Pointwise and Uniform Convergence Visualized

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Saint Jean - / @saintjean6010
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-- track starting at 4:52 - koralle

[@aihamelofairi8977]

visualizing math feels like eating a delicious cake

[@c4chu]

just changed the trajectory of my life - a math major with two midterms tomorrow morning

[@Sarah-mp9lb]

THE best video on pointwise and uniform convergence!!

[@karlrombauts4909]

Wow! this was incredibly well animated and presented! Thankyou so much for making this video. I really hope you continue making videos like these and that your channel gets the recognition it deserves 😁

[@GhostyOcean]

I think these videos are a great tool for people who struggle to understand the differences between the definitions of pointwise and uniform convergence. I had to make my own little drawings to help me understand what it meant, and that's really what helped differentiate them for me.

[@Agrover112]

The production value is simply amazing!

[@patrickbacon3013]

Phenomenal video. The visual "contrapositive proof" at the end really drives the point home.

[@sunnynegi722]

Your explanation is way better than other. You deserves more subscribers

[@saintjean6010]

Pleasing visuals and straight to the point explanation! I really enjoyed composing the Intro.

[@rydiro6713]

Crisp animations.

[@nirhai6025]

these are some stunning visualizations. made very well and explained very well, , thank you for that

[@markus325]

Eureka ! Have never seen an epsilon area neither better visualized nor better explained.

[@efekarsan6571]

It's fascinating being intuitive and mathematically rigorous in same video! Very well explained.

[@Ch.ANKURSINGH]

Thanks 👍 From #INDIA 🇮🇳🇮🇳🇮🇳

[@user-fn9hl9kh4l]

this is probably the best visualisation I have ever seen before.

[@djentgod45]

Wow. I was struggling to understand the intuition between pointwise and uniform convergence but now it all makes sense. thank you so much!

[@user-es4kl5uh8l]

Very neat and intuitive! I wish you'd post more videos.

[@piskounov4136]

Really amazing ! Please dont stop this channel have great potential

[@erfan3944]

looks like he stopped

[@shivpatel8288]

Finally, a god-damn easy to understand video

[@bismajoyosumarto1237]

THANK YOU VERY MUCH!! I'm now studying uniform convergence in calc 3 and the formal definition is quite a mouthful (especially that uniform convergence is established when somehow the choice of big N only depends on ε and not on x), but I tried picturing the entire thing and had a sense that uniform convergence meant the ability to bound the entire function within the ε-neighborhood of f_n (so to speak) for n ≥ N, so that it is not specifically pointwise and therefore no longer depends on x, I knew it would be nice to visualize, and voilà, I found your video which explains it nicer than I thought possible! Again thank you very much for this video!! Why does it only have 35 likes and 7 comments?? I'm sharing this to my friends, it's too good! :D very much underrated! EDIT: Forgot to say, about timestamp 5:46, I think "uniform" here is supposed to be a synonym for "simultaneous" after all (we have points uniformly converging together), so yeah ;)

[@cmodgamma1091]

Hey man I'm very glad I could help you :) Thanks alot for the comment!

[@simonribas4625]

you really shouldn't worry about these formal definitions in calc 3, 2, or 1 (although epsilon arguments can be intuitive). They are defined this way for advanced mathematics in which they utilize the formal definitions to prove other theorems.

[@bismajoyosumarto1237]

@@simonribas4625 Understandable. It just so happens that I took Real Analysis 1* alongside Calculus 3 (as my faculty recommends), so there was some temptation to view it rigorously. *Here, the teaching of introductory real analysis (using Bartle's textbook) is split into two consecutive classes. I have passed Calc 3 and I am now taking Real Analysis 2, discussing continuity, derivatives, integrals, and eventually uniform convergence. Can't wait!

[@shrekkinosciocchino1520]

Congratulations broo

[@renesperb]

This visualisations help a lot to understand these different concepts of convergence .

[@erguhgju3906]

Wow, please the world needs more videos like this! How is it the only video on this channel?

[@VNFilmography]

Great. Please continue uploading.

[@swiike4162]

Firstly i thought that your channel has 278 000 subs but now im shocked that it has only 278( So helpfully video

[@muzamilhussain9908]

What a amazing way of making content

[@juliustilmankrepele7890]

Thanks mate, it really helped me out a lot! Nice music, you got the ID?

[@cmodgamma1091]

:'D IDs in the description mois

[@jeppejabob]

Great video!

[@user-rq8ey9ex5w]

you gained a subscriber for life. keep posting more

[@AnhTuanNguyenHoang-lj6di]

i finally get this now , OMG thanks you so much for the explaination

[@snay6869]

What an amazing and easy to understand video!

[@julioschneider1644]

I never comment on videos, but this was amazing!!! Really beautifull

[@prabhasvedagiri9338]

Wow🤯... that was just SOOOO WELL-EXPLAINEDDDD. Thank uuuu!

[@Sarah-pu8un]

WOW!! Thank you so much!!

[@themasterofherself1109]

Amazing! Thanks. Keep going

[@markbeukeboom7815]

i very much enjoyed this video

[@NobOdy-zg9so]

Whaaaaaaaaat this is amazing!!!!!!!!!!

[@ahmedhasabo6647]

Clear explanation thanks lot

[@snay6869]

The music is lit!!!

