Real Analysis 48 | Riemann Integral - Partitions

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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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(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)
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[@garrettstandifird6080]

You really help me understand this subject. My only regret is that I didn't discover you sooner!

[@brightsideofmaths]

Thank you very much :)

[@tshedisehangkhitshane9811]

Honestly thankful for the series.. went 😂 to class and all I could recall is how clearly you explained everything

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More good material! Thanks 😊

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The lecture is so crystal clear and to the point ❤

[@brightsideofmaths]

Thanks a lot :) And thanks for your support!

[@DanielJanzon]

If I recall correctly all you have to do to give the Riemann integral more power than Lebesque is to allow the widths of the partitioning of the domain to depend on x when taking the limit. The concept was developed Ralph Henstock. But the Lebesque intergal is nicer to work with when the domain is complicated (multi-dimensional or not R).

[@brightsideofmaths]

To be honest, I don't know this Henstock partition idea. Do you have a good reference for this?

[@123sendodo4]

I always wondered what analysis II is about and how is it studied, thanks!

[@محمدرضاقینرلو]

It becomes very simple when you teaching that

[@brightsideofmaths]

Thanks! That was my goal :)

[@sinanakhostin6604]

At 4:25 you mentioned that you have lessons on Lebesque integral as separate series. Which series cover that topic?

[@brightsideofmaths]

Measure Theory :)

[@brightsideofmaths]

Hier you can find it: thebrightsideofmathematics.com/measure_theory/overview/

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@@brightsideofmaths Thanks a lot. I wish I had access to these material before starting my PhD! I am sure these material will help so many of those desperate people along their projects!

[@lawrencecataylo7712]

Does this lesson, Reimann integral, apply in Real analysis II? I hope that makes sense. Thank you.

[@debojitsikdar2046]

Could you elaborate on the difference between Riemann integral, darboux integral and Riemann stieltjes integral? Which is stronger and more general?

[@brightsideofmaths]

This is something for a separate video :)

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@@brightsideofmaths will be highly awaited! 🖤

[@AlvaroALorite]

Was this shot in OneNote? :)

[@brightsideofmaths]

No :)

[@AlvaroALorite]

@@brightsideofmaths :O on what then?

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@@AlvaroALorite Xournal :)

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respect

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Thanks :D

[@Aisha.mohammad23]

صوتو حلو 🤦🏻‍♀️😂.

[@user-km5wt6jx8x]

Please work on your pronunciation I can't concentrate

[@brightsideofmaths]

Haha, I already do that :)