Pointwise vs. Uniform Convergence | Real Analysis (Advanced Calculus)

[@qinisodlamini1139]

I like the fact that this guy is chilled when he is tackling these maths problem ,it's just make them look easier and more doable. Thanks buddy you really helped.

[@jharwood9795]

Thanks for the video! The idea of thinking of Uniform convergence with N as a function of just Epsilon, and Pointwise convergence with N as a function of both epsilon and x, is very helpful!

[@mancinellismathlab7451]

Jonathon Harwood very subtle concept, happy to help!

[@yaseminozturk5863]

The simplest and best explanation I haver ever heard. You really have saved my day. :)

[@cuteafrikancats]

amazing video, cleared up my confusion very quickly within the first 5 minutes

[@mancinellismathlab7451]

At 20 mins. the inequality should be abs(x)/n

[@TheArrowster]

Thank you from Brazil!

[@DoktorSmile]

Thank you very much for this explanation. I really struggle to understand the concept of pointwise and uniform convergence, or even functional series in general, but somehow I found some clarity after watching that. Thanks once again:)

[@jojo23srb]

how are u so fine, and so good at math tf???

[@dangerousangel777]

Lol I watched this at the beginning of the semester because the book we used at first mentioned pointwise convergence for some reason....and I was TOTALLY LOST, now, I actually get what you mean. Especially at 2:34-2:36 ...4:26 also lol I'm thinking that before 23:23 where you wrote |fn-f| |fn-f|

[@ahmadmustafa1]

Thank you for the amazing work

[@Alienman1212]

absolute legend

[@Knackebrod55]

Thank you for making these, really helpful.

[@dragomirbaltov3732]

Great job! Thanks a lot.

[@SzechSauce]

Super helpful, thanks!

[@shihaochen2258]

your logic is so clear. thanks

[@muhammedberkonder7802]

you explained this better than my university professor and it took her 3 hours to do that.

[@suleimanaabdisalan6830]

HanSulh which university?

[@muhammedberkonder7802]

İstanbul University, to be fair, my analysis 1 and 2 teacher was way better than her, she is a new teacher so i would understand for her teachings not being sufficient, but all she does seems to me just writing stuff that she reads on her papers. She doesn't seem to understand the subjects deeply enough in order to explain them better. At least that's how i felt like it, i bet she knows what she is talking about but not a good teacher as far as i can tell from my previous experiences with other teachers.

[@srirams3153]

Well Explained! can you suggest any reference books for practising problems on this concept?

[@Bryan_Pureblood]

thx man helped a lot!

[@shaikmastan1780]

What if x tends to infinity (though x is a real constant, while taking the limit; x can be slightly less than infinity )? Then the limit |x|/n doesn't equal zero ( The value of limit can be between 0 and 1).

[@johnraymondyanez5445]

Thanks a lot! This helped me a lot.

[@suleimanaabdisalan6830]

Thanks this helped me so much

[@danielnewhouse5044]

The point of advanced calculus is that when you find a limit, you are using uniform convergence. The argument is over self consistency. The question is, does your definition of a limit allow you to prove you can switch the order of operations, better yet, does it let you switch the order of differentiation and integration implicitly? And why do we have advanced Calculus instead of putting this in our first year?

[@konstantinosspinakis2839]

really good video, the examples helped me a lot

[@tarinisingh6481]

9:03 - isn't group theory the toughest subject in maths? :P Jokes aside, this was super helpful, THANK YOU! :)

[@mancinellismathlab7451]

tarini singh I think real analysis is the toughest subject in the beginning but modern algebra (group theory bring a subset) eventually becomes tougher.

[@tarinisingh6481]

@@mancinellismathlab7451 I'm a math graduate but conceptually I'm a lost cause when it comes to rings (groups and I became friends after two semesters of struggle 🥺🥰) would be great if you could do some topics from there too!

[@SahilSharma-un7hv]

I am having a doubt at 22:42. While proving that it is not uniformly convergent ,why did you write 0 and not any other f(at 22:42)?Is it correct to consider that we check uniform convergence only at the function f on which fn is point wise convergent to f? Please answer it asap?

