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)


 * 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)