# [texhax] derivatives and integrals: math operators

Toby Cubitt tsc25 at cantab.net
Fri Aug 7 11:26:25 CEST 2009

Phil Parker wrote:
> Since we create the stuff, we get to make the rules, conventions, guidelines,
> etc. Perhaps they want to change it so they can feel some sort of ownership of
> it when they use it. (Who knows? I'm not a psychologist! But I suspect it's
> more to keep us from reading physics too readily: we haven't paid our dues,
> and physics is a lot easier to understand with advanced math than with
> elementary math [a.k.a. "the hard way" or Phys 101 way].)

Goodness! What a tirade against physicists, all over a tiny difference of
notational convention. Did you suffer some sort of converse to the
apocryphal story about Alfred Nobel and the lack of a mathematics prize? :)

> Another physics quirk is to write \int dx\,f(x) instead of \int f(x)\,dx as we
> do. That just creates unnecessary confusion, especially in elementary (as in
> Calculus III) double and triple integrals.

I have to disagree here. I think people do this precisely to avoid
confusion in multiple definite integrals. Writing

\int_0^1 dx \int_{-1}^1 dy f(x,y)

makes it clear which limits belong with which variable, whereas

\int_0^1 \int_{-1}^1 f(x,y) dx dy

can easily lead to mistakes (at least amongst my Calculus I students!).
Especially if f(x,y) is a long and complicated expression, pushing the
measure far away from the limits. An alternative is to indicate the
variables explicitly in the limits,

\int_{x=0}^{x=1} \int_{y=-1}^{y=1} f(x,y) dx dy

but this seems to be too long-winded for most people.

> And THE most annoying physics quirk is to use \otimes (tensor product) for
> \times (set product). That's just plain stupid.

And THE most annoying mathematics quirk is to expend inordinate amounts of
time arguing over notation and trivialities (entire papers of the stuff!)
rather than publishing something with actual content ;-)

Toby

[A lapsed physicist turned mathematician, who agrees that someone ought to
explain the difference between set product and tensor product to the
physicists, bless 'em]