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wrote a few lines at differential calculus, just so that the link does point somewhere. Clearly just a stub, to be expanded.
Correcting the link just to simplify redirecting from this page: differential calculus. It would be nice to have differential calculus of Grothendieck there *linearizing the maps of sheaves of O-modules using the infinitesimal neighborhoods).
I put a bit of context at the top.
Thanks. I have redirected your pointer to differential now to differentiation. Then I thought about it, and added some remarks to differential: this previously talked only generally about the nilpotent maps in a chain complex.
By the way, the use of “calculus” as a textbook synonym for “differential calculus” is not universal. Where I live the corresponding textbooks are titled “Analysis”.
By the way, the use of “calculus” as a textbook synonym for “differential calculus” is not universal.
Right. Calculus is historically an abbreviation for “infinitesimal calculus” (or its Latin counterpart) what includes both the differential and integral calculus. In my area the subject is also “analysis”. There exist other calculi, for example, the stochastic calculus.
The tradition in the UK is that analysis tends to concentrate on the ’why’ whilst ’calculus’ be it differential or integral calculus is more the techniques of applying the theory so more the ’how’. I think that this is also the way in the US. In calculus,you calculate, in analysis, you analyse!
Tim, this was not intentional. The calculus like other abbreviation is for masses, for undergraduates, for parents. In graduate courses, one can use full technical terms and not colloqiual speech. Like in Croatia, there is a Croatian word for geography, zemljopis, and there is an international version, Croatinized, geografija. In elementary school we had zemljopis as an official name, on all the textbooks, and in high school we had geografija. Surely at lower level one does more prosaic things, and less proofs. But this is not a definition, this is a consequence of forces of domesticating technical terminology at proleteriat’s level of discourse.
Certainly there are other calculi; that’s why I wrote “what textbooks call ’calculus’” rather than simply “calculus”. In America, there’s a tendency to push “calculus” even further up, renaming “undergraduate analysis” as “advanced calculus”. Even without this, “calculus” is used also for coverage of infinite series. So all things considered, it’d be better to just say “infinitesimal calculus”, which I will now do.
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