Kronecker delta and Levi-Civita symbol | Lecture 7

Kronecker delta and Levi-Civita symbol | Lecture 7 | Vector Calculus for Engineers

Рет қаралды 108,939

4 жыл бұрын

Definition of the Kronecker delta and the Levi-Civita symbol (sometimes called the permutation symbol or Levi-Civita tensor). The relationship between the Kronecker delta and the Levi-Civita symbol is discussed.
For a proof of the most general relationship between the Levi-Civita symbol and the Kronecker delta, watch my video at the link • The Remarkable Relatio...
Join me on Coursera: imp.i384100.net/mathematics-f...
Lecture notes at www.math.ust.hk/~machas/vector...
Paperback at www.amazon.com/Vector-Calculu...
Subscribe to my channel: kzfaq.info?...

Пікірлер: 84

@ProfJeffreyChasnov 4 жыл бұрын

Find other Vector Calculus videos in my playlist kzfaq.info/sun/PLkZjai-2JcxnYmkg6fpzz4WFumGVl7MOa

@sadiqmirza2685 3 жыл бұрын

Hello Jeff sir , can please tell me that what will be the value of levi-civita symbol if (i,j,k) = (3,1,2) means any random sequences may also come. so in which category will it go -1 or 0

@ProfJeffreyChasnov 3 жыл бұрын

@@sadiqmirza2685 312 would be +1

@sadiqmirza2685 3 жыл бұрын

Jeffrey Chasnov thanku so much, now i realised that my question was wrong, means in 3 numbers (1,2,3) there couldn’t be any random sequence means there will be only clockwise and counterclockwise wise sequence if we write in circular patter.

@aizhili4465 2 жыл бұрын

I‘m learning classical mechanics which introduces the levi-civita tensor, this lecture helps me a lot, thanks for sharing.

@georgeswasilewski6535 Жыл бұрын

Better than most of books: thank you very much to give us the pleasure of learning!

@nikihn Жыл бұрын

What really helped me understand this is the way how you explain it. You really take your time in explaining how it works exactly and that makes it much easier to understand as an unknown student who never heard of this before rather than speeding through this method in university, so thanks ! :)

@corneliariasdita715 3 жыл бұрын

I wish I found your videos before my quiz in tensor analysis :') But it's okay, better late than never understand. Your explanations are always clear and on point, I love them!

@dawiddziuba2960 2 жыл бұрын

Thank You very much for sharing this video and making it public. I just started my 3 semester of Aerospace Engineering and this is very helpful in my Fluid Mechanics course.

@aaniranjansaraf2573 2 жыл бұрын

the way you summarize is just amazing!

@rachelkimemia5897 4 жыл бұрын

I really like the video!!! Very comprehensible and organized! 👍

@NiiAryee 2 жыл бұрын

Your lectures are excellent, easy to follow and understand. Thank you!

@GenesisSoumen 3 жыл бұрын

Beautiful lecture Sir. Absolutely delightful. The problems that follow in the course are a very good supplement to this lecture. Top notch work sir !!

@eleanorterry-welsh7784 Жыл бұрын

We started using the Levi-Cevita symbol in the Math Methods for Physics course I'm currently taking and I was really struggling to figure out how they worked from the lecture. This really helped make sense of both the Levi-Cevita symbol and how the Einstein convention for summation works

@user-iq6ej4nu1w Жыл бұрын

Same bro,,,this really saved me

@jewbaby9143 3 жыл бұрын

Awesome! Does anyone know where I can find a derivation or proof of the determinant form of the product of epsilons?

@h5566771 4 жыл бұрын

So great and clear! THANKS!❤️

@user-qn4iy9et1q 3 жыл бұрын

分かりやすかったです！

@OJA-xb6it 3 жыл бұрын

Finally someone who explains this clearly !!Thank you so much !

@susanca8443 3 жыл бұрын

I cannot prove that there would be 27 terms. Can you?

@carlosbocaz9321 Жыл бұрын

Thanks for this video, it's really hard learn to use the subindices.

@dayanthalankanath4019 10 ай бұрын

Awesome video, clear explanation. Thank you so much !

@sitinuraisyah836 2 жыл бұрын

Thank you sir, thats really clear explanations

@kimi-do1ks Жыл бұрын

This lecture ended my 3 weeks of confusion!!

@talebbbedersabag9820 4 жыл бұрын

this helped a lot! you should have more views!!

@BhanudaySharma506 2 жыл бұрын

Wawwww.... Finally someone did this job. Awesome. So beautifully explained. but it would have been better if you have added how to write the divergence and curl of vector using permutation symbol. Also, When any two indices are interchanged, equal or not, the symbol is negated:

@oscarcepeda4821 4 жыл бұрын

en la definicion del producto de dos pseudotensores de Levi- Civita , va un signo "menos " con el determinante, clase 7

@shashvatpatel3694 Жыл бұрын

Really helped a lot ! Thanks :)

@RohitSinhacr7 2 жыл бұрын

Wonderfully explained

@Tiredallthetime779 3 жыл бұрын

The epsilon ijk and epsilon lmn written in a matrix of deltas - how would your write that when it is summed over all the indices

@emreasslan 4 жыл бұрын

Thank you sir!

@MrTNT49 3 жыл бұрын

you just helped me with my homework :)

@semester-4classes227 3 жыл бұрын

its really nice to imagine everytime that you are writing from the right end of the glass screen and laterally inverting every frame in the video. And you are NOT lefty!

