Tensor Calculus for Physics Ep. 13 | Covariant Divergence (and Laplacian)

[@twistedsector]

From this result, of course, you can quantize gravity - but that's an exercise for the reader.

[@twistedsector]

...and _that's_ how I remember the Laplacian in spherical coordinates

[@AndrewDotsonvideos]

Yeah and since it’s with respect to a scalar, you don’t even have to worry about h_mu business

[@thephysicistcuber175]

@Simple Group I unironically do the same.

[@meowwwww6350]

Andrew is the best tensor boi in KZbin!!

[@pugazharasuad]

I was just binging his tensor calc playlist- Lord Andrew, are you watching us?

[@user-en5vj6vr2u]

Yes, he is the chosen one -- he will bring balance

[@aniketeuler6443]

That's nice that you never miss what your viewers need to see. 👍👍👍👍

[@zayncharania9182]

You teach this so much better than my tutor

[@RC32Smiths01]

Great to see this back! Informative and interesting to learn, especially as a physicist.

[@nadiyayasmeen3928]

Ah yes finally. The most awaited video

[@maureendotson4634]

76th 😫. I wish we had the same time zone! ~Mom 💕

[@meowwwww6350]

You must be a proud mommy of Andrew Dotson!!

[@meowwwww6350]

You must be a proud mommy of Andrew Dotson!!

[@1timoasif]

Taking a Physics dept GR class and I was having trouble figuring out all the tensor calc thrown at me, this entire playlist is a godsend. Also just to let you know, I think the tablet format works great!

[@umutcan450]

Great combination divergence and laplacion in terms of gradyan and spherical coordinates. Also, variable substution and conversions are almost stand out everywhere. Thanks for fertile tensor series as electrical and electronic engineering beginner student.

[@oni8337]

Where can I find the video that you mentioned at 15:06 proving the significance of \sqrt(g)?

[@prateekmishra2070]

I'm a Biology graduate and m preparing for a masters in physics. I just love your videos Andrew. Well, started learning Tensros from your videos almost a couple of months back and now moved on to General Relativity. Still watched this for a quick revision. I cannot explain how easily you taught the concepts of tensors. You have made these concepts look so easy. Now whenever they pop up in general relativity it always looks so damn easy and obvious. Do you plan to include a course on GR in near future or so?

[@AndrewDotsonvideos]

Thanks a lot! So far the end goal is to get to the Einstein field equations. I havent decided if I’m going to make videos past that

[@kharitongorbunov4897]

What a switcheroo

[@abhishekkp7121]

First wanted to say thank you for this series. It helped me to understand the concept. Amazing video by the way

[@AndrewDotsonvideos]

Thank you!

[@osnofla13ify]

You actually teach better than my Relativity Physics teacher, thank you

[@Mforader1792]

Thanks man again! This was very in depth. Again knocked it out the park!

[@cvlad2001]

Im fresh out of covid quarantine and I thought my day could not get better... the lvl 12 tensor boi proves me wrong once again

[@Guztav1337]

Thank you. You are definitely a good resource as a complement to other Uni material

[@zzane4677]

Ayyy another video where I'll understand nothing but still watch anyway

[@JustAjdax]

Thank you, Andrew! These videos have helped me so much. You are amazing!

[@AndrewDotsonvideos]

Thanks a lot!

[@manolotenorio8093]

Oi, you should have a second channel! Absolutely love all your content but I feel like it would be a little more organized if you had 2 channels,like, one for the fun comedic physics videos and one for the educational teaching videos like this one. Great fan of your channel btw

[@javidfazilov3362]

Great content

[@davidlenir7517]

Haha epic. I figured this one out on my first EM assignment this semester. The TA was surprised :p

[@connorbrown5267]

A great series!

[@marshalltaylor6303]

Andrew plz do a skit where you start either two best friends and you derive at least one of them gotta be ugly. Plz

[@mohammadtarshihi364]

Damn you’ve become a lot more active Andrew

[@randomblueguy]

You’re goddamn right.

[@axelc6125]

*attractive

[@v6790]

@@axelc6125 I read that too

[@prateekgupta2408]

You should do a Room tour

[@shayangfkk7948]

yay he's back

[@jakubpuchatek3029]

i hope that someday i will understand these lectures, keep up the good work Andrew ((;

[@amansinghlobana5256]

F= am Regards, Electrical engineer

[@Supercatzs]

Get a load of THIS guy

[@sakshamsharma4184]

Andrew i also want to go to physics gradschool And i love your vlogs Are you planning to make vlogs

[@AndrewDotsonvideos]

Yeah I am

[@aidansgarlato9347]

Will you ever do a series of differential forms and the like maybe showing the Einstein-Cartan equations or showing the Laplac-de Rham operator?

[@taw3e8]

Wow! What a surprise! :p Not sure if I still remember all that stuff...

