I just clicked on the video to feel insignificant. Success!!! These videos have the same recall functions of old music that takes you to an old memory. The minute he was halfway down the board and my world closed tighter, I was taken back to high school math class decades ago, and I was like yup....he's the real deal 0-o¿
I feel great every time I watch one of these because, as I progress through my education, I'm able to understand more and more of what Andrew's talking about.
Super cool. I think my math methods teacher *tried* doing this, but he isn't the best at explaining what stuff means. I can't wait for the derivation of the generalized laplacian for any metric.
Brings back a lot of memories, Andrew. I was a physics major back in the 80s and actually went to graduate school at Washington State between 1990 and 1992 and got a masters degree. I don't do physics anymore so I've regrettably forgotten most of this stuff. But good luck with your graduate school endeavors and make sure to keep us updated until you get your PhD
Wow! Just thank you for your great videos! Last week I finished my Bachelor in Physics and now I am repeating all the stuff I didn't understand or already forgot. Since I found your channel I understand all those great Theoretical Physics! Thanks a lot!
Thanks for showing this cool way of getting to the laplacian, I myself have written the laplacian in cylindrical and spherical enough times in my PDE course that I just have it memorized.
THIS MAN IS MEEE. he wants to derive stuff, just like me. I always found it useful to derive equations if I in the future ever forgot what it was. So it's great to see someone who knows what Im feeling
you know, me and my pals kinda hated our 3th semester mechanic professor cuz he taught us a bit of tensor calculus just to obtain the Inertia Tensor, just afterwards the Hamilton/Lagrangian test, but now, i mean, i kinda like the guy xD (in came in handy w/ the bit of special relativity that we saw in the same semester, tho). Love your work here man, and don't worry about it, every know and them i'd love if you can get a bit more rigorous in some of your videos. Didn't think that i'll find both a great channel 'bout physics WHILE being an amazing 9yo, just doing hes part. PD: i'm starting my 4th semester in my BS - physics, i'm from venezuela; and i know i'm asking a lot but if you can give just a quick shoutout to these friends of mine, they'll drive crazy. Here are the names: Ashli Rodriguez. and Sergio Gonzales. And sorry the request :^$
I like a mix of both memorization and derivation. In Calc 1, my professor always went over stuff like the definition of a limit and the integral tan and sec by showing us how we could find it our self. Calc 2 was like "here's a formula", plug and chug. My Calc 3 professor is just like my Calc 1 so I appreciate a lot more of what the hell is going on.
Very interesting, I once asked how to derive a formula of such equation in tensor style and code it symbolically. I see it is truly helpful if you explain how to do this
I kind of understood. I know laplace equation snd spherical and cylindrical coordinates. I kind of get.....some are like vector functions given by cylindrical coordinates
If metric tensor seems an overkill I suggest using Lame Coefficients. The formulas are limited to orthogonal coordinate systems(less general), the derivation is stupidly simple and all differential geometry formulas are easy to remember(it is the same formulas, but with coefficients written near all entities). I love the following book: "Mathematical handbook for scientist and engineers." by Granino A. Korn, Theresa M. Korn. The last pages have all these formulas conveniently placed together for all commonly used orthogonal coordinate systems. I think there are only 11 of them. P.S. Knowing more coordinate systems is very handy. Elliptic coordinate system is one of the most underestimated in my opinion.
I will probably have to watch this video another 10 times to fully understand it or read myself through some math textbooks; nevertheless: this math was beautiful. Thank you Andrew!
I remember doing the brute force derivation multiple times in undergrad. Then, by force, had to learn these things. While the teacher was truly a terrible teacher, learning this all has changed the way I think of, and approach, these problems. Not so frustrating now. It's also really easy to memorize the major metrics. Not as easy if you don't have an orthogonal basis, but you will rarely need that
Fate has no hold on me now, for if I am ever stranded on a desert island, I can derive the Laplacian from the metric tensor with just a stick, sand and time.
Is there any textbooks written in latex or HTML with mathjax that you know of? I'm blind and PDFs with math symbols won't read properly with screenreaders
this may be dumb, but why in the final equation do the r and 1/r no cancel in the first term? and similarly would it not just be the second partial of r for the first term? like it is for z?
