Definition talk:Smooth Path/Complex

To Lord Farin: You're absolutely right, it isn't enough to claim that $\gamma$ is smooth when $x$ and $y$ are both differentiable. So I've corrected the definition so that the both $x$ and $y$ are $C^1$, though not $C^{ \infty }$. I believe this is the most common definition of "smooth path" in complex analysis, see cf. this Introduction to complex analysis. This is because we are interested in finding the line integrals $\oint_{ \gamma } f( z ) dz = \int_a^b f( \gamma(t)) \gamma ' (t) dt $, which are well-defined if $\gamma$ is $C^1$. --Anghel (talk) 19:17, 3 December 2012 (UTC)


 * Yes, I recall now; I may have overreacted on this possibly conflicting terminology. I suspect you will be adding "piecewise smooth" later today? In any case, I think it'd be good if it were mentioned that this notion of "smooth" is different from that encountered in real analysis. --Lord_Farin (talk) 19:23, 3 December 2012 (UTC)


 * I'll write about "Piecewise Smooth Paths" tomorrow, although I prefer to call them "Contours". I'll also give "Smooth Closed Path" its own section, once I figure out how to that. --Anghel (talk) 19:31, 3 December 2012 (UTC)


 * As a heads up, I'd like to let you know that the current LaTeX formulae you put up are only considered to differ from house style by pedantic perfectionists. Cheers! --Lord_Farin (talk) 21:44, 4 December 2012 (UTC)
 * If you wonder why I changed the links to diff class, it's because the MathJax SVG rendering does not work with MediaWiki internal links; this is the reason for insisting that links always contain at least one word in plain text. --Lord_Farin (talk) 21:46, 4 December 2012 (UTC)

I've noted that other pages on this page uses $\Re$ and $\Im$ to denote the real and imaginary parts, cf. Absolute Value of Complex Integral. I've used $\operatorname{Re}$ and $\operatorname{Im}$ for the real and imaginary parts in this definition, mainly because I've read that the house style discourages the use of fraktur letters. But was I wrong, so we should change the notation on this page to enforce consistency? --Anghel (talk) 12:11, 5 December 2012 (UTC)


 * Well noticed. Fraktur is indeed discouraged as being old-fashioned and unnecessarily difficult to read. For future reference, the notation to be used is that described and discussed on the definition pages in question. (Every entity which you invoke ought to be so described.) Where the notation differs significantly (as in this place), it's where we need to amend it.
 * You have identified a need for a new maintenance template for such instances: "Template:Notation" or some such. This will be actioned in due course.
 * We have noticed that certain editors are emotionally wedded to certain notation and refuse to accept the use of house style on pages for which they were responsible. Our corporate response to this is to refer those editors to the caveat at the bottom of all pages. --prime mover (talk) 12:39, 5 December 2012 (UTC)