What is Uniform Continuity?

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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
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Опубликовано:

14 окт 2024

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Комментарии

@hassanalihusseini1717 3 года назад

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 3 года назад

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 7 месяцев назад

Mee too but I actually not fully grasp the concept

@Jessica-kv2ob 2 года назад

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

@adeelakhtar3540 6 месяцев назад

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

@theunknownscientist3249 3 года назад

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

@tomoki-v6o 3 года назад

epsilon plus delta plus variants

@carlosvargas2907 3 года назад

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

@taehyunahn1786 10 месяцев назад

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

@tinyshiny107 3 года назад

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

@rikthecuber 3 года назад

(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 3 года назад

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

@wtt274 Год назад

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

@yoav613 3 года назад

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

@drpeyam 3 года назад

It will be uniformly continuous until the end 😉

@yoav613 3 года назад

@@drpeyam 😄😃😅

@HimanshuKumar-zh7zx 4 года назад

Explained very well !

@Monirul2512 3 года назад

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

@phukinho 3 года назад

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

@drpeyam 3 года назад

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

@jonko82 2 года назад

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.

@noamyakar8554 Год назад

So helpful, this makes so much sense!

@haniaherbi2857 2 года назад

Sooo simply and well explained TNX 💯

@rikthecuber 3 года назад

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?

@sumittete2804 5 месяцев назад

@GhostyOcean 3 года назад

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 3 года назад

Highly doubt it, sorry

@GhostyOcean 3 года назад

@@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 3 года назад

@@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

@mudkip_btw 3 года назад

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.

@tomascernansky3960 Год назад

thank you, thank you.

@3r3nite98 3 года назад

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

@Eis461 Год назад

Great

@225vikrant3 Год назад

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 Год назад

Exactly

@dgrandlapinblanc 2 года назад

Ok. Thanks.

@kanewilliams1653 3 года назад

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 3 года назад

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 3 года назад

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

@kanewilliams1653 3 года назад

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

@yukijenkins86 Год назад

The questions were so accurate aahahha

@dk7472 3 года назад

Dang where were you in my analysis 1 class

@colleen9493 3 года назад

Haha lol

@Akihikoo_ 3 года назад

I wish you were my teacher!

@dcas7806 3 года назад

Let's go to the N-dimensional functions!

@richardhambel648 2 года назад

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

@drpeyam 2 года назад

Watch the playlist

@aneeshsrinivas9088 2 года назад

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

@aneeshsrinivas9088 2 года назад

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

@drpeyam 2 года назад

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

@aneeshsrinivas9088 2 года назад

@@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 2 года назад

@@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.

@Maraq369 Год назад

Why use y instead of x_0 ?

@drpeyam Год назад

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

@Maraq369 Год назад

@@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

@Amantheparadise 8 месяцев назад

Peyam 001

@timetraveller2818 3 года назад

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 3 года назад

Hahahaha I love this comment, keep it up 🤣