Banach Spaces part 1

[@maitrelame2]

This lecture series saved my life, I was so confused you made everything clear, thank you professor!

[@michaelli8523]

Max, can you tell me how I can find other lectures? I don't know in what playlist this lecture lies. Also, what are the name of the series and the reference book? Thanks!

[@TheTacticalDood]

@@michaelli8523 kzbin.info/aero/PLMn2aW3wpAtOqo0g0OnHndXB1LnYBeMaX

[@waytolearn7893]

@@michaelli8523 kzbin.info/aero/PLMn2aW3wpAtOqo0g0OnHndXB1LnYBeMaX And the name of the book of this course is "Functions, Spaces and Expansions" by Ole Christensen

[@tejasnatu90]

It's a good lecture series for specially those who have studied rather pure functional analysis and now wanna look at concrete applications..

[@Mulkek]

Thanks, and explain so clearly!

[@TheMagic0wnz]

Excellent lecture. Very clear, even I can understand!

[@matron9936]

Thank you! Amazing lecture on this topic.

[@jehushaphat]

Captain Picard is a great teacher.

[@oryana2023]

Great professor.Thanks

[@mithatkursatkaplan7095]

I learned all the necessary information.Thank u so much :)

[@_rachid]

Gorgeous lecturer ! thank you !

[@ghazalfaris8796]

If u cannot guess what v should be in [v - v] 11:28 In many cases banach spaces we want exactly opposite not always 17:43 banach with a simple norm [don't do that now] Some function sitting in the space F - fk =0 at inf Now it's functions and functions 26:07 it's less than epsilon 33:41 infinity norm = max[]

[@Artus506]

Thank you so much. The lecture is very clear.

[@Carolchan09]

very nice lecture! I hope I can have a lecturer like this!!!

[@YuanwenHuang]

yeap, very good video, very good instructor!

[@Ahidousmoderne]

I have a licence mathématiques appliquées in morocco we study this lesson and also Complet Space , helbirt Space...etc Banach Space = espace vectoriel normé complet.

[@amalulaji2171]

Thank you Sir.

[@nirmalduari2098]

Hi

[@hamzahussain3448]

Fantastic ❤

[@mikecohen5887]

excellent; thank-you. A minor point: < means less than not more.

[@thanhbmttcnh]

Thank you so much!

[@jppereyra]

Fantastic Mr Ore is the best ever lecturer I have saw so far, is any long distant subjects for postgraduate students in the University he teach?

[@bierthai4436]

thank to such a good teaching video

[@zapazap]

So is a lecture recapitulating the notion of a Cauchy sequence from one's first analysis course to be expected in all later analysis courses?

[@johnmaina1113]

nicei have learnt alot

[@shorab9856]

i really liked lecture

[@ermenleu]

@ 36:35 Imagine this man could have been a useful window washer ... ; )

[@jehushaphat]

lol

[@klausmathauer3316]

Thank you :)

[@yavarjn2055]

Which is the book he refers to?

[@thepacifier3267]

Where/How can we get the solution manual for his book? There are good questions at the end of the chapters.

[@rainbow-kj3ks]

Thank you a lot

[@mohanakrishnans2791]

thanks sir....

[@gbennardo]

Thanks

[@Circuito28]

Is it possible to know from which book this lecture is from or which is the text used during this course? Also which course is this? In Italy Banach spaces are teached during Analisi matematica 3 which corresponds to calculus in English; is it the same in other countries?

[@franzarviclivia1551]

f in C[a b] ...What's book? (Th. 1.6.6)

[@InCog2020]

I had John Searle in university and he'd do the same thing except instead of blackboards they were books which we were required to buy. The books were his lectures practically verbatim. You'd think the guy in the video would save himself some trouble and effort and print that which he is writing and hand it out.

[@khadimsarr581]

Thanks you very much we have understook banach spaces thank to you I am in licence of mathematic that's why it very good for us if i have a advice to give that's keep going to put these view we are everything with you thankkkkkkkkkkkkkkkkkkkkkkkk

[@RAMPAL-zi5mm]

Better explain

[@kparag01]

What are prerequisites for this class?

[@ottowagner6008]

You can get through this with Linear Algebra and Calculus

[@Easyprogrammingjai]

Good

[@whispererL]

which level is this ?

[@leewilliam3417]

Mmmmn😊

[@mikecohen5887]

Sorry, you said "smaller" not "more than"

[@pedroduarte6672]

The lecture seems to be elementary but instructive and very intuitive. This lecture does not seem to be very mathematical rigorous. Could someone tell me if this lecture is as mathematical rigorous as graduate mathematics lecture for mathematicians or is more like for physicists?

[@ene4s]

I had the same doubt. DTU (Danmarks Tekniske Universitet) is a technical university and think this course is oriented to engineers or physicist ( form my experience with undergraduate physics the same level of math that in Germany or Spain). In fact the only undergraduate program in English in this university is BSc in General Engineering

[@pedroduarte6672]

Thanks!

[@DarthChrisB]

32:38 That's just plain wrong! It's the opposite: You get a different N for (almost) every x you choose. It's easy to show this: if the function fl(x) isn't a constant and fl(x) isn't f(x)+c, then you get different values for different x. There can be values for x so that the absolute difference is bigger than epsilon and N must be chosen larger. This proof is invalid, but it's easy to correct it: Of all the different N for different x one has to choose the biggest N.

[@AlqGo]

+DarthChrisB No, it's not wrong, because the indices k and l refer to two different functions in the Cauchy sequence; they do NOT point to some values of the functions at some arbitrary x in [a,b]. See the difference? So, when he lets the index k approach positive infinity, he's picking the limit of the sequence {f_k}, which is a function, and NOT a specific value of that function evaluated at some arbitrary x!

[@longle863]

+DarthChrisB How can you pick the "largest" N? What if the sequence n(x) (as you said, with different x we can potentially has different n) is unbounded like the sequence 1, 2, 3, 4, ... ? +hmmm, you said that "when he lets the index k approach positive infinity, he's picking the limit of the sequence {f_k}, which is a function", I don't think this is a valid argument. Remember that we are trying to show that {f_k} converges to some function in the first place! Thus, we cannot just assume that {f_k} converges to some function (it'd be circular proof then...). I think the proof should have been something like this. Fix f_k such that |f_k - f_l | < epsilon/2 for all l > k (*). Then, I claim that |f_k - f| < epsilon. Why? For contradiction, let say I can choose x such that |f_k(x) - f(x) | > epsilon. Then , because of (*), we know that | f_l(x) - f(x) | > epsilon (If you like, draw a picture and consider two cases when f(x) > f_k(x) and f_k(x) > f(x) ). But this is a contradiction of our construction that f(x) = lim f_l(x).

[@avarmaavarma]

These lectures are no different from textbook definitions. KZbin videos - I was expecting better explanations. Plus , writing out every spoken word is annoying ( I know he has multiple blackboards )

[@geethatelgani2203]

Thank u sir....