Real Analysis 25 | Uniform Convergence

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

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00:00 Intro
00:44 Uniform convergence
02:52 Measuring distance between functions
04:30 Uniform convergence using supremum norm
05:06 Example
06:28 Uniform convergence is stronger than pointwise convergence
07:30 Credits

#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[angelmendez-rivera]

This is the best explanation of uniform convergence I have ever seen on YouTube.

[starinsky]

Dude you are doing god's work. You are saving students from these tyrannical professor. Keep up the great work man I hope you get more donation.

[punditgi]

These videos are uniformly most helpful!

[karensupreme]

You win, this was easily the best explanation!

[rmb]

Real Analysis and I haven't gotten along very well the past 13 weeks but this has brought some great intuition to some things that were quite difficult to understand. Thank you.

[subhradeepghosh]

Today I studied sequence of functions the entire day. It was quite interesting. Then I watched your video, which was a very nice way to summarise the things I've studied throughout the day. Also your graphs helped me better understand pointwise and uniform convergence.Thank you very much!

[RuizhanGu]

I like these videos. I can only cost less time to consider and try to understand a new knowldege by taking your class.

[demaskoh]

Hello! Many thanks for your videos! At 5:59, why did you simply take the mid-point? Is it correct to say that the sup-norm = 2?

[HuyNguyen-fpoz]

Thank you. I finally understand uniform convergence. I will share your channel to my friends who need to understand math deeply.

[Hold_it]

Wow, even earlier than expected :D
Thanks a lot!

[shawnfoh]

This is exactly what I need! Excellent video and thank you!

[niklasn]

Hast meinen Tag gerettet. Danke dir :)

[sharonnuri]

I will follow a calculus course coming semester. This video helped a lot to prepare for it. Excellent teaching skills

[Raynover]

Great presentation! Very intuitive.. what is the program you use to write with your tablet? Very neat

[MrWater]

The lim_n ||f_n - g ||_oo means that when n=1 I have a list of (possible infinite) values (f(x0) -g(x0), f(x1) -g(x1), ..., f(x2) -g(x_2), ....) where I take the supremum? When a I have n=1, n=2 I have a list of list of values and so on? And in the limit lim_n ||f_n - g ||_oo means I take the supremum over all list of values? I have this doubt because you said that "we started with a sequence of function but we ended with an ordinary sequence of numbers" so I struggle a little with that.

[chair]

The supremum norm seems not to be defined for non bounded functions. Why isn't that a problem?

[thomasjefferson]

It's an epsilon sausage. Lol how I've remembered this

[zyzhang]

Why for the last example at the jump the value is above?