Distributions 1 | Motivation and Delta Function

[@christopherwashington9448]

Thank u for the English version!

[@juaniribas4625]

This video is absolutely eye-opening. It helped me a lot on my bachelor project, thank you for so much.

[@brightsideofmaths]

You're so welcome!

[@mohammadabdulla8601]

One of the best Mathematics channels 👌 .

[@wojciechartichowicz1330]

Your videos are like a good tv series. I just can't wait the next episode!

[@davidawakim5473]

You're an angel on this Earth

[@ajaygunalan1995]

OMG! You saved me! Thank you so much for it.

[@aaronm8248]

You da man BSOM!

[@richardzhou2659]

This is awesome! I'm learning about distributions atm--do you have any sort of schedule you're following?

[@chirantanbiswas9330]

Heaviside's parents must have seen the future to have given him the appropriate name. Funny though, how Heaviside function has a heavy side.

[@paulgraf1979]

Awesome, as usual.

[@marymath6313]

Finally a thing in Distributions

[@davidfmendiola2009]

thank you very much for this series :) (y)

[@mythicmansam1082]

Thank you for the wonderful content!

[@BraianDeLeon]

Thank you so much for sharing!

[@freaxlover]

Thank you, mate!

[@JLseries]

I appreciate you so much!

[@alphamf0]

Hello, just a quick clarification: at 6:55 you say that you use the test functions to "measure" the value of the f function, but how exactly do we do so? Should we not need for the test function to have some sort of unitarity so that when multiplied by the f function it gives back a "measure"?

[@brightsideofmaths]

Yes, you can do that. The important thing is just that you know the test function very well when you use for "testing" the unknown function f.

[@douglasstrother6584]

"WHO INVENTED DIRAC'S DELTA FUNCTION?" by Mikhail G. Katz & David Tall Abstract: The Dirac delta function has solid roots in 19th century work in Fourier analysis by Cauchy and others, anticipating Dirac's discovery by over a century.

[@Winium]

actually, dirac sent anti-information back in time to tell cauchy to start his homework for him.

[@NoNTr1v1aL]

Amazing!

[@DiegoAToala]

Thank you , great video

[@numb2023]

Hi, I had a question. I remember (maybe I am making mistake) we can use the fundamental calculus theorem if that function is cont. in the given interval but here \delta is not cont. at zero! Is it op to use that theorem? I'm mentioning the place we calculate \int_{-\epsilon}^{\epsilon}\delta =1 ! Thank you! It was great as always!

[@brightsideofmaths]

Yes, the ordinary fundamental calculus theorem is not applicable here :)

[@user-ke2vh7vf6u]

in which sense the region of measurement is given by the test functon? phi itself could be considered as a density, so we are calculating the mass in a bar, long as the support of phi, using the density f multiplied by a density of phi, as if we are dilating the density f with phi. Why not to use a characteristic function instead of phi? Of course it is not a proper test function (it isn't C-infinite) but if so, the analogy with the mass distribution wouldbe wrong, unless we consider phi as a "zoom" of the bar, as if we want to dilate the density f intentionally.

[@brightsideofmaths]

You are completely right: Also a characteristic function would do the job of a measurement. However, because we want to do analysis later, we will smooth the sharp edges there and a get a test function as we want.

[@sebastienmartin5183]

Brilliant ! Thank you :)

[@brightsideofmaths]

Glad you liked it!

[@lucaolmastroni6270]

Hi, could you please tell me why the only language available for subtitles is a transcription of the english spoken text interpreted as if it was german language ? Thank you

[@brightsideofmaths]

I change that!

[@ishisanuzumaki5136]

Character In the video It's great, I like it a lot $$

[@ichkaodko7020]

i was expecting the distribution of probability theory. Good to know that there is other "distribution" in math.

[@brightsideofmaths]

Yeah, "distribution" can mean different things in maths.

[@JONASACHUOBIMaths]

please , can you recommend a nice text on the theory of distribution?

[@brightsideofmaths]

There are a lot of books about distributions. What does you want to learn first? :)

[@JONASACHUOBIMaths]

@@brightsideofmaths i want to take a course on non linear PDE.

[@zazinjozaza6193]

Very cool

[@mnada72]

Hi again, which is good to start with the measurement theory or the distribution theory?

[@brightsideofmaths]

Measure Theory helps but it is not necessary :)

[@secretsecret1713]

Why derivative exist for H function if by definition of derivative, left nd right derivatives are not same. Then why does this derivative still exist? Take for example function f(x)={x, x< 1, x+1, x>=1} then does this mean that derviative at x=1 for this function is delta function?

[@brightsideofmaths]

We will not use the classical derivative :)

[@secretsecret1713]

@@brightsideofmaths then what do you mean by non classical one? I mean for function i provided will "general" derivative still exist?

[@brightsideofmaths]

@@secretsecret1713 I mean, the whole series here is about generalising derivatives and functions. I soon will continue the series :)

[@nininounou5078]

can't thank u more...

[@meryamzaghari7523]

Can you make the substitles ..

[@briancannard7335]

Reminds correlation and convolution.

[@SantiagoGonzalez-wy4vx]

I love thisss

[@brightsideofmaths]

I see what you did there ;)

[@depressedguy9467]

Please suggest a book for this

[@brightsideofmaths]

If you can read German texts: Walter: Einführung in die Theorie der Distributionen

[@depressedguy9467]

@@brightsideofmaths any English text

[@brightsideofmaths]

This is harder. Maybe try D.S. Jones, "The theory of generalized functions"

[@depressedguy9467]

@@brightsideofmaths i will try

[@Hippowdon121]

VS Vladimirov Methods of the theory of generalized functions

[@memomemo7341]

thank u so much teacher , can you please add more videos concerning distribution theory ?

[@brightsideofmaths]

Thank you very much! Of course, they will come :)

[@ericchen115]

I really understand the meaning of the distribution through the fundamental solution of the heat equation 😂

[@wellingtonsobrinho5421]

How your references?

[@brightsideofmaths]

Walter and Rudin.

[@riccardobova6738]

You talked about densities and distributions. Is there any relation between distribution theory and the concepts of probability density function/probability distribution function? P.s. Thanks a lot for the free content!

[@brightsideofmaths]

Firstly, they are completely different concepts that just share a name by coincidence. However, on the second look, you might find a lot of connections.

[@angelmendez-rivera351]

There is not a direct relationship between distribution theory and probability theory. However, in so far as you can connect both to measure theory in some strong and meaningful ways, there is some minor correlation between the two. For the most part, though, this is just a naming coincidence, and they do constitute entirely different concepts of study.

[@bouchaibchakouri7970]

we need it withe french's language

[@brightsideofmaths]

My French is not so good, sorry.

[@vilasminamdar]

"Theory of Distributions for Structural Engineering problems" ISBN - 13: 978-3844302448. I have illustrated many examples on Delta Function, Unit step function, Signum function in structural engineering. Additional complementary function for differential equation in presence of Discontinuities developed. This is without rigorous mathematics.