That doesn't mean you need a new integration method. They can be approached by combining more methods, it's hard to do all with one single bullet.
It's a pretty advanced integral, hard to touch (in any sense you want) ...
Well, in the end it's about an art, the art of successfully using your knowledge to get the correct result. It's not the stuff you meet in a top contest, but in some top research rather.
In 3 variables Mathematica doesn't get anything, only errors. In 2015 variables MMA is simply dying slowly.
@infinitesimal Anyone with strong knowledge in calculus should be ready for almost everything there. I like very much doing integrals, series and limits although I have no math degree. It's addressed to people that love this area!
My point is @Chris'ssis why don't you build-up the readers knowledge to the point where they can actually be able to do some of your "insane" questions and thus appreciate the beauty of math as you are experienced in?
@infinitesimal You're starred! I have that in mind, I thought of that, but it's not that easy! :-) Your point is incredibly good, but I need to see how I can make it real.
@infinitesimal On the other hand some told me it would be a great mistake to add such questions in my book. In the worst case to try to add some easier particular cases of the crazy generalizations.
Amazing.....u know if I right a book on new discovered problems on number theory and groups by me I will dedicate it to u @Chris'ssis coz u have given me a grewtidea
Tell me something @Chris'ssis if I use limit for eg limit as x tends to 3 for a polynomial $$\3x^2+2x+4\$$ do I put x=3 in this or find any other value as in how do u find limits
@Committingtoachallenge I am very sad I am still so sick after so long. I am on the verge of breakdown. I need a miracle. I hope I find a way to make myself better soon.
@Committingtoachallenge I need to confess you that after telling me yesterday you read 1,200 messages of mine I laught for one hour or so before being able to fall asleep. :-)
@ABeautifulMind I had depression and anxiety diagnosed, but I am pretty good now in terms of depression(anxiety will ever remain, but isn't too bad), paranoia is undiagnosed and non-serious
@Committingtoachallenge I spend most days in great suffering. On some days I feel alright, but I never really became stable enough to start studying. I don't want to waste my life away like that, but I cannot help it.
I (intend to) study smooth 4-manifold topology, where gauge theoretic/PDE constructions are important tools (as well as some serious homological algebra).
eh, I'd like to learn some physics because it seems like something worth knowing! not just because it would help me understand where certain ideas come from :)
i get why people find it interesting, i'd just rather work on more accessible things
@daOnlyBG: by which i mean, when my intro physics students would take data for springs in lab, extrapolating their measurements all the way down to zero stretch with zero load isn't really valid
since at that point you can't talk about compressing the spring any further
(on the other hand, if you're modeling a certain physical interaction as a harmonic oscillator, then $F=k x$ being valid all the way down to zero may be perfectly reasonable. it's a context thing)
@Semiclassical I think there are interesting philosophical questions there (that are ignored by the falsifiability crowd): suppose you know that your model is insufficient at untestable scales. Is studying other models that modify this still physics, even if one can't test the difference between them?
i think that's my conclusion too, @Semiclassical, but I probably would prefer if less time were spent on such things. on the other hand, I'm a math student, so...
the role of math/theoretical physics in that kind of scenario, though, is not so much to try to 'guess the answer' as to broaden the community's horizons of what options are out there
it's not about deducing the structure of the universe a priori, but extending one's horizons about what we can imagine as being relevant
plus, even if something is beyond your measurement capabilities, your choice/taste for theories will influence the kinds of questions you can ask and which you think are relevant to ask
the mathematics being developed is nontrivially applicable too; I heard from a friend of mine in solids that he uses some of the ideas they've seveloped for some of his (unrelated) computations
another point (which i'm not sure is quite the same as above): as much as physics may (rightly) try to avoid things which can't be made empirical, you have to accept some level of metaphysics in order to reason about the natural world at all.
and it's better to accept that, and try to be disciplined about it, rather than try to pretend otherwise
yeah, that's another point. the math may not change the meaning of the physics, but it can make deducing the physics much more obvious
