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Why does "the continuous functional calculus" contain the word "calculus"? I mean, is there any connection to the "regular" calculus of derivatives and integrals?

Or is there a general definition of calculus that contains these two kinds of calculus?

brazofuerte
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epsilon
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    The first few lines here answer the question in part, and the rest gives a plethora of examples: http://en.wikipedia.org/wiki/Calculus_%28disambiguation%29 – jxnh Mar 01 '15 at 01:22
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    The word "calculus" means "a method of calculating." There is functional calculus, calculus of residues, Schubert calculus, and so on. For historical reasons differential and integral calculus became so prominent that the term "calculus" with no further descriptive label got applied to those particular calculi. – KCd Mar 01 '15 at 01:25
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    http://math.stackexchange.com/a/54824/207264 Relevant. – BHT Mar 01 '15 at 01:35

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It seems to have been named as such historically since it was (in part) an extension of infinitessimal calculus, and by analogy to other branches of mathematics also named calculuses (c.f. calculus of variations):

The somewhat vague denomination of "functional calculus," "calculus of functions" would include the whole of analysis ; and indeed the functional calculus is essentially a generalization and an examination of the principles of classical analysis. ...

The ideas with which we are now about to deal are really the ideas at the very base of the infinitesimal calculus. ...

In a daring generalization, Volterra extended to the functions of lines the fundamental notions of the infinitesimal calculus: continuity, derivative, differential, develop ment in series of power, analyticity.

brazofuerte
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