I will binge watch your tensor calculus series during my summer vacation. I have to learn GR over the summer for my individual student activity in black hole images next semester 🤞🏼
I study physics and I feel the same about engineers. If you have choosen the right path, other peoples exams will seem to you as harder. I couldn't learn some engineering classes I'm sure. I just think differently.
Have had some mech. engineering students in my grad level physics courses. They don't enjoy it hahaha (but depending on the instructor, I don't either).
You already have the electromagnetic tensor and the inertia tensor, but if possible, I think it would be useful to have more videos on specific tensors and how they use the concepts in this series, like the tensors from GR you mentioned in passing and if there are some other tensors out there that I never heard of. It would give a second exposure to the concepts and it wouldn't be a repeat video because it's on the tensor not the concept. Of course you have a schedule and a plan for what you will to post, I'm just giving input on what I hope to see in future episodes. Anyways, good luck in your future years at gradschool! And I love your channel! :-)
I love that everything is calculated off hand very talented. The thing that I wish I could do is see the work as youre writing. I listen a majority of thr time. But when I have to see. Just maybe angle the camer and fool with lighting. Again. Contructive personal wants. Your videos are pretty epic man!
thank you for mentioning the issue as being a problem of relating vectors in different tangent spaces--it's how I think about it nowadays, not using any of this "oh no partials don't transform as tensors" nonsense anymore ^_^ I really recommend reading wald's book if you haven't already, he's got a pretty 🔥 intro to tensor calc in chapter three
Shit I forgot to mention the form of the covariant derivative being motivated from Walds book. He shows you can write an operator as a partial derivative plus a linear transformation if it satisfies the Leibniz product rule. I should have mentioned that.
Just wanted to ask for clarification of the ending explanation for the covariant derivative of a contravariant vector with respect to proper time, where does the derivative in the second term come from? You mention taking the derivative of a vector with respect to components, is that sort of like a gradient of the vector where the components are dependent on the coordinates? Other than that, yet another great video! Really enjoying the series so far.
Nice to learn new things, I’ve got a Masters in Chemical Physics, but focused more on solid state and statistical physics so didn’t do much tensor calculus! It’s been fun to follow so far and kinda wishing I did the general relativity or RQFT class in my Masters year now
Still trying to figure out where the e1xe2xe3 type products come in since everyone is working with components only. Yet tensors defined by that strange basis, something that can have a dot or not!
Great explanation my heart but I would like to see just innparalell in the blackboard what I'm doing with a less general example for example f=f1 (x,y,z);f2 (x,y,z);f3 (x,y,z) to get the connection with something less general because in get lost in some points
Would be awesome if you could make a guide for someone trying to learn QFT. I'm finding it to be quite a big jump coming from Quantum mechanics... especially since I'm missing a lot of math :(
One thing that always bothered me in my tensor class was the upstairs and downstairs indices. When you're expressing a coordinate in the denominator, it seems like it never has a subscript, it always ends up with a superscript, but you still refer to it as "downstairs" cause it's in the denominator. But in the numerator, you can have downstairs and upstairs indices. What am I missing here?
@@AndrewDotsonvideos Thank you, I've watched through the entire series, but it seems you kinda gloss over that part. Can indices in the denominator also appear downstairs?
Do you have notes and prerequisite videos for this particular video? Keep up the good work. I'd like to be able to understand what the hell you are talking about as a non physics major.
At least all of calculus and linear algebra. Differential equations could be a nice one too, but the most important aspects will be Calc 3 and linear algebra. You are doing calculus on manifolds, and that requires understanding traditional multivariate calculus and a bit about linear algebra (for understanding vector spaces and transformations)
Unrelated to the video but is anyone else's university application process a jumbled, confusing and extremely stressful process? It just doesn't seem to let up.
a tensor is something that has a unique transformation property that enables it to change its coordinates through some transformation coefficent, vectors also share this property and thats why theyre also tensors, i think.
I REALLY wanna watch this video it’s just that I’m in 8th grade and we’re doing geometry and at home I just started calculus AB (after prec-calculus) and I know if I watch this video I’m not going to understand anything at all so just hold up give me a year or two and I’ll write cool stuff in the comments
th-cam.com/play/PLu7cY2CPiRjVY-VaUZ69bXHZr5QslKbzo.html I found this brief series from ScienceClic English providing a very visual and intuitive glance at Relativity, curvature, and the Christoffel Symbols. It provides a fantastic animation of parallel transport.