[@beetsreliable]

Beautiful 😌

[@anubhamandal1236]

This was amazing honestly. I finally understand the uniform convergence part . Thankss !!

[@muzamilhussain9908]

Your are very good at understanding the concepts of mathematics please make more videos

[@ParitoshRoy-my9qi]

visual explanation makes the concepts clear. thanks you

[@hiimmomo2802]

insane, good job!

[@thomasjefferson6225]

Woah, I will def teach my friends this.

[@omarmaswadeh5434]

Now that is a great video on pointwise and uniform convergence

[@isabitoch420]

thank you very much, this was very helpful

[@ZenMan902]

Absolutely brilliant demonstration and explanation. Thank you!

[@binhphamtrong8102]

Thank you for this video!

[@marat3632]

Thank you for tthis video. I wish you would make more videos!

[@youssefjemal2433]

Great Video! Keep up the good work

[@amangouraman6789]

Amazing video keep it up

[@shero3896]

Super Video und Animation!

[@ryanalexander6858]

Thank You

[@shriramhari9439]

Really great explanation!

[@YumeMiteru]

thank you so much

[@abishekranyal2713]

thanks a lot.....

[@castagnos509]

great explanation !

[@mattetor6726]

Thank you!

[@sarkersunzidmahmud2875]

U deserve an Oscan man. Don't stop, please make more videos like this 😃

[@oussemabenameur5045]

Bro has one video and it's perfect.

[@db9021]

great!

[@sejadna4552]

Great video bro :) and by the way may I ask if your German ;)

[@cmodgamma1091]

Thanks, you are very right. :)

[@thisukainol]

Thanks a lot

[@gitikaparthiban7196]

amazing video

[@marian_a25]

Good job! You helped me a lot to understand calculus, you should continue presenting these types of concepts!

[@FranciscoRamat-lm2uu]

gracias amigoooo sos gigante saludos desde la argentina, FAMAF.

[@sophiaxiao5071]

Let (M, d) and (N, rho) be metric spaces. Let f_k be a sequence of functions. Assume \forall k, f_k is a mapping from A \subset M \to \N, and assume f is a mapping from A \subset M \to \N. Pointwise convergence: \forall \varepsilon > 0, \forall x \in A, \exists K such that if k \geq K, then rho(f_k(x), f(x)) < \varepsilon. Uniform convergence: \forall \varepsilon > 0, \exists K such that if k \geq K, then rho(f_k(x), f(x)) < \varepsilon \forall x \in A. For uniform convergence the K must not depend on x. That is, there must be a universal K that works for any x. This is similar to the idea of uniform continuity compared to continuity (delta cannot depend on x for UC, but delta can depend on x for continuity). Theorem: if f_k is continuous for all k and f_k converges uniformly to f, then f is continuous. Contrapositive: if f is not continuous, then there exists a function f_n such that f_n is not continuous or f_k does not converge uniformly to f. Hence if f_k is continuous for any k but f is not continuous (on A), then f_k does not converge uniformly to f.

[@pawanyadav3399]

Nice explanation🙏🙏🙏🙏🙏🙏 sir

[@geetRH]

Please continue the concept of maths through visualisation

[@christir2605]

WOW! You're video helped me finally understand the different types of convergence for sequences of functions! Really great video, thanks!

[@nguyenhoangnam5149]

Great video

[@johnericsson5286]

Beautiful presentation, thank you!

[@tsunningwah3471]

god

[@carlosraventosprieto2065]

Thanks man!

[@andreacernilogar3578]

great video

[@Sarah-mp9lb]

So helpful!

[@cryme4640]

bro dropped a banger than just quit 😭

[@Morphism]

Thank you so much! These videos are super useful to digest the material :D

[@suryanarayanan757]

Please do more videos 🙏

[@juanparedes1702]

This is an excelent video. Great voice and a very intuitive mix of defiiniton and visuals.

[@AENoel-dc6vf]

Wow great video. It helped me out so much. The visualisation is exactly what I needed to grasp this concept. Thank you and keep up the amazing work!

[@Wurmbrands]

great video man,thanks

[@TheRevAlokSingh]

I enjoyed the cocompact group from your username

[@MohamedAli-rv7kt]

This video is absolutely amazing! Thank you!

[@subhradeepghosh2523]

Great visual explanation.

[@user-fg9uv2pk7i]

Amazing video, thank you so much!

[@prakashbharwad6484]

It's Just.... excellent ✨❤️

[@federicoruellicubertie2296]

Outstanding animation. Thank you sir

[@mohammedmarhnine8194]

What!? One video for only one lesson, which I looking for ❤?

[@amithkumar6870]

Beautiful explanation, thank you🙂🙂🙂

[@mr.arikodus7527]

Thank you so much, outstanding work!!

[@filipubovic8868]

Thank you very much!

[@liacouve299]

amazing! beautiful explanation and visuals

[@calderonortizkevin9470]

Nice, bro. Thanks for the video.

[@davidmurphy563]

That was very good. Why not make another one. :)

[@alonelyphoenix8942]

Great video man! Learned a lot from this😊

[@ebog4841]

Supplementary problems: Extrapolate when the next video will come out XD

[@abbe23456789]

Excellent explanation!

[@devjyoti5614]

Great video Man highly appreciated।