Oh no! An army of Dark Beings led by *Ansem, Xemnas, and Master Xehanort* is forcing me to join its cause! Upvote this comment and subscribe to my channel in order to help me use the power of FRIENDSHIP to banish these nefarious evildoers whence they came!
@@Silver_G Because I referenced the χ-blade towards the end of the video. But if you don't like these KH references, then perhaps you should focus inward and let your heart be your guiding key!
I just recently started watching your videos on complex variables so I could better understand the derivation of kramers-kronig relations myself. This is the perfect video to wrap everything up for me. Your videos are great, thanks for posting them.
Your channel is great! Thank you very much for increasing the frequency of posting new videos! Are you planning to create a sequence on topology? That would be awesome!
Great video! I have one quesion. At time = 3:07, you introduce the contour integral over Chi/(z-a). Why this integral? what motivates it? how do you know that this integral i needed to start the derivation?
I have a question that has been bugging me for quite a while. Why the the function has to be analytic in the upper half plane? Why it cannot be analytic in the lower half plane as well? or analytic in the whole domain?
Thank you very much for the video, this is the best explanation I found on a complex and fascinating topic. I've just a question: at the end of the video, when you equate imaginary parts to write the second Kramer-Kronig relation, shouldn't we have x_1(z) inside the integral? Otherwise I'm missing something
Hi, I was just wondering how you could use Jordan's lemma when there's no guarantee that X(z) is in the form of exp(iaz)*g(z). I accept that the integral is zero but not because of Jordan's lemma. By the way, you shouldn't put the negative sign for the inequality of the magnitude of Xprime, and a typo in the last line you wrote :) Thank you.
Hi Faculty of Khan, long time fan of your videos. I am just wondering which drawing/notepad application you use in your videos? Any help would be appreciated.
If it's any consolation, I always thought "Chi" was pronounced "Chai" like the "chai" in "Chai tea" :/ Swear to god the look of my statistics professor in office hours when I asked her about the "Chai/Chi square test"... Anyway, thanks for covering this. I never got to it in my complex analysis course, does this appear more in "grad-level" textbooks? If so, which ones?
Oh, also going to take a wild stab and ask, does this have any connections with harmonic analysis? My guess is obviously it's deeply related, but just thought I'd ask. Can't find anything on wikipedia yet...
Hahaha that's somewhat reassuring :P And yea this is more of a grad-level topic. Typically you'd see something like this discussed in an upper-year (like 3rd-4th year) or grad level Physics course though. For instance, you can see these relations come up in Jackson's Classical Electrodynamics, which is an upper-level text.
@@ummwho8279 I haven't gone that deep into Physics, but I'd imagine there's a relationship. Harmonic analysis comes up in electrodynamics and optics, which the Kramers-Kronig relations also show up in. There's also the Hilbert Transform (which is one of the link that shows up on the Kramers-Kronig wiki), which explicitly relates a function to its harmonic conjugate (and is very closely connected to the Kramers-Kronig relations): en.wikipedia.org/wiki/Hilbert_transform
@@FacultyofKhan I see. Many thanks for the reply. Good thing a friend of mine has a copy, I don't think they publish the Jackson's Classical ED anymore. I also saw the link to Hilbert transforms and Sokhotski-Plemelj theorem, I just thought there'd be a more explicit sentence, perhaps along the lines of "for the relationship between harmonic analysis and K-Krelations, see here". Anyway thanks again. You do amazing work as always. Hope medical school is treating you well!
It is an empirical fact that English speaking people have no feeling for non-English languages. I laugh my socks off when I hear them pronounce the names of De Broglie and DeBye, haha.
Oh no! An army of Dark Beings led by *Ansem, Xemnas, and Master Xehanort* is forcing me to join its cause! Upvote this comment and subscribe to my channel in order to help me use the power of FRIENDSHIP to banish these nefarious evildoers whence they came!
Just why the f there is a Kingdom Hearts reference LOL
@@Silver_G Because I referenced the χ-blade towards the end of the video. But if you don't like these KH references, then perhaps you should focus inward and let your heart be your guiding key!
Yes I do not like it but *I love it* (I am a die hard KH fans LOL)
Just feeling shocked as someone seldom find a KH reference in a math video😂
I just recently started watching your videos on complex variables so I could better understand the derivation of kramers-kronig relations myself. This is the perfect video to wrap everything up for me. Your videos are great, thanks for posting them.
