Note: At 4:10 that’s supposed to be the integral of x d(x^2), not dx. I am NOT calculating the integral of x dx, that’s why the answer is 2/3, not 1/2.
@drpeyam6 жыл бұрын
Omer Lublin Wow, that’s a great way of putting it!!!
@quickmath82906 жыл бұрын
Ah now I see it ... I am so sorry 😐
@willyou21996 жыл бұрын
xd(x^2) = x*2xdx = 2x^2dx = 2/3 x^3 What's the difference? This is like Riemann integrals but u-subbed.
@drpeyam6 жыл бұрын
Will You No difference for smooth alpha, but the approach I gave works as well for alpha that is not differentiable
@manimaran9685 жыл бұрын
@@drpeyam Thank you...
@brunomartinez50026 жыл бұрын
Your videos just keep becoming more interesting... this last month or so has been crazy! Keep up with your work!
@weltkaiserendzeit24175 жыл бұрын
is it me or is this guy very VERY happy to introduce us this integral ?
@johnteran8889 Жыл бұрын
I saw this Dr Peyem video in my search for "reimann stieltjes integrals" and immediately understood it would be exactly the video i was searching for.
@azzteke5 ай бұрын
What does "reimann" mean?
@ilyboc4 жыл бұрын
if only my teachers sound happy like you do :-)
@vangrails5 жыл бұрын
The German word Matjes comes from the Dutch word maatjes and means small hearings. Via adding the suffix "je" you can make a diminutive of a word in Dutch and the last s makes it a plural. But "Stieltjes" is a strange word/name even for Dutch people. The Dutch word stiel means craft but it is strange to make a diminutive of that.
@drpeyam5 жыл бұрын
This is awesome, thank you!
@azzteke5 ай бұрын
What is "hearings"? Nonsense!
@AndDiracisHisProphet6 жыл бұрын
The question is: How many of your viewers know what Matjes are?
@drpeyam6 жыл бұрын
Hahahaha, I was hoping someone would get the reference 😂😂😂😂
@AndDiracisHisProphet6 жыл бұрын
Well you have quite some german viewers, so q few would, I think^^
@blackpenredpen6 жыл бұрын
i dont...
@AndDiracisHisProphet6 жыл бұрын
You are good at math, but your german could use some polish^^
I love your videos! I saw this in an undergraduate-course-level Introduction to Measure Theory. Hardest course I've taken as an undergrad, and I remember the professor calculating this integral, as well as Lebesgue integrals, in the midst of Statistics and Probability. It was hard to get approved for this one! I will check your "Lebesgue Integral Overview" video.
@drpeyam6 ай бұрын
Thank you!!
@martinsanchez-hw4fi4 жыл бұрын
I have yet the doubt about the procedure in 9:06 in treating de differentials like numbers or fractions. I know the chain rule, though
@Gamma_Digamma4 жыл бұрын
Now I get it... The name was Rumple stieltjes skin
Thank you very much! You are very talented at transferring knowledge.
@lalitsharma8986 Жыл бұрын
What does this amount of integration means physii
@amanmahendroo17846 жыл бұрын
could you please do a tutorial on the inverse Laplace transform?
@drpeyam6 жыл бұрын
Flammable Maths Sounds like a job for you :)
@amanmahendroo17846 жыл бұрын
Dr. Peyam's Show thanks! amazing content though👍
@jesusalej14 жыл бұрын
Absolut capo! Total genius...
@camilosuarez97244 жыл бұрын
Super!!!! Thanks a lot, I really enjoyed it !!!!
@thedarkspeedninjashadittsux6 жыл бұрын
So could you do int xda(x), where a(x) = e^x?
@drpeyam6 жыл бұрын
int x (e^x)’ dx = int x e^x dx and then integrate by parts
@thedarkspeedninjashadittsux6 жыл бұрын
Dr. Peyam's Show Thanks!
