Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.symbolic.independent

Topic: Delta functions.
Replies: 14   Last Post: Apr 22, 2013 8:58 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
clicliclic@freenet.de

Posts: 961
Registered: 4/26/08
Re: Delta functions.
Posted: Apr 13, 2013 2:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Waldek Hebisch schrieb:
>
> Using delta functions can lead to problems with zero divisors.
> For example in Maple I get:
>

> > (x - 4)*Dirac(x - 4);
> (x - 4) Dirac(x - 4)
>

> > simplify((x - 4)*Dirac(x - 4));
> 0
>

> > (x - 4)*Dirac(x - 4)/(x-4);
> Dirac(x - 4)
>
> which is clearly inconsistent. I wonder I there is any theory
> how to avoid such problems? I mean, what CAS can do to
> protect users from wrong results?



I was a bit tooooo fast - so once again:

Maple's evaluations are consistent applications of the rule

f(x)*delta(x-a) -> f(a)*delta(x)

which defines the meaning of a Dirac delta times a function that is
differentiable infinitely often. So the cofactor must not be split into
subfactors here.

The Dirac delta is a so-called "distribution"; these object are defined
via their action on certain spaces of "test functions". You may for
example refer to Constantinescu (1974), "Distributionen und ihre
Anwendungen in der Physik", but any other text on "distributions" should
do as well.

Martin.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.