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.
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
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.
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.
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.
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
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 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
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.
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 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 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
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.
"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
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?
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.
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?
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
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!
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.
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
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.
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.
after watching this 2 years ago as a freshman vs now , I am now starting to understand what you are talking about.
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.
This is wildly cool! Now I want to do out the spherical coordinate version! Derivation requested!
Please keep making these kind of videos.
They're a great help to all physics and math community!
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.
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 😊❤️
Great video!! I am very glad that I found your channel!! Thank you!
Thanks. We spent half an hour in class deriving the laplacian in cyl. coordinates
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
Another complex math concept made simple, thanks Andrew.
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. :)
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
Thanks man!! I did it for spherical coordinates and got it right!!!!
But I just trusted your Laplace equation!!
Waiting for the derivation!!
Nice!
Dude, your beard is looking great. Pls don't change it, bb
Man this is awesome 👏👍!! Keep up the good work and thank you for this great vid
I'm an econ / finance major, and have literally -1354 ideas on what's going on, but I enjoyed this
@Andrew, Why in 1/r *d(r*d/dr)/dr don't the 1/r and r cancel out? Thank you
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
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.
noice, the huge tensor boi is back at it
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 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!
Thank you! My electrodynamics professor just went over this, but I was confused
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.
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.
I vaguely know the idea and a little of the math going on but I enjoy learning
the beard is looking majestic man, so jealous
This is awesome thank you 🙏🏻
cant wait till i finish collage so i can finaly understand this
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.
Welcome to Wolverine does physics.
the tensor memes were actually true I would be interrested what happens to this if you do it in 4 coordinates IE relativity
The beard is actually legendary
ur like my role model boi
GIVE US SOME MORE OF THE PUNIES TENSOR BOIS, ANDREW!
Thanks so much!
"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
Andrew how to derive the laplacian in terms of the metric tensor
What is tensor?
Nicccce!!!
Ur handwriting though!!!
Much better than mine.
What is that question called that you used with the metric tensor ?
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?
Tensor Calculus For Physics Majors Part 6 Confirmed (hopefully xD - made notes on it as well).
Whoooop
thank u so much dude xDD
What if he didn't have the use of equal signs.
Do a derivation!
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!
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
Why did you cancel r in d/dz part but didn't in d/dr ? What is the point of keeping that r?
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?
Do you know any good intro to tensor calc?
David M I’m doing a series on it
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!
Just don't let Jesse Kyle derive the Laplacian equation.
tensorboi is gut friend yaya
Aw, I was hoping to see christoffel symbols
Is there a generalized tensor version of curl that doesn't use differential forms?
Booooooooooooi. Nice
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?
So essentially the jacobian?
The square root of the determinant of the metric is the jacobian. So yes
He he i am imagining you without beard ...😜😜😜
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
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
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!