@yuvalpaz37526 жыл бұрын
Great video! But, in 9:40 you said smooth, ain't it enough for alpha to be Differentiable? or it has to be smooth? also in the last example alpha is called RELU(rectified linear unit). Maybe you should do a follow up video and do integration by parts for Stieltjes Integral :). P.S. Do you know any good pure math books(for third year of uni or so)? preferably something with differential equations
@drpeyam6 жыл бұрын
Once differentiable is enough! I use smooth in a broad sense, as in “take as many derivatives as you need” (which may be 1 or infinity :P). Good idea, but I think that might just follow from the product rule (for once differentiable alpha). Oh, and I highly recommend the 4 books by Stein and Shakarchi, they’re a great introduction to post real analysis topics. And I also like the differential equation book by Hirsch/Smale/Devaney, and the PDE book by Evans
@yuvalpaz37526 жыл бұрын
The books are "Princeton Lectures in Analysis" series and "differential equation dynamical systems and an introduction to chaos"? I failed to find the last one. I'll look into them thanks very much, I'll probably start with the third book of "Princeton Lectures in Analysis"
@drpeyam6 жыл бұрын
Partial differential equations by Lawrence C Evans
@qiguosun1299 ай бұрын
anyone want to know applications can refer controlled different equations.
@rizkyagungshahputra2156 жыл бұрын
11:06 I think the upper bound should be 0(LHS)
@drpeyam6 жыл бұрын
It is, though, no?
@user-ph2jf4ji1j2 жыл бұрын
You are one awesome person.
@GabrielPohl6 жыл бұрын
Ooooh this is kind of about what i commented before of the diferential in the argument
@lunjapaobaite40715 жыл бұрын
Dr.payem... Sir can u make a video on malmsten's integral
@drpeyam5 жыл бұрын
Vardi Integral kzbin.info/www/bejne/jWO0d5uveMR1h5o
@ekueh6 жыл бұрын
Ito integral coming next lol
@stydras33806 жыл бұрын
That is A W E S O M E :)
@千里之行-z5r3 ай бұрын
thank you sir, keep going
@jesusalej14 жыл бұрын
Int(x da(x))=x a(x) - int(a(x) dx) is another simmilarity.
@zemania45353 жыл бұрын
Amazing, thank you!
@sandmann68516 жыл бұрын
I don't get 7:37. Why "2N³"?
@yoavshati6 жыл бұрын
When N approaches infinity, N(N+1)(2N+1) approaches 2N^3
@huehuehuehuehuehuehuehuehu47802 жыл бұрын
goat
@geraltofrivia9424 Жыл бұрын
Still yes
@mr.soundguy9682 жыл бұрын
Stieltjes was Dutch
@Franki-me3vc2 жыл бұрын
Stieltjes!
@mike.022 жыл бұрын
the meme now be real
@NaderKarimi936 жыл бұрын
You look cool :D
@kenichimori85336 жыл бұрын
0 ∫ 1 fobicult alphabet
@scruffysean36404 жыл бұрын
Dr. Peyam, you have a wonderful style. I wish more professors could have just a little of your enthusiasm. Glad I stumbled across your Stieltjes integral lecture!
@kenichimori85336 жыл бұрын
0 ∫ 1 fobicult alphabet
@riccardoagazzi12586 жыл бұрын
Use the CHEN-LUUUH!!!
@koenth23596 жыл бұрын
Riky Agazzi yeah great. It's from black pen red pen ISN'T IT?!
@blackpenredpen6 жыл бұрын
No, Dr. P started it! He's the original!
@koenth23596 жыл бұрын
blackpenredpen ok good to know, thanks!
@drpeyam6 жыл бұрын
blackpenredpen Technically Xuemin Tu started it 😂😂😂😂
@blackpenredpen6 жыл бұрын
Dr. Peyam's Show ahhhh yes!!!!
