Re: Dirac-Delta function

From: Adam (addam_at_rogers.com)
Date: 10/03/04 

Date: Sat, 2 Oct 2004 22:23:01 -0400

"A N Niel" <anniel@nym.alias.net.invalid> wrote in message
news:021020042211149692%anniel@nym.alias.net.invalid...
> It is a "generalized function" or a "distribution". Mathematicians
> cover these in a course known as "Functional Analysis". Maybe you
> will take that course one day.
>
    I'm not sure what you mean. It has been expressed multiple ways. In each
course, it is taught slightly differently. I searched online and there are
so many forms of it that it tends to make me think not so nice things about
"it." I say "it" because it seems that many of the things that are said to
be the same dirac delta function are not the same at all. Unless the
"function" is pathological, lol.

    There is also the kronecker delta function taught in relation to tensor
notation.
    delta_a_b = { 1 if a = b, 0 if a != b } where a and b are einstein index
notation indices.

    That seems to me to be the same object but for discrete cases. When
continuous cases occur, the object becomes the dirac delta function.

    The dirac delta is said to have a limit over infinity of 1 but be
infinite at 1 and 0 everywhere else, or some other nonsense.

    I'm starting to think that this is some sort of object that when used in
specific ways and specific situations, just happens to result in desired
outcomes. It doesn't seem logical at all.

> True. Perhaps you can convince the theoretical physicists to stop using
> it.
> But I wouldn't count on it.
>
    More and more areas of physics are using it as time goes on. Dirac gave
it to us for good. I'd rather take longer to do mathematics, but have an
actual understanding of it and have it use common logic, than to use some
strange thing in strange ways to save time or simplify notation. However,
that's just me.

Relevant Pages

  • Re: A consideration concerning the diagonal argument of G. Cantor
    ... With a common definitions of operations in N*, yes 1/oo = 0 and so ... Your choice of notation is strange. ... depends upon what sort of limit you are using - which you haven't ...
    (sci.math)
  • LISP code example matching an abstract construct
    ... Sorry if this question sound a bit strange or off-topic. ... I use notation --> result ... Center for CANONICAL |SCIENCE) ...
    (comp.lang.lisp)
  • Question on Shredder
    ... Shredder evaluates lines with a strange notation ... Jim ...
    (rec.games.chess.computer)
  • Re: Here is an idea!
    ... perhaps another bit of humor might include the notation near the top, ... "buy on ebay". ... Strange though, I kind of recall something of this car from years ago ...
    (misc.transport.road)