Functional Sequences (Part 1 of 2)

[@klairehoang667]

OMG, this is like the best explanation I can ever imagine. I comb through countless books in real analysis, tons of videos on KZbin and this is the only one that gives a clear and intuitive understanding of what exactly functional sequences are!!! Thanks a bunch!

[@profcoconut]

This is my first comment on KZbin. Very clear, very informative and very helpful! Thank you very much!

[@joetursi9573]

This is, by far , the best explanation I've seen of what is a very difficult concept to understand. You must understand that convergence is to a FUNCTION and not number. You must also understand that the rate of convergence varies with x in pointwise convergence Uniform convergence means the rate of convergence is uniform throughout the interval and that's the difference between pointwise and uniform convergence. It's simply difficult to visualize and this is where Rob's work shines!! Bravo Rob.

[@sangwonlee5669]

Explanation of the difference between Uniform vs. Pointwise convergence was super clear. I appreciate this!

[@erikpolano]

I just wanted to say thank you for providing such an incredibly clear explanation of functional sequences in both videos. I hope your department realizes how lucky they are to have you, especially when teaching undergrads.

[@ss850624]

better than any other tutorial that i have found so far

[@sinansalameh]

I've been struggling with this concept until I found this video, thanks a lot, I hope you will consider making new videos.

[@DewyPeters96]

Funnily enough, this helped me with complex analysis even though your video is about real analysis.

[@raphile01]

Following on from the last video on sequences of numbers, my latest tutorial video looks at the convergence of sequences of functions. This topic is covered in one of the second year modules at Cardiff Uni (Analysis III). Many thanks to the module leader, Dr Karl Michael Schmidt, for lending me his course notes to help me prepare this video and also for reviewing the finished version. *Functional Sequences:* The notion of convergence requires a more precise definition when we are dealing with a sequence of real-valued functions, as opposed to a sequence of numbers. Two distinct types of convergence exist, which we refer to as pointwise and uniform convergence. A pointwise limit function can be identified by considering fixed points in the functional sequence's domain, but we may also be interested in the stronger notion of uniform convergence, under which the limit function retains important properties of the constituent functions in our sequence, including continuity and Riemann integrability. This video illustrates the concepts of pointwise and uniform convergence using diagrams and examples. Part 1: Functional Sequences (Part 1 of 2) Part 2: Functional Sequences (Part 2 of 2)

[@souadabumaryam2779]

wonderful !

[@divyaacharya8378]

Thank you so much. I really appreciate the graphical representation. It helped me to understand both the convergence very well.thanks a lot

[@olusoladehinsilu3014]

hello, thank you for your videos, they are very helpful. However, please, can you share the link to watch the previous videos "sequence of numbers"?

[@AdmCornFlake]

Ohhhh thank you for making this video. This is so much easier to understand that what my prof gives. It's really helpful that you give examples and nice concise pictures with each new definition as it really helps to understand the nature of the topic. My prof just gives the definitions and does proofs without many pictures or examples which makes everything seem overly complicated and abstracted when it's really not. I love that you also draw analogies to sequences.

[@PunitSedani]

As of now, 479views. 400 are Probably just me.. Best set of tutorials online! Thank you so much!

[@logio7663]

Damn, one of the best explanations I have ever seen .

[@jency9686]

It s my first u tube comment. This video s very useful. Thank u very much. Very precise and Gud presentation and gud language

[@mathsetc.]

Very best explanation for pointwise convergence and uniform convergence taken using simple and appropriate examples which so the difference diagrammatically.

[@praveenkumarbrathod7299]

It's really very useful sir and very clear explanation make more vedios on real analysis sir

[@hammadiazaiez9337]

man, you're example is amazing. thank you very much!!!

[@kaka-pb1zx]

The best explanation!!! Thank you so much!

[@pw7414]

you are an excellent math teacher

[@karimaddas7617]

excellent explanation. visual explanation is always the best

[@MonikaVerma-is1rd]

very very thanks to you . thank you so much for clearing my doubts.

