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.
Continuity Playlist: • Limits and Continuity
Subscribe to my channel: / drpeyam
Check out my TikTok channel: / drpeyam
Follow me on Instagram: / peyamstagram
Follow me on Twitter: / drpeyam
Teespring merch: teespring.com/stores/dr-peyam

[@hassanalihusseini1717]

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

[@Dudecar77]

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.

[@Mathematics-with-MohsinRaja]

Mee too but I actually not fully grasp the concept

[@Jessica-kv2ob]

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

[@carlosvargas2907]

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

[@adeelakhtar3540]

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

[@tinyshiny107]

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

[@taehyunahn1786]

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

[@noamyakar8554]

So helpful, this makes so much sense!

[@HimanshuKumar-zh7zx]

Explained very well !

[@haniaherbi2857]

Sooo simply and well explained TNX 💯

[@wtt274]

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

[@theunknownscientist3249]

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

[@meguellatiyounes8659]

epsilon plus delta plus variants

[@Monirul2512]

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

[@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.

[@drpeyam]

Check out my video on separation of variables (for the heat equation), it’s very similar

[@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?

[@tomascernansky3960]

thank you, thank you.

[@yoav613]

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

[@drpeyam]

It will be uniformly continuous until the end 😉

[@yoav613]

@@drpeyam 😄😃😅

[@Eis461]

Great

[@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.

[@yukijenkins86]

The questions were so accurate aahahha

[@dgrandlapinblanc]

Ok. Thanks.

[@Akihikoo_]

I wish you were my teacher!

[@GhostyOcean]

Would you consider doing some abstract algebra? I believe your insights would be really useful, you have helped me so much with analysis and linear algebra.

[@drpeyam]

Highly doubt it, sorry

[@GhostyOcean]

@@drpeyam ah ok. I'm leaning that way too, but I haven't really explored some of the areas I'm intrigued by yet. Anyways, thank you for all your videos! You do a great job

[@zaheercoovadia4745]

@@drpeyam Do you consider yourself an analyst? This was an awesome video btw - really helped cement a concept that had never exactly clicked for me before

[@sumittete2804]

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 ?

[@phukinho]

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

[@drpeyam]

I don’t think so, I think you can construct something like x sin(1/x) or something

[@jonko82]

Very interesting. So if I am understanding this correctly the function itself does not necessarily need to be bounded on the interval in question but the magnitude of the slope (derivative) must be bounded in order for a function to be uniformly continuous on said interval.

[@3r3nite98]

Ooh awesome,also Syber as always has a premiere so join if u can.

[@dk7472]

Dang where were you in my analysis 1 class

[@colleen9493]

Haha lol

[@225vikrant3]

5:46 did u mean that even if sometime delta depend on xnot is can be uniformly cont. But if it does then didn't it violated the def of uniform cont.

[@drpeyam]

Exactly

[@dcas7806]

Let's go to the N-dimensional functions!

[@kanewilliams1653]

Please tell us a story about your beautiful handwriting. Did you ever train it? I'm a math teacher in awe of what I see, and it's very inspiring and beautiful!

[@drpeyam]

Awwww thanks so much!!! I went to a French school, where they taught me cursive, but they can’t read that in the US, so I have to write in capital letters. The neatness comes from my French background though

[@colleen9493]

@@drpeyam actually we can read cursive here, I mean at least we were taught it in my school

[@kanewilliams1653]

@@drpeyam you're welcome, I should spend a few years in France then, if these are the results =)

[@Maraq369]

Why use y instead of x_0 ?

[@drpeyam]

Because we’re not fixing a point x0, it works for any points x and y

[@Maraq369]

@@drpeyam so x and y are points instead of inputs and outputs, f of a point instead of f of an element in the domain? it can be written as f(p) and f(p_0) where p=x,y and p_0 = x_0,y_0 ? instead of f(x) and f(y) as in the video

[@aneeshsrinivas9088]

What do you mean, continuous in exactly the same way?

[@aneeshsrinivas9088]

I still dont get how this has anything to do with that

[@drpeyam]

You can choose the same delta for every x, it doesn’t depend on where you are

[@aneeshsrinivas9088]

@@drpeyam so its uniform in terms of the detla choice. by the way hey if continuity means that changing x by just a little bit, our function shouldn't change by all that much, is there anything like this for uniform continuity

[@aneeshsrinivas9088]

@@drpeyam by the way, in these proofs, can you physically specify your epsilon, like say epsilon=1 right off the bat or something. i think the negation of this statement should tell us yes.

[@jiaxinli1674]

Oh, Math 140A stuff

[@drpeyam]

Yeah haha

[@Amantheparadise]

Peyam 001

[@timetraveller2818]

hey present human i am back again time travelling in the 4th dimension quick reminder : that there's this Aash syed guy who thinks time travelling is not real Don't believe him! he does not know the theory of relativity and and the properties of the 4th integral !

[@drpeyam]

Hahahaha I love this comment, keep it up 🤣

[@richardhambel648]

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

[@drpeyam]

Watch the playlist