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In some of my previous questions, I have noticed that something "real analysis" tends to come up. From context, it seems to be the analysis of real valued function's graphs. However, this confuses me. I thought Calculus was the study of graphs of functions?

Now I'm not asking for a detailed description of real analysis. A simple description will do fine.

user64742
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1 Answers1

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Neither calculus nor real analysis is the study of the graphs. Both study the properties of functions $f:\mathbb{R}\to\mathbb{R}$, particularly with regards to differentiation and integration.

An application of these studies is to graphs of functions, e.g. local maxima, concavity.

Generally real analysis is considered a theoretical subject, with rigorous proofs, while calculus is more about the calculation/computation.

vadim123
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  • For example: in calculus the intermediate value theorem might be essentially taken as an axiom, whereas in analysis you spend 20 pages defining what a number is in order to be able to prove it as a theorem. – Jack M Oct 28 '16 at 17:35
  • Calculus, both integral as well as differential, constitutes a part of the much larger domain of mathematical analysis. The relationship is thus one of inclusion. The same goes for real analysis, which, along with complex analysis, also forms a part of the same. The relationship between the two sub-domains, however, is one of intersection, since each has parts not belonging to the other. – Lucian Jan 23 '17 at 05:34