MathGroup Archive 1996

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  • To: mathgroup at
  • Subject: [mg5418] Abs[]
  • From: fast at magellan.Colorado.EDU (Bruce Alan Fast)
  • Date: Sat, 7 Dec 1996 00:25:47 -0500
  • Organization: University of Colorado at Boulder
  • Sender: owner-wri-mathgroup at

robpeterson at writes
 > I may not understand the limitations of Abs[].
 > ......
 > This works just fine:
 > s[L_]=I/(L+1/L);(* a complex function *)
 > Plot[Evaluate[D[Abs[s[L]],L]],{L,1,2}]
 > (*The Abs[] of a complex function, which is real, apparently
 > has a real derivative and it is plotted.*)

 Bad news:  Abs[] is not analytic -- i.e., as a function of
 complex values it does not have a derivative.  So a lot of
 attempts to get numerical values or plots of derivatives of
 Abs[Anything] are doomed.

 I tried your example and it did *not* work --- which is good,
 because it would be in error.  If f[x] is a real function of
 real values x, then it's possible to make sense of D[Abs[f[x],x]],
 but not if f is complex.

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