@hamsterdam19425 жыл бұрын
integral x d(x^2) = integral sqrt(x^2) d(x^2) = integral sqrt(t) dt = t^1.5*2/3 + C = x^3*2/3+C So answer is 2/3
@francescocostanzo82253 ай бұрын
Does this substitution work due to us being in the positive domain? Or would we be able to get complex solutions?
@EL-eo8dh6 жыл бұрын
It will be nice if you would like to have a talk on stochastic integral!
@bballfanmobile25445 жыл бұрын
I love saying “Stieltjes” too! 😂
@tylerwu6016 жыл бұрын
I really wanna see an introduction to contour integration. Complex analysis is always so much fun to me.
@thisismycoolnickname6 жыл бұрын
Interesting. I've always done this trick called "put smth under the differential". And it has always made perfect sense because it's the same as applying the chain rule backwards. And now I am surprised that there is some additional definition to this integral.
@hishan.farfan6 жыл бұрын
Excellent video as always! could you make one about stochastic calculation please?
@nei28706 жыл бұрын
I didn't know the Dr. Peyam had a channel Instantly subscribed
@shiina_mahiru_90676 жыл бұрын
Well, the name of the integral seems weird at first, but it turns out that, it reminds me the way my teacher taught me to avoid using u-sub. For example, let's say integral (ln x / x dx). Instead of u-sub, my teacher taught me to turn it into integral (ln x d(ln x)) = (ln x)^2/2. I really did not think there is a proper (and awkward) name for such an integral!
@guilhermeguimaraes18586 жыл бұрын
How did u do that ? How do u change dx to d(ln x) can u please explain me ?
@shiina_mahiru_90676 жыл бұрын
d(ln x)/dx = 1/x, so d(ln x) = 1/x dx. That's how my teacher taught me.
@guilhermeguimaraes18586 жыл бұрын
WOw dude ! TYVM ! This is amazing, can be quite helpful with some trick Riemann Integral !...
@badrunna-im6 жыл бұрын
Guilherme Guimarães not really. The premise is still the same as substitution, just less explicit. By letting u=ln x, you're trying to integrate with respect to d(u) (normal substitution) = d(ln x) (the above technique).
@skylardeslypere99093 жыл бұрын
My teacher did the same thing. But, by then I already knew substitution because of youtube videos so I never liked that method
@MrCigarro506 жыл бұрын
Thank you very much. For us, statisticians, this video is very important. We know you go to great lengths to produce this videos and we appreciate it.
@link_z6 жыл бұрын
Thanks for this video. I understand how this kind of integral works but I fail to understand how it could be useful.
@drpeyam6 жыл бұрын
It’s very useful in statistics, but I don’t think it’s used much in math, since the Lebesgue integral is much better! But still, a nice generalization of the Riemann integral
@link_z6 жыл бұрын
Thanks for your fast answer Mr. πm :) Understood!
@povijarrro6 жыл бұрын
Dr. Peyam's Show And Lebesgue-Stieljes integral (instead of (b-a) as the measure of interval (a,b) take (alpha(b)-alpha(a))) is the best
@MrCigarro506 жыл бұрын
In Statistics we use it for ignoring the difference between continuous and discrete random variables. It allows us to express in a close simple form distribution functions and functions of distribution functions (namely Expected values, variances,...etc) that otherwise would be cumbersome. Lebesgue Integral is far more beautiful, elegant,...but things there get far more complicated. You can see Doctor Peyam´s videos about that. He has done a great job for us.
@blackmagicsuiteopus95454 жыл бұрын
Hi, im 2 years late. I've just discovered this integral when studying QM. It is used in the spectral decomposition of general self-adjoint operators, the measure being an orthogonal projector, function of the eigenvalue of the operator.
@mariaguthier10665 жыл бұрын
I love how math excites you, great video! Please keep with the great work!
@yakov9ify4 жыл бұрын
We actually learned this integral instead of a reimann integral in my analysis class, quite challenging but very satisfying when you actually understand it.