"I'm gonna be showing you a middle man" Me: Oh, yay, something simple-ish! Dotson: Just requires you to know a little bit of Tensors... It's really straightforward stuff..." Me:..... yay? :'( ah well... let's dive in
Hey man great stuff. I think this is a really great explanation but I feel like your skipping over stuff you think is trivial but Im new to tensors so I don't quite follow. For example at 8:12 I don't understand why you do that. It may have been more understandable if you wrote it out. But other than that very well explained!
You need to be familiar with the Einstein summation convention, which says that repeated indices in an expression are summed over. So the expression he has written for the Laplacian really has a double sum over i and j from 1 to 3 each, giving 9 total terms. But his g^{ij} term represents elements of the metric tensor (which you can think of as just a 3x3 matrix), and this tensor is diagonal. so only g^{11}, g^{22}, g^{33} will be non-zero, while terms like g^{12} = 0.
Yo guys, i have a question perhaps one of you could help me out. Im currently doing my ba in physics and in my department most test are four to five hours long. Now they(proffesors) claim it is so we can have all the time we need to derive the needed equations, but if that was true then i would assume most students would leave the test before the end of the test, that doesnt happen. What does happen is that the majority of the students wont leave until the last minute. What i think is that this is all desined to justify givibg questions that are way beyond the level of the course. Is this something that happens in other departments or is it something particular to my university?
I looked through your videos and I don't think you've derived this, so if you see this comment, can you derive it? Or if you can't make a video on it (because I'm the only one that asked), if you could send me a paper or something that has it derived, that would be great.
Yup! Also, just wanna say that I grew up in Chesapeake, VA, and had no idea that you went to ODU. So after finding you on youtube is was cool to find that out. I went to JMU and just graduated this past May. I plan to go to grad school for my Ph.D in basically the same thing you are going for. To get to the point of this reply, these videos definitely help me a lot in preparation for grad school and they help sharpen my physics skills (definitely with derivation since my school didn't really focus on derivation to much.) So thank you for doing what you do!
You need to learn differential geometry, it will rock your world. And now you just need to generalise the Laplacian to n dimensions. And then define it as a coordinate free object. XD
why do I keep watching these, I literally have no idea what’s going on lmao
pls dont go
Same omg
@@AndrewDotsonvideos LMAO im not even sure why I'm here, I failed first year Physics
temporarily raises your IQ by 300%
I just clicked on the video to feel insignificant. Success!!!
These videos have the same recall functions of old music that takes you to an old memory.
The minute he was halfway down the board and my world closed tighter, I was taken back to high school math class decades ago, and I was like yup....he's the real deal 0-o¿
I feel great every time I watch one of these because, as I progress through my education, I'm able to understand more and more of what Andrew's talking about.
Super cool. I think my math methods teacher *tried* doing this, but he isn't the best at explaining what stuff means. I can't wait for the derivation of the generalized laplacian for any metric.
Brings back a lot of memories, Andrew. I was a physics major back in the 80s and actually went to graduate school at Washington State between 1990 and 1992 and got a masters degree. I don't do physics anymore so I've regrettably forgotten most of this stuff.
But good luck with your graduate school endeavors and make sure to keep us updated until you get your PhD
after watching this 2 years ago as a freshman vs now , I am now starting to understand what you are talking about.
Wow! Just thank you for your great videos! Last week I finished my Bachelor in Physics and now I am repeating all the stuff I didn't understand or already forgot. Since I found your channel I understand all those great Theoretical Physics! Thanks a lot!
This is wildly cool! Now I want to do out the spherical coordinate version! Derivation requested!
Great video!! I am very glad that I found your channel!! Thank you!
I've never derived these with tensor notation. I did it the long algebra way in undergrad Math Methods, and then always looked it up after that.
Dude, your beard is looking great. Pls don't change it, bb
Thanks for showing this cool way of getting to the laplacian, I myself have written the laplacian in cylindrical and spherical enough times in my PDE course that I just have it memorized.
I have no idea what any of this means, but I still watched the whole thing anyway haha
I don't blame you. He's not exactly tough on the eyes either. :)
Please keep making these kind of videos.
They're a great help to all physics and math community!
