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 realvalued
functions defined on Rn,
and their topics are continuity,
differentiation and integration of
such functions. Isn’t it? But there is also
λcalculus, about which I
honestly don’t quite know. Does it
belong to calculus? If not, why is
it called *calculus? 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

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.

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

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 calculuslevel topic.
Attribution
Source : Link , Question Author : Tim , Answer Author : Qiaochu Yuan