Re: Integration "by parts" [was Re: Functions computed by Turing Machines ...]

On 05/05/2025 16:49, Richard Heathfield wrote:

[...] I hit a hard wall (integration by parts) and never really recovered.

     Is that still a "hard wall" for you?

It's been many years since I last visited that part of the garden.

I know how annoying it is to be told that something you find
hard is "really" very easy, but in this case it really is, and
the problem is usually bad teaching.

I have no doubt that to real mathematicians it's a walk in the park,
but not to me.

This particular topic is not even a "walk in the park";  it's
a step back from where you must have already reached in calculus.
Unless, that is, it was presented to you as an inexplicable formula,
perhaps by a teacher struggling with the whole concept of calculus.
If so, you wouldn't be the only one.  Many years ago a colleague and
I were jointly teaching a postgraduate modelling course, and a
student who had a top first in maths shame-facedly stuck his hand up
and said, "Sorry, but could you please explain integration by parts?".
Gasps from the audience [he really was known to be an exceptionally
good student], but he said he'd struggled with the concept for nearly
a decade.  We explained, and he said "Oh, is that all it is?".  Other
students said then that they had also never understood it, just done
it by rote.  It's a common problem when maths is taught by people who
are at or beyond the limit of their own knowledge.

I managed to pick out a path in which I never needed
more than algebra, trigonometry, and a certain aptitude for bullying
computers. The only integration I've done since sixth form has been
integration testing.

:-).  No-one needs more maths than that unless they are doing
"serious" maths.  But it's a shame if people who are interested and
competent get stuck not when the going gets tough but when something
obvious is explained badly.  I'm sure similar things happen in all
subjects, not least computing.
--
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
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