Are calculus and real analysis the same thing?

  1. I guess this may seem stupid, but
    how calculus and real analysis are
    different from and related to each
    other?

    I tend to think they are the same
    because all I know is that the
    objects of both are real-valued
    functions defined on Rn,
    and their topics are continuity,
    differentiation and integration of
    such functions. Isn’t it?

  2. But there is also
    λ-calculus, about which I
    honestly don’t quite know. Does it
    belong to calculus? If not, why is
    it called *-calculus?
  3. I have heard at the undergraduate course level, some people mentioned the
    topics in linear algebra as
    calculus. Is that correct?

Thanks and regards!

Answer

  1. A first approximation is that real analysis is the rigorous version of calculus. You might think about the distinction as follows: engineers use calculus, but pure mathematicians use real analysis. The term “real analysis” also includes topics not of interest to engineers but of interest to pure mathematicians.

  2. As is mentioned in the comments, this refers to a different meaning of the word “calculus,” which simply means “a method of calculation.”

  3. This is imprecise. Linear algebra is essential to the study of multivariable calculus, but I wouldn’t call it a calculus topic in and of itself. People who say this probably mean that it is a calculus-level topic.

Attribution
Source : Link , Question Author : Tim , Answer Author : Qiaochu Yuan

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