What on earth is the difference between Calculus and Analysis [duplicate]

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I noticed that there isn't a word for Calculus in my native language, Dutch. So I just went to the English wikipedia entry on Calculus, and tried searching for the Dutch article, and as I suspected, it is non-existent. So I tried the opposite, and went to the Dutch wikipedia entry on calculus. There was a disambiguation page, I clicked on the page concerning mathematics (which exists, to my surprise), and I was redirected to a page named 'Analyse'. When I clicked on the English version, I didn't get Calculus again, but I got mathematical analysis. I already noticed before that these 2 are closely related, when I was shopping for a good (english) calculus textbook.

The only thing I found in my research is that Calculus evolved from Analysis, i.e. that Calculus is more basic. But this to me is hard to believe. Some fields of calculus, such are PDEs, are still being developed, so I guess this doesn't perfectly outline the difference between the two.

What is the difference?

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3 Answers

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Calculus refers to a field of mathematics, originally created by Newton and Leibnitz, independently. When studying calculus, you normally start with single variable Calculus, then move toward multivariable calculus. The next part is Real analysis, which is the study of the theory behind Calculus.

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Calculus is Analysis without proofs.

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"Mathematical analysis" can refer to real analysis, complex analysis, functional analysis, abstract analysis, etc. Calculus (especially when being used as a word today) refers to the single/multivariable Leibniz/Newtonian calculus taught in high school and first year university courses for science/social science majors, which is split up into differential calculus (studying functions that are differentiable and that can be approximated by linear functions) and integral calculus (functions that are integrable) on $\mathbb{R}^n$.

Functional analysis considers analysis on infinite dimensional metric spaces, which is unintuitively much different than analysis on finite dimensional spaces.

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