Im a bit confused by terminology:
What is the difference ( if any ) between
- Basic Real Analysis without measure theory.
and
- Basic Real Calculus ( calculus over the reals , not complex analysis nor complex numbers )
I heard people say Real analysis is the successor going deeper into things than (real) calculus, so maybe advanced calculus over the reals = Real analysis ? Something like Real analysis = real calculus "2.0" ?
I also heard that Real analysis is more about limits and proofs.
But I remember using proofs and limits in calculus too. Epsilon delta proofs and such in calculus or was that no longer calculus then ??
Maybe Calculus is more about "nicer functions" like analytic functions and real analysis deals also with " not so nice functions " like complicated nowhere analytic $C^{\infty}$ or even non-continu functions.
With basic I mean beginner level ; the introductions and start of studying the topic.
Wanted to ask this a long time.
