Distributions 10 | Distributional Derivative

[@StratosFair]

Yayyy, good to see a new upload in the more advanced math series :))

[@brightsideofmaths]

More to come in the future :)

[@benmustermann2045]

Saw it the first time in stat mech and thought yeah I guess it makes sense that the delta distribution should be the derivative of the heavyside but this is of course much more lucid

[@brightsideofmaths]

Thanks :)

[@aziz0x00]

Hi, honestly thank you so much for the videos, learned alot from your channel!

[@brightsideofmaths]

Glad you like them!

[@ujjwalmishra492]

Please continue this playlist and also cover Sobolev Space.

[@mudassirmudassir2944]

Thank you sir for access the lectures of distribution theory

[@brightsideofmaths]

You are very welcome!

[@riyadboudjani3895]

Hello ! First the serie is insane thank you a lot ! I have a question : during the serie and in this episode also you define property of distribution with nice function with good property then you apply this properties to all function. Exemple: To define the derivative of a function in this video you use f a C1 function but then you use the derivative define previously for all the function If you can do that, why can you ? Thank you for reading and for the videos :))

[@brightsideofmaths]

Hello and thank you very much for your support! I don't get your question, maybe. We have the space of test functions which consists of C-infinity functions.All this functions are very nice and that's the reason the definitions work.

[@riyadboudjani3895]

​@@brightsideofmaths Excuse me that was not very clear ^^ In this video you show that , but you show that for a regular distribution, so why you can use this definition on the dirac distribution who is not a regular distribution ? I miss something ?

[@brightsideofmaths]

It's simply the definition :)

[@riyadboudjani3895]

@@brightsideofmaths Okaaaaay the motivation help to define the general definition :) Ty a lot and have a good day !!

[@mudassirmudassir2944]

Sir if you don't mind these lectures are from Gerrit van Dijk book

[@brightsideofmaths]

Sorry, I don't know this book. Can you be more concrete what you mean?

[@mudassirmudassir2944]

@@brightsideofmaths actually sir their is a book of distribution theory(written by Gerrit van Dijk) that will be studying me in my M. Phil program and for that purpose I can take help from your lectures

[@brightsideofmaths]

That sounds very good :) Thanks!

[@TheXterminator4]

How many more videos are you planning to make for distributions!? Thank you for this video, very helpful again:)

[@brightsideofmaths]

I planned around 20 videos.

[@nicolassoderberg9477]

@@brightsideofmaths Are there more videos available on Steady (or elsewhere) or do you upload them everywhere at once?

[@brightsideofmaths]

@@nicolassoderberg9477 They will be published first on Steady. However, at the moment, there is no new video there. It will come soon :)

[@nicolassoderberg9477]

@@brightsideofmaths Okay, cool. I really like your teaching/video style. I was introduced to distribution theory during my undergraduate and found it really interesting. Now I’m taking it as part of my masters degree and unfortunately it is taught in a completely different way than how I was introduced to it and it doesn’t feel even remotely as engaging. But your videos are in line with how I was introduced to the subject so I’m super happy that I found them. I’ll just hope that as many more videos as possible get released before my exam in August 😅

[@pascal3458]

🔥🔥🔥

[@mudassirmudassir2944]

Please sir upload more videos

[@brightsideofmaths]

Deal!

[@mudassirmudassir2944]

Sir why you can hidden the eight video lecture of distribution theory.

[@brightsideofmaths]

@@mudassirmudassir2944 They will come.

[@mudassirmudassir2944]

​@@brightsideofmaths please sir

[@pacchutubu]

Hello, thanks for this series. They really accelerated my understanding of distributions. I have a question regarding the definition of Distributional derivatives. @5.04 you say about the motivation for the definition of Distributional derivatives. But I am not able to find the relation of the definition with the previous discussion . What is bothering me is, since T is a functional, it's derivative should also be taken like any functional ( en.wikipedia.org/wiki/Functional_derivative#Functional_derivative ), but instead what is done here is the distribution of derivative of it's function. To conclude I don't know how T'f = Tf'

[@brightsideofmaths]

Simply speaking: we define the distributional derivative and not the functional derivative.

[@pacchutubu]

@@brightsideofmaths oh ok, this is something else. Thanks