you mean have the line be sequentually be created instead of only being shown at the
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Hey, not bad! I would suggest making the particle draw the broken path as it moves, but it's not a big deal. I do worry about the meaning, though. It seems like the integral being illustrated is one of the form
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An additional request: The article includes the complex-plane parameterization example, but what about paths in more than two dimensions? I suggest an example of doing this with a parameterization in, say,
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Absolute value to denote the length (euclidean norm) of a vector is pretty standard also. I've changed it back to that, especially considering that the rest of the article uses absolute value as well.
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I think this error needs to be addressed, because it impedes transition of thinking when the reader is introduced to differential forms. I don't know the best way to fix it, some variants I
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Ohhh cause its a dot product, I see. I still don't understand it well enough to make the picture any more specific. But you can tell me what I should do (since I have the
Imageready file).
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remember doing that last year in vector calculus. If it doesn't return a vector, does it return the length of a vector, or how does it transform the vectors from the field into a scaler?
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Given the discussion so far, I believe "path integral" should be the title of the math physics method, with a disambig note at top with a link to "line integral" or "contour integral". --
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as the integrand on the left). However, the one on the right is not a subset of the one on the left. Caveat: of course we also need to take into consideration the domains and ranges of
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This is my website of contour integral example problems. Please someone add this link to the external links section of the main article if you think it's relevant and helpful.
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The left hand side is pretty standard notation, I've seen it in numerous places. Conceptually, it makes sense on an informal level; and I don't find it confusing at all.
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This recent addition to the text is poorly worded, but promising. I think line integrals can be understood as projections. But this needs to be checked, and sourced...
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pixels frame by frame would be great. I don't just want to mess up this nice diagram, it's a good sort of thing for the page, but I do think it could be corrected.
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is used for paths through the complex plane. I think it's good that a separate letter is used here, since it's for a scalar (complex)-valued function, while
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I tried a really clever picture. Its not super accurate, but I found a similar thing on a different page that really really made me understand the concept.
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In the several editions of vector calculus or multi-variable calculus textbooks my university uses (University of
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Why is it that after all this discussion, the (imho incorrect) term "path integral" is still used in the first sentence of the first paragraph?
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is, and exactly what a line integral is. This page needs a better description, and so do I. Lets work to make this page understandable.
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It would be cool if you could do that. Unfortunately, I am not the right person to advise you regarding the computer application. :-(
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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I think the second variant (maybe with explicit sum) is slightly more acceptable than others, but I'm not sure. Any thoughts? —
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I moved the page (though I now wish I'd checked how many pages link to this page; it will take me some time to fix them up). --
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the formulas currently show |r'| but r is a vector valued function so || is not defined. It should actually be the two norm.
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https://web.archive.org/web/20111219142026/http://www.khanacademy.org/video/line-integral-example-2--part-2?playlist=Calculus
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Look carefully at the two expressions. Clearly, the one on the left is a special case of the one on the right (just define
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The animation represents the integrand, not the integral. The integral itself along that curve would be a single number.
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There are no lemmas in this article, so I'm not sure if we're talking about the same thing exactly, but I noticed that
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Basically is the area under the constraint of the scalar function z=f(x,y), where x=u(t) and y=v(t) is the constraint.
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Although arc length should not be confused with a line integral, it is part of the definition of any integral. See:
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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should be moved to the "Path independence" section. You all have one week to complain, then I'm deleting it.
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Well, you do have a point. Perhaps the image, nice as it is, would be better suited for one of the articles
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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on Google and Google books; also, "contour integral" tends to carry a complex analysis connotation. And
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No, that's not a source of confusion. The integral in the animation is clearly vector valued.
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I have to say that this article offers no basic explanation or definition as called for by
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879:{\displaystyle \sum _{1\leq k\leq n}f(\gamma (t_{k}))(\gamma (t_{k})-\gamma (t_{k-1})).}
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http://knol.google.com/k/john-gabriel/all-integrals-are-line-integrals/nz742dpkhqbi/44#
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Do you mean in the formulas? The text font you can change at will in your own browser.
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If you found an error with any archives or the URLs themselves, you can fix them with
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is an integral where the function to be integrated is evaluated along a path or curve,
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The uppur part of the lemma uses bold r(t) for the parametrization, the lower uses
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http://www.khanacademy.org/video/line-integral-example-2--part-2?playlist=Calculus
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http://www.khanacademy.org/video/line-integral-example-2--part-1?playlist=Calculus
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To support my vote, I have consulted the classic and reputable text by
Ahlfors,
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May someone explain how we come from the first equation to the second one? --
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http://www.exampleproblems.com/index.php/Complex_Variables#Complex_Integrals
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While if you just perform formal operations without thinking it may pass,
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confused "vector-valued integral" with "vector-valued integrand"...
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thing a contour C and call the integral a contour integral along C.
