>>16738069 (OP)
Only anglos have this bizarre distinction between analysis and “calculus” (infinitesimal calculus as it was called in the days of yore).
>>16738069 (OP)
"calculus" is like a walled garden of sorts. You're making assumptions which break down in the general case, such as the difference between the Riemann vs Lebesgue integral, and it's pretty much always true that the fewer assumptions you have the more problems you can apply it to.
>>16738122
What Americans call calculus is the elementary study of integration and differentiation you probably learned as a teenager. When Americans are referencing Real Analysis they mean the rigorous study of real functions which was largely published in the 19th century. When an American references Analysis more broadly, they mean the wider subject which concerns itself with rigorous study of estimation more broadly, not just real finite dimensional real vector spaces and mappings between them.
>>16738069 (OP)
why do you say that? how powerful? if anything i think the abstract is piggy riding the success of the applied lol. most physics and engineering problems were already solved before analysis became a field.
>>16738122
Meh, non-Americans love to point this out. But in grad school, we don't see the difference. Weak students are weak, retards are retards. More hard core curriculum doesn't magically make you better.
t. survivor of "hard core" curriculum
>>16738069 (OP)
Because it's more rigorous and the results are more applicable to any given situation than basic calculus. Not really sure what you're asking but that's why analysis is more powerful than calculus on a basic level.
>>16738069 (OP)
Because calculus is just an artificially delineated part of analysis. Go beyond those delineations and you're no longer doing calculus, but analysis. So analysis is trivially more powerful.
>>16738209
i don't know personally
but i do remember the most intelligent person i've ever met, a research professor, was studying them for an application he was working on
>>16738069 (OP)
True. Philosophy superseed Math, math would be nothing without philosophy, the same thing cannot be say the other way around.
It's a tool derived from philosophy and logical thinking by the ancients after all.
>>16739940
Also European engineers point out how they learn actual analysis but in actuality it is just calculus with slightly more rigour. I assume math majors in America also learn analysis rigorously early on.
im not sure if this is accurate, but my understanding is that analysis is calculus but you apply more proof theory to your propositions rather than just rote execute the methodology, deriving them from axioms as much as possible while also constructing more advanced things besides limit theory, integrals and derivatives.
