Mod-02 Lec-04 Calculus of residues (Part II)

Selected Topics in Mathematical Physics by Prof. V. Balakrishnan,Department of Physics,IIT Madras.For more details on NPTEL visit nptel.ac.in

[@ozzyfromspace]

Using the keyhole contour to “change” the pole you’re evaluating around is actually a really good idea. Amazing technique, I’m learning so much from you, Professor Balakrishnan 😭🙏🏽🎊

[@MrAAMNNITAllahabad]

It's a very standard approach, you can find that on Gamelin. You're finding it new because you ain't read the book at first place.

[@supern0is349]

holy fuck this guy is a beast.It's like he knows everything in physics, mathematics and so on.

[@ozzyfromspace]

Ladies and gentlemen, you are witnessing a very beautiful mind ❤️💯😭🎊🙏🏽

[@prasadmanic]

last thing was so awesome, i literally laughed. Thank you sir. Endrendrum Venkatraman Balakrishnan!

[@pramod120895]

Endrendum balki... Nice to see tamil comment

[@dalitshiv834]

જય સોમનાથ મહાદેવ

[@dalitshiv834]

Why you Laugh? What was so Funny at the End?? I was whole Lecture

[@ozzyfromspace]

I really hope the students in his class appreciated this wonderful lecture

[@dalitshiv834]

Where are you from?

[@ozzyfromspace]

@@dalitshiv834 I'm originally from Zambia, grew up mostly in Botswana, and have lived in the US for about 7 years now :) Professor Balakrishnan is easily one of my favorite lecturers, right up there with Prof. Strang from MIT :)

[@Unexpectedthings007]

@@ozzyfromspace IITIANS ARE MORE WORRIED ABOUT EXAM RATHER THAN ENJOYING LECTURES MAN HAHA

[@shanecarlson7488]

Holy shit this guy is good

[@henrywang6931]

Holy shit I was just thinking about that!

[@ANOLAMCA122]

Holy shit I cannot believe it that I just did it.

[@arunmondal2287]

Holy shit holy shit

[@dalitshiv834]

America

[@nirmalmondal8269]

I feel very bad that why i don't understand from this genius teacher.

[@elamvaluthis7268]

Very excellent.

[@jaskarandeepkaur2278]

But this would mean the residues of these two poles at the 0 and 1 are equal in magnitude isn't it??

[@ozzyfromspace]

Question: he defined an arbitrary generating function using polynomials like z^n. Are we permitted to go with another basis of our choice? It looks like a data-fitting problem to me. Thanks for any answers.

[@GHOSTrex1324]

That was Taylor series of any arbitrary function. As any analytic function would have one so one can assume that.

[@andrewc7898]

How is this related to z transform. I find these two things similar, however, I cannot tell the relationship between these two kind of methods.

[@wxchew]

the generating function is obtain by z transform, the inverse z transform, that is to get the coefficient of the power series, is done by using the contour integration, which is a much more general technique .

[@Vercongent]

does this technique work even when the contour crosses itself? because that's what's going to have to happen in order to deform the contour so that it encloses those two singularities at alpha and beta @26:52

[@maujo2009]

Vercongent You can approximate the two opposite lines as much as you want, so that their contribution vanishes.

[@ephbranch3496]

yaar bata dete ye wali nahi dekhi mene