@Koro interesting set of topics. this could be a very computational class. i would try to find out if there is a requirement to do work in any particular programming language, and maybe opt out if it's not one you know already.
i have $q\in L^{\infty}(\Omega)$ $q\geq 0 a.e x\in \Omega$, how to prove that $||u||_{H^1_0(\Omega)}$ is equivalent to $\int_{\Omega} |\nabla u(x)|^2 dx+\int_{\Omega} q(x) |u(x)|^2 dx$
@leslie Went on a walk with MIT alumni yesterday and on the walk was a mathematician whom I'd met back in the 70s who is now retired from UCSD. Several complex variables person.
@TedShifrin Yeah, I found a proof, it relies on taking an arbitrary point inside the square, that is not P, and proving that the property of 3 equal areas can ONLY be true if and only if the fourth area is equal to the rest as well
Serves me right for attempting to answer a geometry question. But the OP who posted it was truly not far along in geometry. His efforts were ... things like opposite angles cut by a transversal.
@TedShifrin cool. we drove munchkin up to the snow yesterday. she was complaining for weeks about seeing it but not being able to go to it. so she went there now.
@PNDas I'm guilty of similar stuff. Posting "proof without words" in geometry, when I believe its obvious, when in reality it isn't
@TedShifrin To be honest I don't even know where I got this "strength", but its fun so I'll take it. That said, I also do enjoy other areas of math as well. I really like calculus for example
Noob question: what is the geometric interpretation of the inclusion $\Bbbk[x^2]\hookrightarrow \Bbbk[x]$? Is it the branched cover $z\mapsto z^2$? If so, what is the geometric interpretation of the squaring map $A[x]\overset{x\mapsto x^2}{\to}A[x^2]$?
No, that is an advanced course taken by a handful of the best students at a handful of colleges/universities. That is not what calc 3 in the US is at all.
Evans only defined Bochner integral and Banach space valued functions in the appendix. But he is using their properties without even stating. It's making me mad.
Yes, Hades, I have given a lot of As to students in those courses over the years. They were not perfect, but they went on — not surprisingly — to be our best majors. Even some with B's from me have gone on to graduate school and done well.
@Thorgott ah, jolly good. The iso "straightens the parabola" and translates between the projection from the parabola to the y-axis that @TedShifrin mentioned and the 2-cover given by the squaring map.
i wouldn't care much about the dirichlet integral (i assume this is sin(x)/x). it might be an OK homework exercise.
the gaussian integral actually comes up in fourier analysis, most of the other integrals are just the calculus version of these complicated trapezoids and triangles, i.e. if you're me you file them under who gives a shit.
yeah, i mean, it takes all kinds of people to make a world.
i'm not in any sense against the dirichlet integral. i just don't see why it would have to come up. you could spend your life doing analysis and never know or care about it.
i periodically return to polya and szego's problems and theorems in analysis, because it's a cool book, but sometimes i think - man, there's tons of really complicated stuff to learn that you might never use.
although i did steal an idea from those books for a proof once.
@冥王Hades i hear that is pretty common, unfortunately.
my daughter has the use of a tablet, and when the volume on one of her shows is off, or the stream stops and she gets some error, she nerd rages and her instinct is to slap the screen. it is instinctual.
@leslietownes It is very common. Its even gotten me into some trouble for uttering a lot of colorful words in the voice chat after losing due to bad luck
i curse in traffic pretty frequently. my daughter can do it too. someone cut us off on the freeway and my daughter, about 2 and a half years of age, immediately said "this f---ing guy!" it was heartwarming and also inappropriate.
i don't mind my daughter's cursing if it's contextually appropriate, and not gratuitous. she called someone a mother f'er in traffic the other day, and i was like, when you're right, you're right.
my wife is a little more, uh, prescriptive when it comes to this kind of thing.
how are you even driving in japan? don't they have functional transit infrastructure?
most of the routes i drive are heavily patrolled, but 10-20 mph over a posted limit is not uncommon as long as it is the flow of traffic and not one person innovating.