@vasilisvarvarigos3434 2 жыл бұрын

Really useful thank you !!!

@ajilbabu13 3 жыл бұрын

Hey thank you so much prof., why did I miss this in my graduation 😓

@shiroshiro8170 4 жыл бұрын

This is treasure

@eirelavavedecc 3 ай бұрын

Thank you very much

@bunkhuochann917 3 жыл бұрын

Thank you sir

@abner6a Жыл бұрын

great video!

@EricBrunoTV 4 жыл бұрын

It's incredible that I'm french speacking and I did not found any explanation so clear and simple in french on youtube. Maybe I didn't insert the right words but anyway I'm sure that you are a good teacher. Thank you for this video. I subscribe right now to your chanel and I will affort to follow you even if in english.

@Mewtwo13a 3 жыл бұрын

Thank you!

@a_gentlefox3293 Жыл бұрын

much appreciate it

@nsp5821 2 жыл бұрын

You are like God to me Sir I can't thank you enough for this🥰🥰

@Vale246810 4 жыл бұрын

THANK YOU ;)

@yashagnihotri6901 4 жыл бұрын

The lecture is actually from the Vector Algebra course on Coursera !

@ProfJeffreyChasnov 4 жыл бұрын

Yes! Better to take the course on Coursera.

@yashagnihotri6901 4 жыл бұрын

@@ProfJeffreyChasnov I am in Sir !

@Emad8452 5 ай бұрын

Nice!

@satoseitoku 2 жыл бұрын

Thank you

@behnazazadfard8480 3 жыл бұрын

thank you

@mannu_0798 3 жыл бұрын

Impressive....

@Vishal360 4 жыл бұрын

Don't u make live??

@Andertheil Жыл бұрын

Why is it not negative six?

@dachyVAR 3 жыл бұрын

მადლობა

@reddotclips3971 10 ай бұрын

Thanks! Also impresssed by how well you write backwards lol

@comedian619 4 жыл бұрын

What is the product of 2 Kronecker deltas with indices that do not match? For instance delta(1,L)*delta(2,m)-delta(1,m)*delta(2,L)?

@ilgazkuscu5600 4 жыл бұрын

I think it's to be left as it, by their delta functions.

@user-iq6ej4nu1w Жыл бұрын

I think it'll be zero ,,,as delta(ij)=0 for i not equals j ,,, so ut should. Be zero this way

@farifari2704 2 жыл бұрын

Why Kronecker delta becomes 1 when i=j??

@uuuuuu9115 2 жыл бұрын

Because of the orthogonality of two functions.

@serenityspace8892 4 жыл бұрын

Please teach at my University instead, second time taking my course and still didn't understand this until watching your vid

@kanhaiya1825 3 жыл бұрын

Like really It quite easy

@jeffreyl2403 Жыл бұрын

@ztac_dex 3 жыл бұрын

>"for engineers" > didn't encounter this in any of my civil engg class but this is heavily used in physics majors especially with coordinate transforms or repeated indices

@ProfJeffreyChasnov 3 жыл бұрын

I didn't see this until I taught a graduate course in mathematical methods, haha!

@alexv5581 2 жыл бұрын

It is widely used in mechanical engineering (fluid mechanics and solids) Kind of surprising you didn't cover this in civil since civil engineering is just a branch of mechanical engineering. Without dealing with motion (static solids) Coordinate transform is also used in solid mechanics/mechanics of materials

@kuldeepmalik6288 2 жыл бұрын

How e(312) is even permutation and e(213) is odd

@matteocontini9523 2 жыл бұрын

you have 1,2,3 and than you go in order 1,3,2 and than 3,1,2, two moves so it's even , for the other permutation you have 1,2,3 and then you go 2,1,3, you make one move so it's odd

@IdunDied 2 жыл бұрын

Even means you start at (123), You move every number left or right. If you go past the edge (bracket) you move it to the other side. So if I moved everything left once, (123) -> 1(23_) = (231). So even. Left again gives 2(31_) -> (312). And once more gives (123). None of these are (213). You can only get (213) by starting at (321), hence it's odd. Same for (132).

@drvanhelsingz5133 Жыл бұрын

Why 27 terms ?

@jacobsan 5 ай бұрын

3³

@pugazharasuad 3 жыл бұрын

Not my tempo!

@SyedAbdullah529 3 жыл бұрын

so this is what mike did after gus died ?

@jacobsan 5 ай бұрын

😂

@jacobsan 5 ай бұрын

Put your vector away, waltuh

@lyreas1925 7 ай бұрын

Is he writing backwards so it doesn't look mirrored to us? Lmao

@charliedavis2 2 жыл бұрын

Looks like that guy from breaking bad

@paper3162 11 ай бұрын

Mike Ehrmentraut

@marcobaioletti3777 Жыл бұрын

the correct pronounciation of "Levi-Civita" is more or less "LEHvee-CheevEEtah"

@ProfJeffreyChasnov Жыл бұрын

My apologies to all the Italians!

@ttttttttttttttttt3415 10 ай бұрын

i have pictures of spiderman

@flaguser4196 2 жыл бұрын

unfortunately for my past college self, it is at this part where the math lost intuition and just became rote memorization of seemingly arbitrary rules.

@ProfJeffreyChasnov 2 жыл бұрын

Doesn't have to have intuition. But the rules are not arbitrary.

@_dirty_face 2 жыл бұрын

Brothet because this is applied math not the core one we will see only direct applications of concepts