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MathGroup Archive 2003

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PrincipalValue of Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44661] PrincipalValue of Integral
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 20 Nov 2003 03:16:27 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I got the following interesting reply from Alain Cochard to my question 
about the usefulness of the concept of PrincipalValue of an integral. 
(Alain did not want to post the message himself but has allowed me to 
do so).

I am a physicist/mechanician and I can tell you that in my area of
research PVs are used all the time.  In linear elastic fracture
mechanics (LEFM), there are eqs with hypersingular integrals and the
game is to recast them so that they involve only regular integrals,
but it's in general impossible and we are very happy when the "worse"
integrals converge in the PV sense.

Cheers,
Alain


I would like to add from that my reason for asking the question were 
simply curiosity if this concept really deserved to have a special name 
and position within Mathematica (as an option in Integrate), since 
mathematically it amounts to just simple taking of limits in a rather 
obvious way. Since Alain convinced me that it has significant 
applications my doubts have been resolved.

Andrzej Kozlowski


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