@vpambs1pt6 жыл бұрын
What's the purpose of this integral? The result is different from the riemman integral, what does that 2/3 mean?
@Sanntik6 жыл бұрын
I kind of prefer the blackboard, black shirt and the chalk all over it haha! anyway, still awesome :D
@justwest6 жыл бұрын
Very nice! A geometric interpretation would have been very nice, or why we would want alpha to be something else other than just x. You mentioned statistics and blah, maybe it's just not so easy to give easier, practical examples.
@drpeyam6 жыл бұрын
Yeah, I can’t really think of a more practical application, since mathematicians mainly use the Lebesgue integral anyway. But I’m guessing that if you want your integral to emphasize the point 0 more, you’d use alpha(x) = x^2 instead of x, but I agree, it’s more of a statistical thing
@hheg27276 жыл бұрын
Sometimes it can be a nice way to write substitutions. For example in spherical coordinates you integrate over sin(theta) dtheta or even nicer dcos(theta)
@MrR3KK5 жыл бұрын
I found this in a text about creep law for uniaxial stress in viscoelastic materials.
@LS-Moto6 жыл бұрын
Du bist der BESTE 😀
@drpeyam6 жыл бұрын
Danke!!! :D
@quickmath82906 жыл бұрын
Ah noch ein deutscher der Mathe süchtig ist 😂
@nullplan016 жыл бұрын
How do you know he's German? Because he speaks the language? Because then I'm a processor!
@LS-Moto6 жыл бұрын
nullplan01 Who claimed that he is German? I don't see anyone? To my knowledge, I believe to have heard he was born in Austria and was educated in a French school. What citizenship he holds is unknown and irrelevant to me. I'm just asking if he would feel like making some Math Videos of this kind in German because: 1. there aren't a lot of good German math channels and 2. His German is very good and I'm sure it could be fun.
@ralfbodemann15426 жыл бұрын
Awesome video, thanks! Your performance is much better when you don't use any notes.
@ralfbodemann15425 жыл бұрын
Excellent video! You should do more videos without holding your notes in your hands. The viewers can better connect to you.
@presidentatabaki6 жыл бұрын
Gay and happy
@Ritsu-qz3pe4 жыл бұрын
How delightful lecture it is
@johan.de.matan.4 жыл бұрын
Haven't got what's difference between this nicely-named integral and making simple substitution. I was tought that some intergrals can be much easier solved by making impicit substitution kind of: f(u(x))u'(x)dx = f(u(x))d(u(x)) We named it "put under differential" Have using this for a long time without any think that it has its own name, and moreover, is more generilized then Riemann intergal
@partisano756 жыл бұрын
thanks for post it, dear Dr Peyam, for some students is unknown, today i've learned from you... greetings for you.
@Rawan-rq4rg2 жыл бұрын
Mr Peyam First I want to thank you because this video has helped me very much I want you to talk about Hadamard integral next time
@Uni-Coder5 жыл бұрын
For me, it is "still tears"
@irvinep5 ай бұрын
can you please make me understand what do you mean by "taking x and stretching out with x^2". I am trying to understand the picture of this integral
@gelegar50483 жыл бұрын
Estoy aquí porque es el único video con un ejemplo así, con una integral de Riemann Stieltjes a partir de la definición de sumatoria (casi todos usan el teorema del cambio de variable y el del cambio de la derivada de la función integrante). Y es que hice el ejercicio de integrar x^2 con alfa x^3 en el intervalo [0,1]... Y si, me salió como en el vídeo (aunque hice diferente el "prework", pero igual llegué al resultado)... Por cierto, sale 3/5!!!!!!
@drpeyam3 жыл бұрын
Muy bien!!! 😁
@duncanw99016 жыл бұрын
Are there any other high school students here?
@sidharathsharma61975 жыл бұрын
I feel lucky to come across your videos on youtube!
