Mod-01 Lec-32 Continuous groups in physics (Part 1)

[@sureshv.vettoor9249]

A great master teacher of physics. His style of teaching is inimitable.

[@madara_a]

His teaching methodology is marvellous..

[@lengooi6125]

Clarity of the the teaching is absolutely marvellous!!

[@Igdrazil]

Brilliant pedagogue, alsmost a god teachning, a great lovefull alchimist that distilate the jungle into a few drops of enlightening PRANA! Not at all a common skill... A great physicist and an awesome teacher with a shining heart! Pure paradise. Royal Pradesh... Just a little slip, it's not the function f : R1-->S1 who is multivalued but it's "reciprocal" g : S1-->R1 who is multivalued. The former is a well defined single valued function; it just lacks INJECTIVITY, precisely because it's "reciprocal" is MULTIVALUED. These two concepts are twin entangled since they are in fact the same concept seen from two miror perspectives, namely in the exchange xy, or more pragmaticaly "turning your drawing 90°". And to put it 100% precise and rigourous it's wise to define first a more general concept than the one of "FUNCTION", namely the one of "CORRESPONDANCE k between two sets E and F", which is defined as A TRIPLET (E, F, G) where G is "THE GRAPH" of k, namely a part of the cartesian product ExF of couples (x,y) where x and y belong in E and F. In this manner any crazy graph is permited and the concept of CORRESPONDANCE is wide open to a breathtaking category of situation. One more step is then enough to get to the concept of FUNCTION, namely by asking the GRAPH to be "SINGLE VALUED", which means by ovious definition that any "vertical cross section of the graph above a random x" can't have more than one element. In other words, to translate this sentence with symbols : For all x in E, the subset Gx of ExF made of the couples (x, y) where y runs freely in F, has cardinality less or equal to one. Such a FUNCTIONAL GRAPH makes a FUNCTION out of a CORRESPONDANCE. But this graph can well not be INJECTIVE. That is, the dual "horizontal cross sections" Gy, may well be of cardinality greater that one. Thus by a miror process, one can restrict one more the FUNCTIONAL GRAPH to be also INJECTIVE, which is exactly the same as asking the dual correspondance (F , F, G') to be FUNCTIONAL, which means to have a FUNCTIONAL GRAPH G', where G' is obviously the twin graph of G defined as : (x,y) in G iff (y,x) in G' for all x and y in E and F. It may seem "lots of words for nothing", but this is not so : This is a key stone to prevent from soooo much confusions in mathematics and physics. The one who succed have at least instinctively put it right in their heads thow no necessarely consciensly to the roots, but the one that didn't, confusions on this point can be a recurrent trouble maker. More over to see a FUNCTION as simply a TRIPLET OF THREE SETS is prety elegant and enlightening. It pin's up the concept crystal clear to the mind wall of students and gives a clear definition at this otherwise often unbiguous notations f : E--> F, x--> f(x), or even more confusing for students x-->f(x), without specifying the start E and the goal F. Why is that leading to great confusion. Because if this upper definition of a function as a TRIPLET or sets is not clear, a student will falsly believe that R-->R, x-->x^2 is the same function as R+-->R, x-->x^2. THEY ARE NOT THE SAME FUNCTION, even if the graph of the later concides with the half of the former. And even worse when students note f(x) a function f without understanding properly the shortcut, and forget that the number f(x) is extremely different than the function f that is A TRIPLET OF SETS! It generates even more disasters in Calculus, where the Chaine Rule can become a nightmare. And even WORSE in multivariable Calculus, where the Partial Differential Chain Rule will lead, 90% of the time, to incorrect calculations. For the ones that have some doubt about that, test yourself on proving the STOKES THEOREM that claim's the equality between the surface-integral of a 2-form W (over a bounded open surface S defined by the explicite equation z=z(x,y)), and the ligne-integral of its exterior derivative dW (over the border C of the surface S). The proof is straight forword one page calculation if you master multivariable calculus chain rule and some geometric elementary concepts on NORMAL VECTORS and DIRECTIONAL COSINES. But if you don't, you wont get out of the labyrinth alive!

[@titikshadua1878]

Thanks for another marvellous lecture. I feel blessed to have access to it.

[@aps6085]

Yups awesome lecture!! : )

[@harmansingh-tj2cf]

He has indepth knowledge of the subject.

[@elamvaluthis7268]

Desert travel he makes pleasant by his vast knowledge.

[@elamvaluthis7268]

Prof.Balakrishnan Tamil equivalent Elam karuppan and Elamkannan always good explanatory skill and excels.

[@johnbingham6355]

Thank you very much.I now understand the kernel etc for a finite quotient group.

[@ndmath]

Brilliant teaching

[@arjunsigdel8070]

God level teaching

[@aps6085]

Amazing!! great lecture!!!

[@elamvaluthis7268]

குவாண்டம் மெக்கானிக்ஸ் /அலைக்கற்றை எந்திரவியல் /தனித்துகள் எந்திரவியல்.

[@TheRationalDialogue]

"Never read a book linearly."

[@sijojosephdr]

Thank you professor !!!

[@sagarmalhotra1409]

10:00

[@nesaralititumir6153]

19:30

[@bboyHarrypotter]

Hahaha the useful way to learn group theory

[@randhirsingharora4548]

Looks like he's forgotten to include associativity in definition of groups. That's crucial!

[@pramod120895]

That's what he said this is not a formal course in group theory..He just wanna give hints on the intuitve way on applying this.

[@CiroSantilli]

OMG that intro rocks. Next one: kzbin.info/www/bejne/i57NfqeLp9Nqo6s