[@tolgasnbl]

thanks for video, when i havn't found turkish video about functional sequences, i have found this video. my english not good but i have understood. Thank you very much!

[@RajivSambasivan]

Superb... amazingly clear presentation.

[@ss850624]

perfect tutorial i finally understood , thanks a lot , indeed,diagram teaching is easy to understand

[@tuongnguyen9391]

This is the best explanation !

[@ameyvedpathak634]

Thank you so much... such a clear explanation.

[@rahulsajee2553]

It made perfect sense. Thank you so much.

[@kevingrimes6658]

Beautiful, it made perfect sense. Thank you so much!

[@furkanakman2230]

Thank you! You are the best!!!

[@surfing_youtube]

Thanks a lot. This video was very helpful to me in understanding this concepts.

[@BusyBanana721]

This is a really clear explanation, thank you!

[@donzai9829]

Really helpful sir,Please do keep up the good work.

[@abdelrahmanzahran9697]

Amazing! thx alot. the best explanation i have ever seen!

[@Arneallan]

Yes! Finally I got it!

[@deloittedave3283]

How great! Do still post Dr?

[@xer_t3661]

wow thank you so much!!🙌👌 love to see more videos like this😃✨

[@isiyaramuthumuni4676]

So clear and love the examples, thank you so much :)

[@KuldeepSingh-wo4yl]

Well explained thnq Very much 👍👍

[@JOJOXXP4]

wonderful !

[@khoabangnguyensi5453]

Wonderful explaination

[@uncle_bae]

This is very helpful stuff. Thanks a lot.

[@speedbird7587]

awesome explanation thanks!

[@wahtsfgsgwwwsxq]

Very helpful.

[@mohamedbenali3069]

Excellente vidéo. Merci beaucoup !!

[@adamradekmartinez1536]

Very very clear.

[@eefanny]

That is a very nice explanation. Thank you!!

[@NabeelMustafaSMM]

extremely helpful

[@j0oe]

Wow Thank you so much! great examples and explanation..

[@mikisHaft]

Thank you for this lesson!

[@Andrei-ds8qv]

Dude, that wasa awsome! ty, you clarified so many things!! thanks;!!! VERY VERY GOOD EXPLANATION!!! CONGRATULATION!

[@wunks7]

I appreciate this. Thank you.

[@elmoad2055]

super clear thank you

[@begumozdemiroluk7525]

Thanks, it was really helpful.

[@feiwang9892]

very clearly!! Thank you very much!!

[@jeangavroche1956]

Team L3 luminyyyy on est laaaaa

[@jbergamp]

Rob for president!

[@johnathanmaximillian1877]

yes , but f(x) = x/n is uniformly convergent on a closed interval of R correct?

[@justadreamerforgood69]

No, it's just pointwise convergent

[@djsocialanxiety1664]

THANKS BRO

[@davud7525]

God bless you!

[@wobius]

great video!

[@aletsiko1128]

This is nice. Thanks a lot!

[@sumitw7]

Nicely done ..

[@SoukainaAmaadour]

Can you please upload a video about the Weierstrass function, that would be great.

[@FFV416]

Thank you so much

[@ieimagine]

Thankyou!

[@philippchristou6856]

φοβερός !

[@nebalsadek8881]

Thx sir 🙏♥️♥️

[@PRAKHAR1997ful]

thanks a lot .

[@leonardosoto5669]

very helpful video,some books are ok but leave some concepts in the air,others are terrible for people that arent going to study pure mathematics

[@hafezshirazi8567]

perfect,

[@assilchoukeir8892]

The definition of pointwisely conv is wrong

[@justadreamerforgood69]

It's right

[@gauravverma6608]

Aaah! Nice Nice

[@user-us9yy4jn4r]

explanation = hitting the bull's eye

[@andrear.2881]

da gara!

[@NabeelMustafaSMM]

extremely helpful

[@NabeelMustafaSMM]

extremely helpful