[@mancinellismathlab7451]

If f_n converges uniformly, then it would have to converge to f=0 (the zero function)

[@chetedoherty]

I am having trouble with this part also. Why must f always converge to 0? Since we are taking x=n, it seems intuitive that it converges to 1 not 0. Thanks!

[@tobeornottobetobeornottobe974]

Maybe my answer came late, but it will help you. Taking f at this example converges to 0 but f is not alwayse converge to 0. Also x is considered fixed while n is the time of the function so as long as n goes up to infinity whatever you choose for x the ratio x/n will be almost 0. Keep in mind this course is abstract, and the idea here is this we have a bunch of functions are going close to f = 0 while in real line x chosen.

[@chetedoherty]

Thanks. But in which case, if x is fixed, why are we allowed to let x=n, since n is not fixed?

[@hanishsutaria8105]

x is not necessarily fixed in uniform convergence, it can range over R. basically you can either choose n first and then x, or choose x and then n (since they are the same quantifiers and come directly after one another in the definition). The def says it will work for any n>=N and for any x in R. It's easier to choose n first, say it is n*. Now as x can range over R, we can let x=n*. The def says that mod(f_n(x)-f(x))=N and x in R. So it should hold for (n,x) = (n*,n*). Putting this in, we get mod(f_(n*)(n*)-f(n*))=mod(1-0)=1

[@fatushemarke9243]

would you be able to show that sequence does uniformly converge?

[@ag4rw4en92]

why would we choose that the f_n converges to 0 when we take x=n? doesn't the f_n in that case converge to 1?

[@FlowMindsAI]

Thanks bro. Very helpful.

[@imanebasraoui4619]

THANK YOU

[@mdimteyazalam196]

hello sir can you tell me about interval of uniformly convergent ,or at a point where a uniformly convergent fails to in any interval,actually we need a concept to locate a point where it fails

[@WesleyMukanzu]

Helpful

[@jxphjbte4743]

Hey.... Thanks very much.. i've gotten the concept now...

[@mancinellismathlab7451]

You're welcome. I didn't like how your other requested video came out so ill redo it. thanks for the request!

[@jxphjbte4743]

okay ... cool..but you didn't talk about the weierstrass m-test and the example i sent

[@mancinellismathlab7451]

Yes, that is what I'm referring to... I'm will make a second video covering the M-Test with an example

[@jxphjbte4743]

okay..

[@maskbakchodars2271]

Legend is here.....

[@imalkavindawickramasingha4331]

Damn you look like the Banshee sheriff exactly

[@BSplitt]

Wait, are you writing on a SMART board?? I didn't realize they made dry erase boards!

[@mancinellismathlab7451]

Blake Splitter that's right!

[@tribalpermaculturalist1377]

Thank you so much this helped me understand this finally

[@priyanshubansal6776]

at 14:28 he wants us to cheat lol ...i am just kiddin bro don't be offend

[@bigfuncafe8724]

very helpful but if only the speed could have been faster ... :D

[@Coco01]

That's why the option to change the speed of the video is helpful!

[@pseudolemon8272]

im learning this in first year calculus wtf

[@mancinellismathlab7451]

um pseudonimo haha! Yes this topic may be covered in first year calculus, although 99% of students have no idea wth is going on! Don’t feel guilty if you don’t either! Just try and I assure you that you’ll be fine

[@reajulchowdhury8534]

before we jump into the definition, it is better to explain the intuition... The following video is fantastic kzbin.info/www/bejne/a6O8YZ15h7xqa7M

[@decentengineer8413]

he is copying the notes which he has put of in front of him and also on right side on other white board... his knowledge is very limited and expression of teach very dull...

[@kevinmartin2730]

Well, where is your video explaining this stuff? You probably still live in your mom's basement. Do us all a favor and take your negativity elsewhere. This guy is mad smart, and works out a lot too.... obviously! -Kmart

[@decentengineer8413]

@@kevinmartin2730 hello dear... i have my you tube channel where i upload useful videos ... you can visit my channel - Er. Kumar Upendra