Ahh, the Good ol' Hairy Ball theorem. There's no global continuous, everywhere non-zero basis on the 2-sphere. Also Tensors are just spicy Matrices (Multi-linear maps as opposed to linear). The gradient isn't a vector, it's a COVECTOR WAKE UP SHEEPLE
I wrote everything down and said it out loud and my furniture started floating
Pakuja funniest shit ive read swear to god
I realize it's kinda randomly asking but do anyone know a good site to stream new tv shows online?
🤣🤣🤣🤣
Tensor calculus: * exists *
Andrew dotson: *DROWN IN IT*
Don’t know what any of this means yet but I see Andrew Dotson and I watch!
I will binge watch your tensor calculus series during my summer vacation. I have to learn GR over the summer for my individual student activity in black hole images next semester 🤞🏼
Just an engineering student watching the video and realizing how much worse my finals week could be. Thanks for the cathartic videos.
I study physics and I feel the same about engineers. If you have choosen the right path, other peoples exams will seem to you as harder. I couldn't learn some engineering classes I'm sure. I just think differently.
Have had some mech. engineering students in my grad level physics courses. They don't enjoy it hahaha (but depending on the instructor, I don't either).
Thanks from a hobbyist who left college in 1970. Never finished . Got as far as Calc 3 and Linear Algebra. SOme DE but all long ago.
Born and raised in Norfolk. You make me rethink my college of choice since ODU has the best physics lecturers I know (you included).
Art Ken Fontelera thanks a lot!
Bless you and your work! Now I've got a whole list of episodes to watch instead of just wallowing in my sorrows doing my derivations
You already have the electromagnetic tensor and the inertia tensor, but if possible, I think it would be useful to have more videos on specific tensors and how they use the concepts in this series, like the tensors from GR you mentioned in passing and if there are some other tensors out there that I never heard of. It would give a second exposure to the concepts and it wouldn't be a repeat video because it's on the tensor not the concept. Of course you have a schedule and a plan for what you will to post, I'm just giving input on what I hope to see in future episodes. Anyways, good luck in your future years at gradschool! And I love your channel! :-)
Yessssss
to all hand-wavey explanations
When a tensor mans says "jesus christ the indeces"
I love that everything is calculated off hand very talented. The thing that I wish I could do is see the work as youre writing. I listen a majority of thr time. But when I have to see. Just maybe angle the camer and fool with lighting. Again. Contructive personal wants. Your videos are pretty epic man!
Yeah very true, I think I’ll do these via tablet from now on to avoid blocking what I’m writing. Sorry about that!
@@AndrewDotsonvideos nice dude thanks! Im soak it in Merry Christmas man🤙
This connection you are using here will always be torsion free, the schwarz theorem grants it.
Zoltán Kürti ah I was trying to be super careful with making that assumption. Good to know, thanks!
@@AndrewDotsonvideos if the partial derivatives are continuous at a point, they can be exchanged.
Thanks for this! Helping me review tensor calc for my relativity midterm!
thank you for mentioning the issue as being a problem of relating vectors in different tangent spaces--it's how I think about it nowadays, not using any of this "oh no partials don't transform as tensors" nonsense anymore ^_^
I really recommend reading wald's book if you haven't already, he's got a pretty 🔥 intro to tensor calc in chapter three
Shit I forgot to mention the form of the covariant derivative being motivated from Walds book. He shows you can write an operator as a partial derivative plus a linear transformation if it satisfies the Leibniz product rule. I should have mentioned that.
Brilliant videos. Have you considered a series on QFT?
ohh that would be a great idea
I enjoyed the video, Andrew! :)
just here to drop my like...
Just wanted to ask for clarification of the ending explanation for the covariant derivative of a contravariant vector with respect to proper time, where does the derivative in the second term come from? You mention taking the derivative of a vector with respect to components, is that sort of like a gradient of the vector where the components are dependent on the coordinates?
Other than that, yet another great video! Really enjoying the series so far.
Nice to learn new things, I’ve got a Masters in Chemical Physics, but focused more on solid state and statistical physics so didn’t do much tensor calculus! It’s been fun to follow so far and kinda wishing I did the general relativity or RQFT class in my Masters year now
i applaud your ability to not break down when dealing with that many indices
Now, that is what a call THE PARTIAL DERIVATIVE
This man is speaking the language of gods!
very nice explanation
I think he might be smart then Albert Eyestein
Excellent effort..