@lalitsharma8986 Жыл бұрын
Like integration means the area under the curve what does riemann stieljes integral means physically
@michelkhoury14705 жыл бұрын
Doctor, I remark that Riemann integral is a particular case of Lebesgue integral. Am I right?
@drpeyam5 жыл бұрын
More or less, at least for a finite closed interval [a,b]
@drpeyam5 жыл бұрын
There’s a video on Riemann vs Lebesgue Integral actually!
@michelkhoury14705 жыл бұрын
Okay thank you doctor Peyam :)
@reminasashes69306 жыл бұрын
Would a substitution also work? For example, integral of x d(x^2) from 0 to 1. We set y=x^2, so x=y^1/2. That means we have the integral of y^1/2 dy, from 0^1/2 wich is 0, to 1^1/2 wich is also 1. Integrated that would be (2/3)y^3/2 evaluated from 0 to 1, wich would also be 2/3. Am i right, or is it a coincidence?
@drpeyam6 жыл бұрын
Yep, if alpha is smooth, then it’s substitution, but this method also works if alpha is not differentiable!
@muuganesan1185 Жыл бұрын
You didn't give any interpretation and illustration about alpha x. Please do that.
@armandobuzzini91716 жыл бұрын
genial
@NAMEhzj6 жыл бұрын
Hey Dr. Peyam, great video as usual! But i was wondering why you said the Stieltjes Integral was less general than the Lebesgue Integral. In our lecture we defined the lebesgue integral via first defnining a Lebesgue pre-measure, then extending that to the Lebesgue-measure and then defning an Integral by any measure. We also defnied a "Stieltjes-pre-measure", so i would imagine if you would extend that to a measure in the same way you could define the Stieltjes-integral with that and you would have something thats definitely more general, because the Lebesgue-measure is just the special case alpha = x. Or is that going to lead to problems in some of the nice proofs?
@drpeyam6 жыл бұрын
Since a Stieltjes pre-measure is a special kind of pre-measure, the Lebesgue integral is more general, since it works for any kind of pre-measure, not just the Stieltjes one! Also by Stieltjes Integral I’m referring to the one in this video, where I’m presenting it the Riemann way (it’s sometimes called the Riemann-Stieltjes integral)
@NAMEhzj6 жыл бұрын
Ah that makes sense. Thanks :)
@thomaskim53943 жыл бұрын
Where did you get the square for i instead of just i? Also how did one become i?
@quickmath82906 жыл бұрын
Have a question : what is this useful for because normaly the answer to this integral with dx is 1/2 but you got 2/3 so how could you solve some integral with this technique to get the normal dx answer ? I feel kind of uncomfortable with this
@drpeyam6 жыл бұрын
It’s not very useful in math, but apparently more useful in statistics. I don’t think you can use Stieltjes integrals with alpha to solve integrals with dx.
@quickmath82906 жыл бұрын
Dr. Peyam's Show thanks I feel better now 😂 but it's nice to do some math for fun
@camrouxbg2 жыл бұрын
What is the motivation for doing this type of integration?
@권땡아3 жыл бұрын
thank you so much😭 from Korea
@reeeeeplease11782 жыл бұрын
11:27 thats not discontinous :P
@elgazeta2 жыл бұрын
Dr. Peyam you and math are amazing
@joseluisarmenta5 жыл бұрын
the are a errro in f(x_i) is diferent yo x_i
@quickmath82906 жыл бұрын
You forgot to put d alpha x in the integral at first this kind of confused me
@drpeyam6 жыл бұрын
Well yeah, that was on purpose; I wanted to show how the Riemann integral and the Stieltjes integral are similar!
@quickmath82906 жыл бұрын
Dr. Peyam's Show i ment at minute 4:10 ... sorry I love your work its no criticism or am I wrong
@drpeyam6 жыл бұрын
QuickMath My bad, you’re right! That’s what I get for improvising 😂
@Sad-mm8tm2 жыл бұрын
love your energy
@sundayolabisiodeleye90716 жыл бұрын
Is Stieltjes integral the same thing as Reimann Stieltjes integral?
