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This question might be a little soft as it does not have a definite answer, so I hope I do not break the conventions of this forum by posting it here.

I have now come across the term "calculus of operators" several times in various books, as well as the "calculus of several variables", "calculus of variations", calculus of residues", "calculus of pseudodifferential operators", and so on.

Each time I don't really understand what is meant by this - my guess is it involves an algebraic system that contains operations broadly to be understood as differentiation and integration - but I am not sure at all, in fact I don't think it fits the bill.

I would be really grateful if I could get some better explanation than mine for the term "calculus of [something]". Many thanks !

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    @MarkDominus: I guess it depends on how one defines modern. Effectively, counting board methods had disappeared in Western and Central Europe by the 17th century. But it is true that the abacus either persisted in Russia, or was reintroduced, I don't know which.2012-05-30

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While it's often used to refer to various areas of...calculus I guess...in general it's "a system of rules and procedures for performing calculations". While many of these are related to ideas in differential/integral calculus (matrix, vector, stochiastic, residue, etc.) some are not (or at least much less so), such as lambda calculus, or even propositional calculus.

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"Calculus of" usually refers to the methods of differential and integral calculus in conjunction with the topic at hand. It often excludes many forms of calculus, which is a common misconception.

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    "Calculus" often excludes many forms of calculus? What does that mean?2012-05-30