I feel like every physics student has a whiteboard
Where may I find the Nth covariant derivative of a vector and of a tensor?
You have a beard of a God.
Still trying to figure out where the e1xe2xe3 type products come in since everyone is working with components only. Yet tensors defined by that strange basis, something that can have a dot or not!
Great explanation my heart but I would like to see just innparalell in the blackboard what I'm doing with a less general example for example f=f1 (x,y,z);f2 (x,y,z);f3 (x,y,z) to get the connection with something less general because in get lost in some points
Great video, as always. The audio quality was a little distracting, though. Any updates on the mic?
I’m really not too sure what’s up with it, I might just get a new one and use my other mic until then
Would be awesome if you could make a guide for someone trying to learn QFT. I'm finding it to be quite a big jump coming from Quantum mechanics... especially since I'm missing a lot of math :(
It's easy to do a covariant derivative; simply place a tittle over the comma, transforming into a semicolon. Voilá!
Why don't you add this video to the playlist, Andrew???
One thing that always bothered me in my tensor class was the upstairs and downstairs indices. When you're expressing a coordinate in the denominator, it seems like it never has a subscript, it always ends up with a superscript, but you still refer to it as "downstairs" cause it's in the denominator. But in the numerator, you can have downstairs and upstairs indices. What am I missing here?
I think you might benefit from earlier videos in the series on covariant/contra variant indices.
@@AndrewDotsonvideos Thank you, I've watched through the entire series, but it seems you kinda gloss over that part. Can indices in the denominator also appear downstairs?
no torsion means no descent chains
that beard is growing wild
Do you have notes and prerequisite videos for this particular video? Keep up the good work. I'd like to be able to understand what the hell you are talking about as a non physics major.
Ryan Schreck I made a playlist of my tensor videos
CAn somebody give me a quick intrution on the difference between cliffords and tensors. Thanks
wait.... torsion has no relation to torque, does it?
Can I ask what are the pre-requisites before studying Tensor Calculus?
I'm planning to take Physics-related on my Undergraduate thanks :>
At least all of calculus and linear algebra. Differential equations could be a nice one too, but the most important aspects will be Calc 3 and linear algebra.
You are doing calculus on manifolds, and that requires understanding traditional multivariate calculus and a bit about linear algebra (for understanding vector spaces and transformations)
what university did you go to for undergrad?
I love you Andrew-senpai. Visit Canada and Queen's University one day.
Okay buddy
Unrelated to the video but is anyone else's university application process a jumbled, confusing and extremely stressful process? It just doesn't seem to let up.
Add it to the "New To Tensors? Start Here" list.
i want to know how pappa flammy feels about your pronunciation of the authors name
Im in Calculus 2 this summer, and i still only understand 5% of this
Andrew Dotson look a lot like Sam Gorski from NODE, no?
So I just finished calc bc/ calc ii (got a 5!), anyone wanna try and explain this? Or just tell me what the hell a tensor is?
a tensor is something that has a unique transformation property that enables it to change its coordinates through some transformation coefficent, vectors also share this property and thats why theyre also tensors, i think.
I REALLY wanna watch this video it’s just that I’m in 8th grade and we’re doing geometry and at home I just started calculus AB (after prec-calculus) and I know if I watch this video I’m not going to understand anything at all so just hold up give me a year or two and I’ll write cool stuff in the comments
I’m in 8th grade and I’m trying to understand this now. Also I want to see you write cool things in the comments
Ill be back.😎
I understand SOME of these words... I think.
th-cam.com/play/PLu7cY2CPiRjVY-VaUZ69bXHZr5QslKbzo.html
I found this brief series from ScienceClic English providing a very visual and intuitive glance at Relativity, curvature, and the Christoffel Symbols. It provides a fantastic animation of parallel transport.
Mais videos, more videos
Wtf everything was okey until we start with derivar es of tensors, but anyway its such a great explaination
Goes without saying
Ahh, the Good ol' Hairy Ball theorem.
There's no global continuous, everywhere non-zero basis on the 2-sphere.
Also Tensors are just spicy Matrices (Multi-linear maps as opposed to linear).
The gradient isn't a vector, it's a COVECTOR
WAKE UP SHEEPLE
Whats your instagram though?
Yeah, um I don't speak whatever language that is...
jajajaajajajaja
You're a tau-el
This is an awful lecture!
Was there anything in particular you didn’t find helpful?
Ah this was the one with the bad audio, I see now.