What differentiates Advanced Calculus from Real Analysis?

[quantumdude]

Has anyone ever seen this? It's an interactive online textbook in analysis in a single real variable. As an undergrad, I wussed out and took Advanced Calculus instead of Analysis, and this is a subject I've been meaning to learn. Is anyone interested in going through this?

http://www.shu.edu/projects/reals

It looks like it could serve as a springboard to get into more advanced books that I've found online.

 

[Hurkyl]

This will seem like a really silly question but...

As long as we're sticking to real functions of a single variable (and not delving into abstract spaces and measures), what's the difference? (I'm beginning to suspect that my teacher taught us both in my advanced calc courses)

 

[phoenixthoth]

i think "analysis" has to have the word "real" in front to be compared to advanced calculus.

otherwise, things like metric spaces are included in the subject.

 

[selfAdjoint]

To a mathematician, the word analysis by itself means functions of a complex variable. Other discplines mean other things by it. The Freudians...

 

[Hurkyl]

I talked with a coworker, and he confirmed my suspicions; my advanced calc class did indeed delve a decent bit into real analysis, which is the source of my confusion!

 

[Nereid]

An (almost) pure PF Mentor page!

 

[phoenixthoth]

i think the term "function theory" is what is used for complex analysis.

not all mathematicians have the same definition of "analysis."

http://mathworld.wolfram.com/Analysis.html

Originally posted by selfAdjoint
To a mathematician, the word analysis by itself means functions of a complex variable. Other discplines mean other things by it. The Freudians...

 

[quantumdude]

Originally posted by Hurkyl
As long as we're sticking to real functions of a single variable (and not delving into abstract spaces and measures), what's the difference? (I'm beginning to suspect that my teacher taught us both in my advanced calc courses)

OK, sorry I took so long to get back to you. As far as I know, the thing that differentiates Advanced Calculus from Real Analysis is theorem proving. In my Adv Calc class, we covered multivariable calculus (differential and integral), vector calculus, calculus of variations, and a very little bit of PDEs. We learned nothing of spaces, measures, Lebesgue integration, etc.