Integrate with explicit integration variable/infetesimal...
Subject: Integrate with explicit integration variable/infetesimal...
From: Stavros Macrakis
Date: Thu, 23 Sep 2004 13:05:07 -0400
Maxima's notation for differentialis like di is del(i), but this is
only used in return values from complete differentiation, e.g.
diff(sin(x)^a) =>
a*cos(x)*sin(x)^(a-1)*del(x)+sin(x)^a*log(sin(x))*del(a)
It knows nothing else about them. So, for example, integrate(del(x))
does NOT return x.
Also, though it's pretty clear what integrate(del(x)) and even
integrate(del(x)+del(y)) ought to mean, I am not sure what something
like integrate(log(del(x))) or integrate(del(x)/(1+del(x))) or for
that matter integrate(3) would mean. Am I alone in always having been
confused by the Leibniz notation? It looks so pretty for the chain
rule, for separation of variables solutions of differential equations,
and for integration by parts, but I've never been comfortable with it.
Perhaps non-standard analysis makes all this clear?
-s