[@BeLikeNexus]

Here early to tell you to make an only fans

[@twistedsector]

OnlyFriends 😪

[@v6790]

Haha

[@BeLikeNexus]

@@twistedsector Hate to see it lmao

[@godzilla362]

I am a computer Science student... And I just watched the whole video😶😶😶 And I liked it...❤️

[@chiragkshatriya9486]

Sir the result at 15:08 is not working, Suppose we take spherical coordinates : If we calculate gamma(r, r theta), gamma(theta, theta theta), and gamma(phi, phi theta) by using the above formula we get, gamma(r, r theta) = cot(theta) gamma(theta, theta theta) = cot(theta) gamma(phi, phi theta) = cot(theta) But if we calculate using the original formula we get, gamma(r, r theta) = 0 gamma(theta, theta theta) = 0 gamma(phi, phi theta) = cot(theta) Sir, we can also think in this way that the right side of the formula you have written at 15:08 is only dependent on lambda so on the left side you take mu value anything it won't change the answer as the determinant value of metric tensor won't change.

[@monkerud2108]

when comparing oranges and mangoes, make them both into apples so you can compare them.

[@connorbrown5267]

Hello, was wondering what tablet device you use for taking notes this way?

[@javidfazilov3362]

are you planning on doing vlogs?

[@mohammedatef8856]

I don't think it's obvious what you mean by "ordinary vectors". It might be in the case of displacement, in order to get the units right and all that. But it's not obvious for a general vector without any reference to its physical dimensions. The scale factors (h) are denoted in many books by (h_ij) which are given by the particular coordinate transformations we use. You can use them to get the components of a vector in any coordinate system from its components in any other coordinate system or to obtain the line element in the new coordinate system, so on and so forth. But they don't help explain what an "ordinary vector" is or how to "relate covector and contravectors to ordinary ones".

[@kamalnawhal9356]

Can you suggest all books need to understand STR AND GT

[@AndrewDotsonvideos]

Griffith E&M for SR, carrol for GR

[@twistedsector]

@@AndrewDotsonvideos my picks as well (although David Tong's lecture notes are top notch too)

[@kamalnawhal9356]

@@twistedsector where I have to search for these

[@JustMrHill]

A suggestion; either turn your camera so it's in front of you when using the tablet, or turn yourself so you stay in front of the camera when using the tablet. The audio gets quieter and louder every time you rotate yourself to/from the camera, audio would be consistent if you're sat in a way that's always facing the camera

[@thephysicistcuber175]

Skipped step at 14:35.

[@Anyideas14]

Ha I’m going to do history and Philosophy but I still love this

[@chritophergaafele8922]

I enjoyed this video

[@user-kf5cr1kf2w]

My Prof just started the introductory QM class (3rd Semester) in Theoretical physics by deriving the Pathintegral for 60min... I‘m not sure how to feel about it because on one side I think I‘ts awesome but he also said that one of our homework assignments will be calculating the harmonic Oszillator with the Pathintegral so I‘m a bit scared^^ If you plan on expanding the pathintegral series I would love to see the harmonic Oszillator otherwise I will have to harmonic approxilator it

[@davidfenoll2332]

Oh god are you sure you entered the right class.

[@user-kf5cr1kf2w]

@@davidfenoll2332 Pretty sure, but I just finished watching the second lecture in wich he derived the schrödinger equation from the pathintegral formulation so we are moving on to the regular approach to QM - i guess he just wanted to give an elegant entrance

[@AndrewDotsonvideos]

Harmonic oscillator using the path integral will test all of your math capabilities, that’s for sure. Definitely not an easy problem by any stretch of the imagination

[@tomkerruish2982]

@@AndrewDotsonvideos Actually, it's super easy, barely an inconvenience.

[@jeff9846]

hi sorry to bother but do you think it would be possible to do an ncaa sport while also getting a phd? I know youre probably more busy than a regular phd student because you make youtube videos and tutor but do you think its possible. Btw i love the vids im planning on getting an Applied Mathematics degree

[@faithfulEman6288]

My my I don't even have anything to do with Tensor Calc in my plan but I still watch this Playlist for some reason haha

[@sofianhanifeh4602]

Are you actually writing with your left hand 😲? I thought you were right-handed from your other videos!!

[@nikosandrianopoulos4185]

hey andrew !you might have addressed this issue already , but what equipment do you have for this very A E S T H E T I C digital notetaking?

[@tomkerruish2982]

Andrew, would you do something on spinors? About my only experience with them is what's in Gravitation. They talk about dotted and undotted indices and something called a vierbein. The only thing I got out of it is that they're kinda like square roots of vectors. (I'm a little more comfortable with the Pauli spin matrices, and even SU(2) being a double cover of SO(3), but I was lost with this stuff.) Edit: where are my manners? Excellent video as always!

[@iflashlantern4292]

I’m a cs major. What am I doing here?

[@SiegfriedFafnirsbane]

Kakashi sensei

[@kylechouinard4341]

Bruh I’m studying journalism the fuck

[@johns9579]

First! love your videos!!!

