Talk:Line integral

message: Since when are brackets used for nested functions?
RoboJesus 05:26, 16 August 2005 (UTC)
replies: text: Where? Melchoir 22:42, 16 June 2006 (UTC)
thread_title: Brackets

message: Currently, you find this in the article
----
:\int_\gamma f(z)\,dz
may be defined by subdividing the interval [a, b] into a = t0 < t1 < ... <  tn = b and considering the expression
:\sum_{1 \le k \le n} f(\gamma(t_k)) ( \gamma(t_k) - \gamma(t_{k-1}) ).
----
May someone explain how we come from the first equation to the second one? --Abdull 10:47, 27 May 2006 (UTC)
replies: text: The last factor, gamma-gamma, is a discrete version of dz. Melchoir 22:32, 16 June 2006 (UTC)
thread_title:  Equation understanding problems 

message: I would find it helpful to see examples contrasting when to use \int_a^b f(\mathbf{r}(t)) |\mathbf{r}'(t)|\, dt. versus simply \int_a^b f(\mathbf{r}(t)) \, dt..  (Not sure if the latter is technically considered a line integral)
: 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 product one'.  —Preceding unsigned comment added by 88.106.245.46 (talk) 12:19, 25 December 2007 (UTC)
replies: text: Look carefully at the two expressions. Clearly, the one on the left is a special case of the one on the right (just define g(r(t)) 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 f and r. FilipeS (talk) 21:42, 31 December 2007 (UTC)
thread_title:  Additional examples 

message: 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)
replies: text: Do you mean in the formulas? The text font you can change at will in your own browser. FilipeS (talk) 20:17, 14 January 2008 (UTC)
thread_title:  Font 

message: 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)
replies: text: That sentence is correct. What is misleading about it? Oleg Alexandrov (talk) 05:28, 11 June 2008 (UTC)
thread_title:  Delete incorrect sentence 

message: 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)
replies: text: 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 integral is the constant (scalar) function equal to unity. FilipeS (talk) 16:33, 2 April 2010 (UTC)
replies: text: 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.  114.225.82.14 (talk) 09:43, 18 April 2010 (UTC)
thread_title:  Arc length and integrals 

message: It's about this definition:
:\int_C \mathbf{F}(\mathbf{r})\cdot\,d\mathbf{r} = \int_a^b \mathbf{F}(\mathbf{r}(t))\cdot\mathbf{r}'(t)\,dt.
While if you just perform formal operations without thinking it may pass, \mathbf{F}(\mathbf{r}) \cdot \mathrm{d}\mathbf{r} really makes no sense, because \mathrm{d}\mathbf{r} is not a vector (is it differential of r as a function of t?). The right hand side is correct in \mathbb{R}^n.
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:
* \int_C \mathbf{F}^\flat — I think it's too cryptic, but it's correct.
* \int_C F_i \, \mathrm{d}x^i — It no longer tries to 'dot product' a differential form, but it now instead relies on a cartesian coordinate system with its trivial index lowering.
I think the second variant (maybe with explicit sum) is slightly more acceptable than others, but I'm not sure. Any thoughts? — Kallikanzaridtalk 13:58, 21 January 2011 (UTC)
replies: text: 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 — Kallikanzaridtalk 18:39, 21 January 2011 (UTC)
replies: text: 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. 209.252.235.206 (talk) 10:25, 3 March 2011 (UTC)
thread_title:  Line integral of a vector field: the definition is wrong 

message: :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.
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)
thread_title:  "Basically is the area under the constraint..." 

message: 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)
thread_title:  [[:File:Line integral of scalar field.gif]] to appear as POTD 

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thread_title:  External links modified 

message: 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)
replies: text: 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.  --Deacon Vorbis (talk) 22:23, 3 August 2017 (UTC)
replies: text: 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 :-) --Moyalingde (talk) 06:11, 23 November 2017 (UTC)
replies: text:   --Deacon Vorbis (talk) 13:52, 23 November 2017 (UTC)
thread_title: Absolute value of r' for archlength

message: The uppur part of the lemma uses bold r(t) for the parametrization, the lower uses  \gamma(t). 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)
replies: text: 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 \gamma(t) 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 \mathbf{r}(t) is used for vector-valued (in \mathbb{R}^n) paths.  --Deacon Vorbis (talk) 13:44, 23 November 2017 (UTC)
thread_title:  r or gamma 

message: I would this article to explain the notation \oint_{C} \mathbf{F} \cdot d\mathbf{r}, used to integrate around a closed loop. The-erinaceous-one (talk) 07:38, 8 September 2020 (UTC)
thread_title:  Closed loop integral?