Pointwise and Uniform Convergence Visualized

made with manim Community

Custom Intro music by Saint Jean, check him out!

Main music by Yami Tarek, check him out too!
-- track starting at 0:13 - perlmutt
-- track starting at 2:31 - orange
-- track starting at 4:52 - koralle

[aihamelofairi]

visualizing math feels like eating a delicious cake

[Sarah-mplb]

THE best video on pointwise and uniform convergence!!

[cchu]

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

[karlrombauts]

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.

[patrickbacon]

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

[saintjean]

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

[Agrover]

The production value is simply amazing!

[markus]

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

[nirhai]

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

[efekarsan]

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

[piskounov]

Really amazing ! Please dont stop this channel have great potential

[sunnynegi]

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

[asdasdaaa-go]

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

[djentgod]

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

[shivpatel]

Finally, a god-damn easy to understand video

[bismajoyosumarto]

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 ;)

[Francielli-ym]

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

[juliustilmankrepele]

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

[julioschneider]

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