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 !