I’m all about open-source materials, as a rule. But the fact remains that the
best damn table of integrals is that fruit of the cellular automaton that
implements Stephen Wolfram’s mind, Mathematica. I should probably work out
what else it does, while I have a their evilly cheap student-license edition
chugging away doing quadrature.
Pros:
Beautiful calculus engine. Beautiful like the Fae, and as possessed of
glamour. Like them, it does not reveal how it does its magic.
Automatic compilation to GPU-friendly code, apparently. Any extra
performance gratefully accepted.
Mysterious introspection techniques and GUI integration make visualising
and exploring with exotic functions fluidly, making them concrete and
tractable to my monkey mind.
Cons:
It’s a weird language, with more horrible default scoping than even
javascript (Cross-document namespace pollution? Really?)
Lack of any decent published work explicitly using Mathematica or
libraries for it in the years approximately 2001-2009, when the newness
had worn off and before they had added functions anyone cared about. (c.f.
the explosion of R or scipy in that time)
Here are some links that I am finding useful to explore it with.