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Hello! This is a note to let the editors of this article know that
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always used to refer to an integration over a set of paths in the
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I would find it helpful to see examples contrasting when to use
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on November 12, 2013. You can view and edit the POTD blurb at
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Shouldn't the font of the title to this article be larger??
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integral is the constant (scalar) function equal to unity.
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The last factor, gamma-gamma, is a discrete version of dz.
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for additional information. I made the following changes:
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Line integral of a vector field: the definition is wrong
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Any suggestions, then? Perhaps a really clever picture?
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That sentence is correct. What is misleading about it?
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while the only two forms discussed in the article are
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1444:00:02, 3 January 2008 (UTC)
1415:16:23, 2 January 2008 (UTC)
1401:14:48, 2 January 2008 (UTC)
589:05:26, 16 August 2005 (UTC)
50:New to Knowledge? Welcome!
3014:
2809:{\displaystyle \gamma (t)}
2765:{\displaystyle \gamma (t)}
2690:22:23, 3 August 2017 (UTC)
2673:22:02, 3 August 2017 (UTC)
2611:(last update: 5 June 2024)
2537:Hello fellow Wikipedians,
2489:to be integrated, be it a
1986:09:43, 18 April 2010 (UTC)
1840:15:31, 8 August 2006 (UTC)
1222:21:33, 2 August 2006 (UTC)
1192:21:28, 2 August 2006 (UTC)
1167:21:28, 2 August 2006 (UTC)
1127:20:07, 2 August 2006 (UTC)
951:19:51, 2 August 2006 (UTC)
445:should simply redirect to
2526:More featured pictures...
2389:10:25, 3 March 2011 (UTC)
1967:16:33, 2 April 2010 (UTC)
1910:05:28, 11 June 2008 (UTC)
1895:03:52, 11 June 2008 (UTC)
1880:Delete incorrect sentence
942:22:40, 16 June 2006 (UTC)
932:18:13, 10 June 2006 (UTC)
905:22:32, 16 June 2006 (UTC)
599:22:42, 16 June 2006 (UTC)
543:11:34, 21 June 2006 (UTC)
519:18:50, 20 June 2006 (UTC)
488:21:38, 19 June 2006 (UTC)
454:22:21, 16 June 2006 (UTC)
314:
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80:Be welcoming to newcomers
2648:09:44, 16 May 2017 (UTC)
2438:Template:POTD/2013-11-12
2416:09:29, 14 May 2012 (UTC)
1930:Arc length and integrals
895:10:47, 27 May 2006 (UTC)
421:11:07, 29 May 2006 (UTC)
321:project's priority scale
2533:External links modified
2497:, is evaluated along a
386:00:40, 1 Jul 2004 (UTC)
382:. Any other ideas? --
278:WikiProject Mathematics
2963:C-Class vital articles
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447:Functional integration
380:Functional integration
75:avoid personal attacks
2934:
2892:Closed loop integral?
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2513:vector in the curve).
2432:will be appearing as
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923:. It states that it "
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650:comment was added by
616:comment was added by
470:Complex Analysis, 3/e
205:level-5 vital article
100:Neutral point of view
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301:mathematics articles
105:No original research
2582:After February 2018
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1539:Additional examples
449:, with a dab note.
2941:The-erinaceous-one
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2587:InternetArchiveBot
2460:Picture of the day
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270:Mathematics portal
214:content assessment
86:dispute resolution
47:
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2424:to appear as POTD
2213:as a function of
1856:Rosa Lichtenstein
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345:sense of Feynmann
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483:. Ergo, move. --
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376:Contour integral
368:Contour integral
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2596:have permission
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1709:product one'.
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1407:Oleg Alexandrov
1300:Line integrals
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2493:as here or a
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394:integrals".
292:Mathematics
283:mathematics
239:Mathematics
148:free images
31:not a forum
2957:Categories
2774:Moyalingde
2739:r or gamma
2697:Moyalingde
2643:Report bug
2503:arc length
2485:where the
2253:like are:
1307:Xantharius
1122:Thoughts?
384:Abqwildcat
2626:this tool
2619:this tool
2515:Diagram:
2442:Main Page
929:He Who Is
586:RoboJesus
208:is rated
88:if needed
71:Be polite
21:talk page
2661:unsigned
2632:Cheers.—
2487:function
2483:integral
1713:unsigned
1496:unsigned
1432:unsigned
1347:unsigned
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1124:Melchoir
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902:Melchoir
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660:contribs
648:unsigned
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56:get help
29:This is
27:article.
2546:my edit
2522:Archive
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594:Where?
319:on the
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154:WP refs
142:scholar
2481:is an
921:WP:MSM
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516:(talk)
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216:scale.
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1465:, or
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911:What
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559:Pzinn
485:KSmrq
197:This
169:JSTOR
130:books
84:Seek
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2716:Done
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