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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?

AnalysisuluclaC
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    Seems like a duplicate of http://math.stackexchange.com/q/32433/264 – Zev Chonoles Mar 01 '13 at 18:53
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    Simon Stevin was of the opinion that Dutch is the best language for mathematics. So perhaps we should drop the term "calculus." And even "mathematics," since Dutch is as far as I know the only Western European language that doesn't use it. – André Nicolas Mar 01 '13 at 18:55
  • @AndréNicolas The Dutch have a word for mathematics, 'wiskunde'; but people trying to sound impressive may also (correctly) say 'mathematiek' – AnalysisuluclaC Mar 01 '13 at 19:00
  • Calculus is a form of analysis. Analysis includes a lot of stuff we wouldn't call calculus. For example, complex analysis is "like" calculus in a lot of ways, but I've never heard anybody call it "complex analysis." – Thomas Andrews Mar 01 '13 at 19:06
  • @AnalysisuluclaC, from my German (which is closely related to Dutch) I'd suspect "wiskunde" is like "Wissenshaft" (something like "study of knowledge"), i.e., plain science in English. – vonbrand Mar 01 '13 at 19:45
  • @ThomasAndrews With all due respect, I guess you meant "complex calculus". – smwikipedia Oct 10 '23 at 07:56

3 Answers3

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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.

MITjanitor
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  • Yes. Whenever I think of analysis, I always think of "theory of calculus" or "advanced calculus" – TakeS Mar 01 '13 at 18:59
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    There are parts of analysis that I wouldn't call "theory of calculus." For example, Fourier analysis is not something many people would call "calculus," even though it uses integration and has a lot of practical applications. Complex analysis, too, is rarely referred to as calculus, and is quite practical - indeed, many colleges offer two complex analysis classes, one for engineers and one for math majors – Thomas Andrews Mar 01 '13 at 19:12
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    But Newton and Leibnitz did a lot more than what is usually considered calculus: e.g. differential equations, calculus of variations, Newton's identities for power sums and symmetric functions,... – Robert Israel Mar 01 '13 at 20:06
  • When you goes into theory, you leave the domain of God and enter the domain of mortals. – smwikipedia Oct 10 '23 at 08:12
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Calculus is Analysis without proofs.

azimut
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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.

noobProgrammer
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