@drpeyam6 жыл бұрын
Yes
@sundayolabisiodeleye90716 жыл бұрын
Is Stieltjes and Reimann Stieltjes integral the same?
@drpeyam6 жыл бұрын
Yes
@DylanD-v9g Жыл бұрын
Thanks for the video. What is the difference between the Stieltjes integral and the Riemann-Stieltjes Integral?
@drpeyam Жыл бұрын
Same I think!
@sundayolabisiodeleye90716 жыл бұрын
Sir! Kindly help me find the value of ∫(x^5 d(x^2 ) where x is from -2 t0 3
@drpeyam6 жыл бұрын
Integral from -2 to 3 of x^5 times 2x dx where
@hausinchiu55255 жыл бұрын
Convert x^5 into (x^2)^(2.5) so the integral will be in the form t^2.5 dt , use the power rule backwards
@SupriyoChowdhury5201 Жыл бұрын
Sir does alpha(x) need be a continous monotone function for it to work?
@drpeyam Жыл бұрын
Not continuous, I think right continuity is enough
@adityaekbote84982 жыл бұрын
So cool both the video and the integral hehe Other videos never give me this kind of intuition as much as your videos give Dr.P And now that I have made it a ritual: noice
@umairfarooq58623 жыл бұрын
Sir do you have playlist for this topic
@drpeyam3 жыл бұрын
Yeah it’s called Real Analysis
@stabulo2 жыл бұрын
They have this same problem in Advanced Calculus by David V. Widder. I thought I recognised it haha.
@drpeyam2 жыл бұрын
Oh wow, really? What a coincidence :O
@stabulo2 жыл бұрын
@@drpeyam If interested out of curiosity see page 153 of the second edition. I just recognised the 2/3 in problems I did in similar content.
@hheg27276 жыл бұрын
In general you can use integration by parts and get: Integral from 0 to 1 of x da(x) = a(1) - Integral from 0 to 1 of a(x) dx
@rubus922023 жыл бұрын
Should alpha(x) at least monotone ?
@drpeyam3 жыл бұрын
Yeah something like that, and left continuous
@stydras33806 жыл бұрын
Dr Peyam did you read your personal messages? :P I've left one :3
@gigispence60113 жыл бұрын
Your enthusiasm made me really happy to study RS integrals
@leif10754 жыл бұрын
Why do you multiply i/n times the squared terms?
@elenag.224 Жыл бұрын
Thank you professor!
@michelkhoury14705 жыл бұрын
Very nice problem
@harisimer6 жыл бұрын
Aber das ist doch garnicht gleich dem Riemann - Integral oder wie muss ich das sehen? int_0^1 x dx = 1/2. Riemann and Lebesque calculate for the area under the curve 1/2, which area is given by Stieltjes with 2/3?
@drpeyam6 жыл бұрын
Tut mir Leid, aber in diesem Video rechne ich die Integrale von x d(x^2), nicht x dx, darum ist die Antwort 2/3, nicht 1/2
@harisimer6 жыл бұрын
but what area describes that? or isnt there a visualization?
@drpeyam6 жыл бұрын
It’s the area under x, but where your axis becomes x^2, so think like bending your axis to become x^2.
@dlevi676 жыл бұрын
If I understand what is happening correctly, more than bending this is stretching (or "modulating" - given alpha could be anything, not just a monotonic function!) the x axis itself. [This is almost (again if I understand this correctly) like a double integral, except that rather than integrating the same function twice with respect to two variables we integrate once with respect to two "simultaneous" functions in the same variable. But I may have misunderstood the concept completely!]
@armandobuzzini91716 жыл бұрын
el diferencial de la integral no es dx, sino el diferencial de una funcion. en este caso una parabola