THIS MAN IS MEEE. he wants to derive stuff, just like me. I always found it useful to derive equations if I in the future ever forgot what it was. So it's great to see someone who knows what Im feeling
Definitely would like to see the derivation.
This made me learn the concept of tensors, but it was worth learning as it will help me a lot in laplacian. Thanks 😊❤️
noice, the huge tensor boi is back at it
Man this is awesome 👏👍!! Keep up the good work and thank you for this great vid
you know, me and my pals kinda hated our 3th semester mechanic professor cuz he taught us a bit of tensor calculus just to obtain the Inertia Tensor, just afterwards the Hamilton/Lagrangian test, but now, i mean, i kinda like the guy xD (in came in handy w/ the bit of special relativity that we saw in the same semester, tho).
Love your work here man, and don't worry about it, every know and them i'd love if you can get a bit more rigorous in some of your videos. Didn't think that i'll find both a great channel 'bout physics WHILE being an amazing 9yo, just doing hes part.
PD: i'm starting my 4th semester in my BS - physics, i'm from venezuela; and i know i'm asking a lot but if you can give just a quick shoutout to these friends of mine, they'll drive crazy. Here are the names: Ashli Rodriguez. and Sergio Gonzales. And sorry the request :^$
Another complex math concept made simple, thanks Andrew.
Thanks. We spent half an hour in class deriving the laplacian in cyl. coordinates
I like a mix of both memorization and derivation. In Calc 1, my professor always went over stuff like the definition of a limit and the integral tan and sec by showing us how we could find it our self. Calc 2 was like "here's a formula", plug and chug. My Calc 3 professor is just like my Calc 1 so I appreciate a lot more of what the hell is going on.
Very interesting, I once asked how to derive a formula of such equation in tensor style and code it symbolically. I see it is truly helpful if you explain how to do this
I'm an econ / finance major, and have literally -1354 ideas on what's going on, but I enjoyed this
Hahaha why am I even watching this I have no idea what half the words you’re saying even mean.
I kind of understood.
I know laplace equation snd spherical and cylindrical coordinates.
I kind of get.....some are like vector functions given by cylindrical coordinates
Haha, I'm watching these videos while using laplacian in cylindrical coordinates to solve E&M problems.
If metric tensor seems an overkill I suggest using Lame Coefficients. The formulas are limited to orthogonal coordinate systems(less general), the derivation is stupidly simple and all differential geometry formulas are easy to remember(it is the same formulas, but with coefficients written near all entities). I love the following book:
"Mathematical handbook for scientist and engineers." by Granino A. Korn, Theresa M. Korn.
The last pages have all these formulas conveniently placed together for all commonly used orthogonal coordinate systems. I think there are only 11 of them.
P.S. Knowing more coordinate systems is very handy. Elliptic coordinate system is one of the most underestimated in my opinion.
I will probably have to watch this video another 10 times to fully understand it or read myself through some math textbooks; nevertheless: this math was beautiful. Thank you Andrew!
Thanks man!! I did it for spherical coordinates and got it right!!!!
But I just trusted your Laplace equation!!
Waiting for the derivation!!
Nice!
I remember doing the brute force derivation multiple times in undergrad. Then, by force, had to learn these things. While the teacher was truly a terrible teacher, learning this all has changed the way I think of, and approach, these problems. Not so frustrating now.
It's also really easy to memorize the major metrics. Not as easy if you don't have an orthogonal basis, but you will rarely need that
This is awesome thank you 🙏🏻
Fate has no hold on me now, for if I am ever stranded on a desert island, I can derive the Laplacian from the metric tensor with just a stick, sand and time.
the tensor memes were actually true I would be interrested what happens to this if you do it in 4 coordinates IE relativity
Welcome to Wolverine does physics.
Thanks so much!
Thank you! My electrodynamics professor just went over this, but I was confused
I vaguely know the idea and a little of the math going on but I enjoy learning
@Andrew, Why in 1/r *d(r*d/dr)/dr don't the 1/r and r cancel out? Thank you
the beard is looking majestic man, so jealous
Where can I find a good book that explains tensors intuitively, where they come from, how and why to use them?
Tensor Calculus For Physics By Neuenschwander.
