Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Problem with the Derivative of a Arg-function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48637] Re: Problem with the Derivative of a Arg-function
  • From: klishko at mail.ru (Alex Klishko)
  • Date: Wed, 9 Jun 2004 04:16:54 -0400 (EDT)
  • References: <c9k37o$fbo$1@smc.vnet.net> <c9pfq9$t79$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

ab_def at prontomail.com (Maxim) wrote:

> The short answer is that the derivative of Arg is undefined: Arg is
> not an analytical function. Just consider what happens when you move
> along different directions, for example, from 1 to 1+eps and from 1 to
> 1+I*eps, with real eps.

Yes, you are right.
I think that when Mathematica take numerical derivative, it's ought to
show error message in case of complex argument (without using
ComplexExpand) .

> In[1]:=
> ComplexExpand[(Arg[z + h] - Arg[z])/h, z,
>     TargetFunctions -> Abs] //
>   Limit[#, h -> 0] & // FullSimplify
> 
> Out[1]=
> -Im[z]/Abs[z]^2

It's right for real argument, when Re'=1 or dRe[z]=dz
It common case it should be (-Im[z]*Re'[z]+Re[z]*Im'[z])/Abs[z]^2

Best wishes
Alex Klishko


  • Prev by Date: RE: Combining plots
  • Next by Date: Re: Combining plots
  • Previous by thread: Re: Problem with the Derivative of a Arg-function
  • Next by thread: Re: ANFIS