Kronecker delta and Levi-Civita symbol | Lecture 7 | Vector Calculus for Engineers
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- Опубликовано: 12 сен 2024
- 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...
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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
@@sadiqmirza2685 312 would be +1
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.
I‘m learning classical mechanics which introduces the levi-civita tensor, this lecture helps me a lot, thanks for sharing.
Better than most of books: thank you very much to give us the pleasure of learning!
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 ! :)
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.
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!
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
Same bro,,,this really saved me
the way you summarize is just amazing!
Finally someone who explains this clearly !!Thank you so much !
I cannot prove that there would be 27 terms. Can you?
Your lectures are excellent, easy to follow and understand. Thank you!
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:
Beautiful lecture Sir. Absolutely delightful. The problems that follow in the course are a very good supplement to this lecture. Top notch work sir !!
Thanks for this video, it's really hard learn to use the subindices.
I really like the video!!! Very comprehensible and organized! 👍
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.
Awesome! Does anyone know where I can find a derivation or proof of the determinant form of the product of epsilons?
This lecture ended my 3 weeks of confusion!!
Thank you sir, thats really clear explanations
this helped a lot! you should have more views!!
First off, thank you, this helps in my E&M class, second, I am going to school to teach physics, how on Earth do you produce a video like this? what software do you use and how did you get the board to do that???
Awesome video, clear explanation. Thank you so much !
分かりやすかったです！
The lecture is actually from the Vector Algebra course on Coursera !
Yes! Better to take the course on Coursera.
@@ProfJeffreyChasnov I am in Sir !
Really helped a lot ! Thanks :)
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!
you just helped me with my homework :)
So great and clear! THANKS!❤️
Thank you sir
Hey thank you so much prof., why did I miss this in my graduation 😓
Wonderfully explained
Thank you very much
You are like God to me Sir
I can't thank you enough for this🥰🥰
Thanks! Also impresssed by how well you write backwards lol
Thank you sir!
much appreciate it
This is treasure
en la definicion del producto de dos pseudotensores de Levi- Civita , va un signo "menos " con el determinante, clase 7
Really useful thank you !!!
Nice!
great video!
Thank you!
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
Why is it not negative six?
THANK YOU
;)
Thank you
>"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
I didn't see this until I taught a graduate course in mathematical methods, haha!
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
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)?
I think it's to be left as it, by their delta functions.
I think it'll be zero ,,,as delta(ij)=0 for i not equals j ,,, so ut should. Be zero this way
Please teach at my University instead, second time taking my course and still didn't understand this until watching your vid
Like really
It quite easy
Impressive....
მადლობა
Don't u make live??
so this is what mike did after gus died ?
😂
Put your vector away, waltuh
Is he writing backwards so it doesn't look mirrored to us? Lmao
Why Kronecker delta becomes 1 when i=j??
Because of the orthogonality of two functions.
Not my tempo!
Why 27 terms ?
3³
How e(312) is even permutation and e(213) is odd
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
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).
the correct pronounciation of "Levi-Civita" is more or less "LEHvee-CheevEEtah"
My apologies to all the Italians!
Looks like that guy from breaking bad
Mike Ehrmentraut
i have pictures of spiderman
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.
Doesn't have to have intuition. But the rules are not arbitrary.
Brothet because this is applied math not the core one we will see only direct applications of concepts
thank you