I wish I could do this do bad😀 Did you find the transition from biology to physics major hard or did it just come natural?
ur like my role model boi
The beard is actually legendary
cant wait till i finish collage so i can finaly understand this
Is there any textbooks written in latex or HTML with mathjax that you know of? I'm blind and PDFs with math symbols won't read properly with screenreaders
this may be dumb, but why in the final equation do the r and 1/r no cancel in the first term? and similarly would it not just be the second partial of r for the first term? like it is for z?
thank u so much dude xDD
GIVE US SOME MORE OF THE PUNIES TENSOR BOIS, ANDREW!
YA should derive it in part 6 :P And is the book video happening later today or maybe a few days time (GMT where I am)?
Sometime this week I'll make that video!
Andrew how to derive the laplacian in terms of the metric tensor
Nicccce!!!
Ur handwriting though!!!
Much better than mine.
"I'm gonna be showing you a middle man"
Me: Oh, yay, something simple-ish!
Dotson: Just requires you to know a little bit of Tensors... It's really straightforward stuff..."
Me:..... yay? :'(
ah well... let's dive in
What is tensor?
What is that question called that you used with the metric tensor ?
Why did you cancel r in d/dz part but didn't in d/dr ? What is the point of keeping that r?
Hey man great stuff. I think this is a really great explanation but I feel like your skipping over stuff you think is trivial but Im new to tensors so I don't quite follow. For example at 8:12 I don't understand why you do that. It may have been more understandable if you wrote it out. But other than that very well explained!
You need to be familiar with the Einstein summation convention, which says that repeated indices in an expression are summed over. So the expression he has written for the Laplacian really has a double sum over i and j from 1 to 3 each, giving 9 total terms. But his g^{ij} term represents elements of the metric tensor (which you can think of as just a 3x3 matrix), and this tensor is diagonal. so only g^{11}, g^{22}, g^{33} will be non-zero, while terms like g^{12} = 0.
Yeah I guess I assumed people knew about the summation convention! Sorry about that!
Yo guys, i have a question perhaps one of you could help me out.
Im currently doing my ba in physics and in my department most test are four to five hours long. Now they(proffesors) claim it is so we can have all the time we need to derive the needed equations, but if that was true then i would assume most students would leave the test before the end of the test, that doesnt happen. What does happen is that the majority of the students wont leave until the last minute.
What i think is that this is all desined to justify givibg questions that are way beyond the level of the course.
Is this something that happens in other departments or is it something particular to my university?
What if he didn't have the use of equal signs.
Do a derivation!
Tensor Calculus For Physics Majors Part 6 Confirmed (hopefully xD - made notes on it as well).
Whoooop
I looked through your videos and I don't think you've derived this, so if you see this comment, can you derive it? Or if you can't make a video on it (because I'm the only one that asked), if you could send me a paper or something that has it derived, that would be great.
Michael Padgett derived the generalization? I haven’t done it yet but I will!
Yup! Also, just wanna say that I grew up in Chesapeake, VA, and had no idea that you went to ODU. So after finding you on youtube is was cool to find that out. I went to JMU and just graduated this past May. I plan to go to grad school for my Ph.D in basically the same thing you are going for. To get to the point of this reply, these videos definitely help me a lot in preparation for grad school and they help sharpen my physics skills (definitely with derivation since my school didn't really focus on derivation to much.) So thank you for doing what you do!
Do you know any good intro to tensor calc?
David M I’m doing a series on it
Booooooooooooi. Nice
tensorboi is gut friend yaya
He he i am imagining you without beard ...😜😜😜
Aw, I was hoping to see christoffel symbols
Is there a generalized tensor version of curl that doesn't use differential forms?
Just don't let Jesse Kyle derive the Laplacian equation.
So essentially the jacobian?
The square root of the determinant of the metric is the jacobian. So yes
You need to learn differential geometry, it will rock your world. And now you just need to generalise the Laplacian to n dimensions. And then define it as a coordinate free object. XD
When are you gonna learn GR
Gr is too complex....i think its for theoretical physics
oscar obioha if he’s in grad school and doing tensor Ik Andrew is capable. At my undergrad program you only need differential equations for GR
I did an independent study of GR with one of my professors
Andrew Dotson do some videos!
@@chymoney1 howww.
Like i know u need quadrics, differential topology, reimannian geometry