This video is bloody helpful! Thanks from Japan
Most helpful Video on this Topic I found!
This video is great! It is encouraging me to study Complex variables even deeper! Thanks for an amazing content!
That was a great watch, thank you for the work you put into this. It was very understandable, nicely paced and well explained at all times!
Please continue these videos! 10/10 as usual.
Your channel is great! Thank you very much for increasing the frequency of posting new videos! Are you planning to create a sequence on topology? That would be awesome!
Thank you! As for topology, I'm not planning to do it in the immediate future, but I will once I get through more Real Analysis!
Thank you so very much from NM, USA.
Honestly, your kai pronunciation irritated me a bit but I love that you knew what I felt and commented on that. You are very considerate!
Fantastic video as always!
Great video! I have one quesion. At time = 3:07, you introduce the contour integral over Chi/(z-a). Why this integral? what motivates it? how do you know that this integral i needed to start the derivation?
Great. Thank you
The kh reference during a 4am math video binge really took me by surprise 😂
I have a question that has been bugging me for quite a while.
Why the the function has to be analytic in the upper half plane? Why it cannot be analytic in the lower half plane as well? or analytic in the whole domain?
Thanks a lot for your explanations. May I ask you the physical meaning of this relation in terms of causality?
Ralph Kronig was my great grandfather
Who asked?
Super helpful, thank you
Nicely done
amazing video sir...very helpful
Thank you very much for the video, this is the best explanation I found on a complex and fascinating topic. I've just a question: at the end of the video, when you equate imaginary parts to write the second Kramer-Kronig relation, shouldn't we have x_1(z) inside the integral? Otherwise I'm missing something
Yes.
Hi,
I was just wondering how you could use Jordan's lemma when there's no guarantee that X(z) is in the form of exp(iaz)*g(z). I accept that the integral is zero but not because of Jordan's lemma.
By the way, you shouldn't put the negative sign for the inequality of the magnitude of Xprime, and a typo in the last line you wrote :)
Thank you.
Hi Faculty of Khan, long time fan of your videos. I am just wondering which drawing/notepad application you use in your videos? Any help would be appreciated.
If it's any consolation, I always thought "Chi" was pronounced "Chai" like the "chai" in "Chai tea" :/
Swear to god the look of my statistics professor in office hours when I asked her about the "Chai/Chi square test"...
Anyway, thanks for covering this. I never got to it in my complex analysis course, does this appear more in "grad-level" textbooks? If so, which ones?
Oh, also going to take a wild stab and ask, does this have any connections with harmonic analysis? My guess is obviously it's deeply related, but just thought I'd ask. Can't find anything on wikipedia yet...
Hahaha that's somewhat reassuring :P
And yea this is more of a grad-level topic. Typically you'd see something like this discussed in an upper-year (like 3rd-4th year) or grad level Physics course though. For instance, you can see these relations come up in Jackson's Classical Electrodynamics, which is an upper-level text.
@@ummwho8279 I haven't gone that deep into Physics, but I'd imagine there's a relationship. Harmonic analysis comes up in electrodynamics and optics, which the Kramers-Kronig relations also show up in. There's also the Hilbert Transform (which is one of the link that shows up on the Kramers-Kronig wiki), which explicitly relates a function to its harmonic conjugate (and is very closely connected to the Kramers-Kronig relations): en.wikipedia.org/wiki/Hilbert_transform
@@FacultyofKhan I see. Many thanks for the reply. Good thing a friend of mine has a copy, I don't think they publish the Jackson's Classical ED anymore. I also saw the link to Hilbert transforms and Sokhotski-Plemelj theorem, I just thought there'd be a more explicit sentence, perhaps along the lines of "for the relationship between harmonic analysis and K-Krelations, see here". Anyway thanks again. You do amazing work as always. Hope medical school is treating you well!
Educater name? ??
This guy is crazy
Wow, such a great explanation on the topic. #becoming-a-patreon
It is an empirical fact that English speaking people have no feeling for non-English languages.
I laugh my socks off when I hear them pronounce the names of De Broglie and DeBye, haha.
Nice video! But Cauchy is pronounced as ko-shee, not kow-shi :-)
Huh?