What is the difference between Real Analysis, Mathematical Analysis, Functional Analysis, and Calculus? [closed]

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What is the difference between Real Analysis, Mathematical Analysis, Functional Analysis, and Calculus?

And is Analysis is the general field to all of them?

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1 Answer

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The "Mathematical" in "Mathematical analysis" is just to distinguish this from non-mathematical uses of the term "analysis". The basic branches are

1. "Real analysis": generally concerned with functions of one or more real variables, and measures
2. "Complex analysis": generally concerned with analytic or harmonic functions of one or more complex variables
3. "Functional analysis": generally concerned with various spaces which have both algebraic and topological structures, in particular various types of topological vector spaces, usually infinite-dimensional.

"Calculus" is not much seen these days outside of undergraduate courses.

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