[@iWrInstincts]

I feel like this may not be the place to ask but what's there to lose.. Can anyone offer any tips in regards to understanding concepts in physics? Especially at higher levels. I often see that I have an understanding in the majority of the math, however; when it comes to starting the problem and thinking about concepts (since the rest of problem-solving is just math rearranging) I find myself not being able to figure out what assumptions I need to know. I feel like re-reading page after page in a section of the book is quite inefficient. I watch Andrew's videos and I wish to be able to know these little (but important) concepts that help him with problem-solving. I know that in order to build physical intuition, one must *do* problems, but I can't even do the simple ones lol...

[@lightninbolt74]

Great video, but just wanted to say that there was an annoying fan sound in the background, hope you fix that next time!

[@cyberkotatsu]

I'm at a weird point in my life where everything is coming up tensors.

[@AndrewDotsonvideos]

That's an exciting point

[@youtubegaming3281]

Do some quantum series cause your a great speaker

[@burcuylamatematik8883]

Where can I find the excersis and solutions of nazul islamin tensorlar book?

[@jasonliu1181]

physics is fancy greek

[@joshissa8420]

Andrew if you put the time stamps in the description it will chop up the video into the sections you want

[@AndrewDotsonvideos]

Woah that’s pretty neat

[@prakharanand7012]

WHY DO I HAVE GORDON RAMSAY ALL OVER MY RECOMMENDATIONS

[@rickbeatty9936]

Did you ever spill the big trick, Andrew? The log ( det M) = tr (log M) one? I was was unhappy until Sean Carroll explained it to me.

[@victorhugo9839]

I really want to learn how to read this

[@connorwinterspianotutorial9253]

Do you play osrs? I saw your comment on Settled’s vid lmao.

[@AndrewDotsonvideos]

Hell yeah

[@uruhara6713]

My college starts in march (it's a local college offering a 3years general science course )but I have started studying physics and mathematics on my own...I today completed method of undetermined coefficient in 2nd order diff eq and I'm also studying calculus 3 (from online lectures by Prof Leonard) ,I intend to complete differential equations, cal 3(vector calculus) ,linear algebra till March and after that I think I will start with forier series ,PDEs (I intend to study this from Chris tisdell 's lectures on these subjects on KZbin) and then probably complex analysis..intend to complete this all in one year and then I will start tensor calculus and then probably some general relativity....It would be really nice to hear some feedback and can you make a video on guiding people how to start studying physics/math on ur own and what online sources to use?

[@thedoublehelix5661]

You should also get a lot of books (if you can afford them). In my opinion books are the best way to learn

[@uruhara6713]

@@thedoublehelix5661 I'm studying mathematics from Erwin kreyszig's Advanced Engineering mathematics

[@dhyangandhi4344]

Currently, I'm following the same path that you said. First the lectures on MIT OCW, and then tensors and so forth. I'd personally recommend you start doing a bit of physics side by side, for example Griffiths. My point is, you don't necessarily need to take a linear path.

[@uruhara6713]

@@dhyangandhi4344 I am studying physics side by side..

[@capitanpenguin]

my man andrew lowkey doing anything but his phd lol, procrastinators gang rise up

[@AndrewDotsonvideos]

Gang gang

[@misscontreras8031]

I love bread 🍞

[@GastroenterologyPINNs]

Can someone​ recommend books for higher math like in this video​?

[@AndrewDotsonvideos]

These lectures are based of "Tensor Calculus for Physics" by Dwight Neuenschwander.

[@brandontouchet451]

"Tensors made easy" by Giancarlo Bernacchi

[@joshuamariano1663]

My guy, is that an iPad you're using?

[@Sam-lj3zl]

What level physics is this?

[@omermuharremyagcioglu]

handsome and clear physics:) Keanu Reeves

[@asdfkekl9250]

calculus is ez, if differentiation is the opposite of integration if u wanna solve an integral just differentiate it and 1 over it ez

[@letspass3465]

Wait a minute, I thought that you were right-handed, but you are writing with your left hand in this video. Are you ambidextrous?

[@AndrewDotsonvideos]

The world may never know

[@garvett6660]

Andrew could you please give an explanation to the fact that you and Papa posted videos almost simultaneously?

[@AndrewDotsonvideos]

We can schedule videos to be uploaded and then they’re uploaded automatically

[@NPCooking69]

@@AndrewDotsonvideos Also, he lives in my basement.

[@AndrewDotsonvideos]

@@NPCooking69 No, you live in my attic

[@NPCooking69]

@@AndrewDotsonvideos no u

[@garvett6660]

Get out of my house. Both of you.

[@dr.apoptosis1101]

Ya lost me in the first few seconds, damn it!

[@hshhsjhahsvs7728]

GIVE THIS COMMENT A HEART!

[@canyadigit6274]

Hi

[@nicolasjimenez6395]

Tf am I doing here, im in ap calc

[@lorenzonioi7855]

[@thephysicistcuber175]

You mean not everyone knows this? I'm disappointed.

[@irtheLeGiOn]

hrmm.. I agree. Shallow and pedantic.

[@1980sDude]

Instruction unclear. Created a black hole.

[@dotsonsvlogs7573]

Hey Andrew, Loves From India. We want Donald Trump.

[@themightyai3495]

Get a load of THIS guy