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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 always used to refer to an integration over a set of paths in the sense of Feynmann. This may be a may vary based upon country of even university, but it's probably worth consideration.
Since when are brackets used for nested functions? RoboJesus 05:26, 16 August 2005 (UTC)
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 thing a contour C and call the integral a contour integral along C. —The preceding unsigned comment was added by Tbsmith ( talk • contribs) 02:54, 29 December 2005 (UTC)
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.
http://www.exampleproblems.com/wiki/index.php/Complex_Variables#Complex_Integrals
—The preceding unsigned comment was added by Tbsmith ( talk • contribs) 02:57, 29 December 2005 (UTC)
Currently, you find this in the article
may be defined by subdividing the interval [a, b] into a = t0 < t1 < ... < tn = b and considering the expression
May someone explain how we come from the first equation to the second one? -- Abdull 10:47, 27 May 2006 (UTC)
I have to say that this article offers no basic explanation or definition as called for by WP:MSM. It states that it "is an integral where the function to be integrated is evaluated along a path or curve," which doesn't really offer an definition that would be understandable to someone who doesn't already know what it is, because it's too vague and ambiguous to really understand. I definitely think the introduction should be rewriten. He Who Is 18:13, 10 June 2006 (UTC)
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 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.
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 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.
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 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). —Preceding unsigned comment added by 88.106.173.149 ( talk) 03:51, 29 December 2007 (UTC)
I would find it helpful to see examples contrasting when to use versus simply . (Not sure if the latter is technically considered a line integral)
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, .
sbump 15:31, 8 August 2006 (UTC)
Shouldn't the font of the title to this article be larger??
I'd change it but I do not know how to.
Rosa Lichtenstein 16:07, 11 September 2007 (UTC)
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 should be moved to the "Path independence" section. You all have one week to complain, then I'm deleting it. 129.78.64.106 ( talk) 03:52, 11 June 2008 (UTC)
Fixed ambiguity RobotMacheen ( talk) 04:04, 16 November 2008 (UTC)
Although arc length should not be confused with a line integral, it is part of the definition of any integral. See:
http://knol.google.com/k/john-gabriel/all-integrals-are-line-integrals/nz742dpkhqbi/44#
94.2.151.209 ( talk) 11:35, 20 October 2009 (UTC)
It's about this definition:
While if you just perform formal operations without thinking it may pass, really makes no sense, because is not a vector (is it differential of r as a function of t?). The right hand side is correct in .
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 don't like are:
I think the second variant (maybe with explicit sum) is slightly more acceptable than others, but I'm not sure. Any thoughts? — Kallikanzarid talk 13:58, 21 January 2011 (UTC)
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... FilipeS ( talk) 09:29, 14 May 2012 (UTC)
Hello! This is a note to let the editors of this article know that File:Line integral of scalar field.gif will be appearing as picture of the day on November 12, 2013. You can view and edit the POTD blurb at Template:POTD/2013-11-12. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. Thanks! — Crisco 1492 ( talk) 21:47, 23 October 2013 (UTC)
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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. — Preceding unsigned comment added by 192.136.116.2 ( talk) 22:02, 3 August 2017 (UTC)
The uppur part of the lemma uses bold r(t) for the parametrization, the lower uses . I cannot see any reason for this different use. Shouldn't this be unified? I'd prefer to use gamma all over this lemma just to do it the same way as in the german lemma. :-). -- Moyalingde ( talk) 06:18, 23 November 2017 (UTC)
I would this article to explain the notation , used to integrate around a closed loop. The-erinaceous-one ( talk) 07:38, 8 September 2020 (UTC)
This is the
talk page for discussing improvements to the
Line integral article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
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 always used to refer to an integration over a set of paths in the sense of Feynmann. This may be a may vary based upon country of even university, but it's probably worth consideration.
Since when are brackets used for nested functions? RoboJesus 05:26, 16 August 2005 (UTC)
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 thing a contour C and call the integral a contour integral along C. —The preceding unsigned comment was added by Tbsmith ( talk • contribs) 02:54, 29 December 2005 (UTC)
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.
http://www.exampleproblems.com/wiki/index.php/Complex_Variables#Complex_Integrals
—The preceding unsigned comment was added by Tbsmith ( talk • contribs) 02:57, 29 December 2005 (UTC)
Currently, you find this in the article
may be defined by subdividing the interval [a, b] into a = t0 < t1 < ... < tn = b and considering the expression
May someone explain how we come from the first equation to the second one? -- Abdull 10:47, 27 May 2006 (UTC)
I have to say that this article offers no basic explanation or definition as called for by WP:MSM. It states that it "is an integral where the function to be integrated is evaluated along a path or curve," which doesn't really offer an definition that would be understandable to someone who doesn't already know what it is, because it's too vague and ambiguous to really understand. I definitely think the introduction should be rewriten. He Who Is 18:13, 10 June 2006 (UTC)
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 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.
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 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.
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 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). —Preceding unsigned comment added by 88.106.173.149 ( talk) 03:51, 29 December 2007 (UTC)
I would find it helpful to see examples contrasting when to use versus simply . (Not sure if the latter is technically considered a line integral)
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, .
sbump 15:31, 8 August 2006 (UTC)
Shouldn't the font of the title to this article be larger??
I'd change it but I do not know how to.
Rosa Lichtenstein 16:07, 11 September 2007 (UTC)
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 should be moved to the "Path independence" section. You all have one week to complain, then I'm deleting it. 129.78.64.106 ( talk) 03:52, 11 June 2008 (UTC)
Fixed ambiguity RobotMacheen ( talk) 04:04, 16 November 2008 (UTC)
Although arc length should not be confused with a line integral, it is part of the definition of any integral. See:
http://knol.google.com/k/john-gabriel/all-integrals-are-line-integrals/nz742dpkhqbi/44#
94.2.151.209 ( talk) 11:35, 20 October 2009 (UTC)
It's about this definition:
While if you just perform formal operations without thinking it may pass, really makes no sense, because is not a vector (is it differential of r as a function of t?). The right hand side is correct in .
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 don't like are:
I think the second variant (maybe with explicit sum) is slightly more acceptable than others, but I'm not sure. Any thoughts? — Kallikanzarid talk 13:58, 21 January 2011 (UTC)
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... FilipeS ( talk) 09:29, 14 May 2012 (UTC)
Hello! This is a note to let the editors of this article know that File:Line integral of scalar field.gif will be appearing as picture of the day on November 12, 2013. You can view and edit the POTD blurb at Template:POTD/2013-11-12. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. Thanks! — Crisco 1492 ( talk) 21:47, 23 October 2013 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Line integral. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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Cheers.— InternetArchiveBot ( Report bug) 09:44, 16 May 2017 (UTC)
the formulas currently show |r'| but r is a vector valued function so || is not defined. It should actually be the two norm. — Preceding unsigned comment added by 192.136.116.2 ( talk) 22:02, 3 August 2017 (UTC)
The uppur part of the lemma uses bold r(t) for the parametrization, the lower uses . I cannot see any reason for this different use. Shouldn't this be unified? I'd prefer to use gamma all over this lemma just to do it the same way as in the german lemma. :-). -- Moyalingde ( talk) 06:18, 23 November 2017 (UTC)
I would this article to explain the notation , used to integrate around a closed loop. The-erinaceous-one ( talk) 07:38, 8 September 2020 (UTC)