What is Uniform Continuity?

Uniform Continuity Definition and Intuition

In this video, I give a quick introduction to uniform continuity, and provide some useful intuition as well. In the playlist, you can find some worked out examples, as well as applications.

[Dudecar]

For sure, one of the harder concepts of analysis for me to grasp. Nonetheless, I think you helped me understand what it means by uniform.

[hassanalihusseini]

Yes, it is really a difficult concept to grasp when you see it first time. Thank you for explaining it so clearly Dr. Peyam!

[theunknownscientist]

One of my favourite concepts of analysis, the epsilon-delta formalism is just so beautiful.

[Jessica-kvob]

I always understand everything with your videos !!!! Thank you so much Dr. Peyam ❤️❤️❤️

[carlosvargas]

Cada vídeo tuyo confirma mi ignorancia. Un gran saludo, profesor!

[adeelakhtar]

You’re a superstar! Would appreciate it you can explain some concepts of differential geometry, like covariant derivatives, connections, geodesics, etc.

[tinyshiny]

This is awesome! I'd love to hear you explain uniform convergence of a sequence :)

[taehyunahn]

This is a great introduction to uniform continuity, thanks Dr. Peyam!!

[yoav]

I wonder if this continuity series will be continuous until the end or you will break it with unrelated video

[Monirul]

Your videoes are very good .do more videos sir .thank you

[noamyakar]

So helpful, this makes so much sense!

[rikthecuber]

(Just asking) Hey Dr. Peyam, would you mind solving the Schrodinger's eqn? I know its more of a Physics concept but it requires partial differential eqns. I just learned laplace transform for ODEs. Just need a demonstration for PDEs. Hope it reaches to you.

[wtt]

Thank you sir for your very clear explanations in this great video ❤!

[mudkip_btw]

Actually the square root example being uniformly continuous is not very surprising when you consider that it is not singular at x=0 and its derivative is monotonically decreasing. Nice video.

[rikthecuber]

Hey I have 1 request. I came upon Descarte's Law of sign in my equations chapter in my maths reference book of class 11. But the derivation is not given there. Can you show it in a video?

[richardhambel]

Lost me at 1:15. I have no clue where delta came from.

[phukinho]

If f is UC on some interval, does it imply that f' is bounded on this interval? Thanks for your great videos ;)

[sumittete]

If a function is uniformly continuous on a closed interval, could we refine the definition of uniform continuity by replacing the condition |x-y| < δ and |f(x) - f(y)| < ε with |x-y| ≤ δ implying |f(x) - f(y)| ≤ ε ?

[dk]

Dang where were you in my analysis 1 class

[yukijenkins]

The questions were so accurate aahahha