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From: kludge@panix.com (Scott Dorsey)
Newsgroups: rec.arts.sf.written
Subject: Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"?
Date: 21 Aug 2024 21:52:36 -0000
Organization: Former users of Netcom shell (1989-2000)
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Joy Beeson  <jbeeson@invalid.net.invalid> wrote:
>On Tue, 20 Aug 2024 08:09:49 -0700, Paul S Person
><psperson@old.netcom.invalid> wrote:
>
>> They never even once mentioned that integration and differentiation
>> are inverses of each other? With various caveats and details, to be
>> sure.
>
>It was asserted, but never explained.  The two courses were entirely
>separate.
>
>I've read that the proof is childishly simple.

There are three kinds of calculus class.

There is a calculus for math majors class, which is all about proofs and
all about how the calculus works inside.  Every procedure that is shown
is proved and students will be expected to explain the proofs.

There is a calculus for engineering students class, in which you won't
see any proofs at all but where you will be expected to memorize a huge
number of procedures and drilled in order to be able to do differentiation
and integration as quickly as possible.  There is no emphasis on how
anything works, just on how to make it work fast.

And there is a calculus for poets class, sometimes called an intuitive
calculus class, in which the proofs are handwaved and you get to see some
of the easier mechanisms so that students get a basic understanding of 
what integration and differentiation is and how it can be used.

Some universities teach all three kinds, some only one.  Which one is 
appropriate depends on your personal relationship with the calculus.
--scott

-- 
"C'est un Nagra. C'est suisse, et tres, tres precis."