Who here does calculus in Banach spaces? Can someone redpill

>>8121863
>pill-faggotry
yeah, kill yourself

>>8121895

You sound bluepilled as fuck.,

>>8121863
engineer here
we use them to establish properties of wavelets and to study finite elements techniques, but that's about it I think

>>8121923

Tell me more, I thought engineers were mathematically inept.

>>8121942
well when you want to study signals and you want to decompose them, you're basically looking for a basis of a space of functions that you're interested in.
That's where fourier transform/wavelet transform/hough transform etc come from.
Most of the time, you want to prove that a certain decomposition converges to the initial function you're decomposing. So you need a notion of distance and a notion of completeness. That's where banach spaces are useful.

As for finite elements, it's roughly the same idea: you discretize space, you look for solutions of a diff eq, and you want to find the conditions under which those "discrete solutions" get close to the real solutions, and at what convergence rate, and so on.
So once again you need a notion of distance to measure the error on the function and its derivatives, therefore you need sobolev spaces, which are banach spaces.

When you say engineers are mathematically inept, it really depends on the country more than anything

>>8122047

This sounds interesting, I'm considering doing a masters in engineering but I had a fear of getting stupider doing in. I want to use math theory.

What field are you in you do?

>>8122060
I think you will have to choose your courses carefully.
I did something close to EE and now I'm doing microengineering.

Look for control theory, signal processing, finite elements, image processing, machine learning and the likes
I have a friend who does computational physics and has a lot of courses from the math department as well.
You won't get stupider (hopefully), don't worry anon

>>8121942

stop listening to the math fags here they only know toy problems. and how to talk shit

>>8121942
No anon, if you major in engineering you will become a master in all STEM fields, even better than those who specialize in those fields.

>>8122137

I have interacted with electrical engineers at my university and I can promise, most are not masters of mathematics.

>>8122060
study physics and to your masters at a engineering institute.

>>8122142
which university is that? So that I can avoid them pls

>>8121863
calculus on banach spaces is a very important tool for many analysts, geometers, and mathematical physicists. It's a very natural generalization from the usual calculus. It should really be in more undergrad classes, but few undergrad level books touch on banach spaces.

Remember that differentiability in multiple variables is a linear operator (on phone too lazy to text the limit n shit). If you know this is easy to generalize to banach spaces. It's almost as natural but a bit subtler when you are talking about integration, or calculus on manifolds modeled on banach spaces. For the former, I would look into the bochner integral and the gelfand Pettis integral. The latter is a whole other can of worms I won't open for now.

It's hard to just explain all of this in a post because a lot of it is straight up generalizations of standard theorems like the implicit function theorem and inverse function theorem and many other standard calculus theorems. To learn this stuff at a basic analysis level, I recommend amann escher i-ii. This is essentially a first analysis course but most things are introduced in a good level of generality. As such there is a ton of other material you may not be interested in. For other basic expositions of banach space calculus, look at cartans calc book (you can find it online because it may be out of print. This may be the most concise intro on the differential side of things), or dieudonne. For modern grad level books which cover the differentiation and integration side, see lang, barry simon volume 1(only touched really, not a big theme in the book or anything), marsden ratius manifolds book, choquet Bruhats analysis manifolds and physics. Related: Richard hamilton has a very nice exposition on calculus of frechet spaces in his article on the nash Moser inverse function theorem.

>>8122564

Thanks, I have had a course on measure theory and basic banach/Hilbert spaces.

I want to take it to the next level, I also self studied multivariable calculus so I have the basic theorems down now.

>>8122564

What is lang, barry simon volume 1?

>>8121863
> banach spaces
worst math meme ever

File: wachowskis.jpg (330KB, 612x380px) Image search: [Google]

330KB, 612x380px

>>8121863
Regular reminder redpilled is actually code for realizing you have been born in the body of the wrong gender.