Are calculus and real analysis the same thing? 
*

*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 $\mathbb{R}^n$,
and their topics are continuity,
differentiation and integration of
such functions. Isn't it?

*But there is also
$\lambda$-calculus, 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!

*

*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 calculus-level topic. 
