Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Today's jaw dropper


On Tue, 7 Oct 1997 15:35:13 -0700 Leigh Palmer <palmer@sfu.ca> writes:
Don't you mean the way electrical engineers do mathematics? Wasn't
Heaviside the originator of generalized functions and Laurent Schwarz
the
legitimizer? I see Dirac's name, but ... Wouldn't the function
precede
its derivative?

Schwartz's (with a "t") "Theory of Distributions" was indeed the
legitimizer. Even after Schwartz's work one of my references says
the Dirac delta function was *not* considered a respectable
function by mathematicians, but they admitted the use of a symbol
with all the same properties. Physicists persist in this "error"
with considerable profit, however.

I think the Heaviside unit function predates the delta function,
but so what? *****Heaviside knew the whole calculus of generalized fns
and solved many problems. He must have used the delta fn. ****** Where
is it written that a function must precede its
derivative (and what does that mean)? And how does that relate to
the discovery of the circular functions, sine and cosine? Clearly
neither could now exist had it relied upon the previous existence
of the other.

Leigh



At Courant the delta function was very popular. I think the derivatives
are related to the Sobelev spaces. I think Donald Ludwig who was
Courant's last student did a thesis on sequences of generalized fns for
solving PDEs. It's in Courant Hilbert II. Donald says it's wrong.
These generalized fns are in the dual space of L2. I am very rusty, you
know. The sin and cos are waves. At Courant we always talked
physically. The Neumann fn is a spherical wave. The Bessel fns also
had similar roles on vibrating beams I think. Whether a fn comes before
its deriv is irrelevant. If not, an integral would come before its
integrand. :-) I'm still interested in the personal life of Dirac. I
took his QM book out of the library. Is it too old? Who was his
'greatest' student?

Regards / Tom