Tensor Calculus For Physics Ep. 12: Christoffel Symbols 

*Typo*: The second term containing the connection coefficients in the definition of the covariant derivative of a second rank tensor has a typo. In general, the rho mu should be a mu rho. What I wrote holds only for symmetric second rank tensors. Since we took covariant derivatives of the metric which is symmetric, nothing was affected in the derivation itself.

You know COVID-19 is bad when all there is to do is going back to Tensor Calculus.

I literally and honestly got excited when I saw the notification. Now you have a blackboard, you have progressed in the physics field: time to learn Walter Lewin's dotted lines! You go, Andrew!

Engineer: *Now tell me, how does all of this helps me on my future*

I love how he just talks like we know everything he is talking about. Good job, Andrew😂

My classmate: are you playing hangman?

Guys make sure you really understand this, you're gonna need it to understand my General Theory of Relativity & to derive my 10 field equations.

I don’t think I’ve ever seen you work on a blackboard. Thanks for getting my account back! ~Mom

Excited for this one man! Also please stay safe and sound from the virus my man, wish the best for ye!

At 14:12 you said "non-zero Christoffel symbols does not mean your space is curved". Finally, I see how to generate the Euler and centifugal "fictitious" forces. Your videos are gold!

Me: On youtube RU-vid: We recommend tensors Me: What the hell is a tensor? Me, after watching video: What the hell is a tensor?

I am a simple man, I see the first equation, I quit but leave the video playing so I can support Andrew

Andrew- " you know what I'm saying " ... Me who studies intellectual property law and Computer engineering - "yes, I was never lost" I love the videos!! even if I understand 10% of the video ! Keep it up !!!

GR exam tomorrow and you the only one person to make a clear distinction between connection coefficients and the Christoffel symbols, thanks man

I absolutly did not understand this

Am I the only one who has no idea what he is talking about, but still loves listening and supporting him?

I've been learning tensor calculus in preparation for learning about special relativity and radiation at university this year. These videos help to consolidate the knowledge and practice that I did maybe two days ago, and help to clarify pieces left out by my textbook.

Been waiting on this so long I had to use Alex Flournoy as a substitute! Dr. Dotson is finally back giving lecture :D

The series was so awesome that I actually binge-watched it, and eventually learnt a great deal of tensor calculus I've been struggling with! I just cant wait for the next videos to come up!!

Oh so this is an actual lecture!? I thought this was one of those professor jokes blabbering some shit

I'm learing tensors through your videos. Please don't stop this series it has been very useful. Thaks a lot man. Keep up the good work buddy.

Thanks that felt like a introductory GR lecture, in an entertaining way! More of those ASAP!

i love your videos, please release more of then, you are helping me a lot with my master degree.

A very short way is to write the KE of a free particle, with a general metric g, as a lagrangian and find the EOM. These EOM will give you a geodesic equation and Christoffels symbols comes out naturally in this procedure. Only thing I have found bit tricky is that one has to adjust the indices to the wanted answer.

Hyped to see this series continue.... I’ve been struggling to connect all this tensor stuff back to the intuition I developed for cartesian/euclidean coordinates/spaces. Great presentation through the whole series. Suddenly GR self study seems much less insurmountable. Please keep them coming!

Love the ending. It was a very important observation.

I love watching these videos!!!

Thanks again man. I CAN NOT WAIT till the nextepisode!!! 🤙explained crystal!!

I really enjoy your videos...excellent teacher

Hey Andrew I have a channel suggestion for you. Videos like this one where you explain high level physics to us as if we're PhD students is a good thing to have online, but is frankly impenetrable for most of the viewers. We have NOO idea what you're saying given the jargon and absence of explanation. However one thing that's lacking on youtube is physics teachers like yourself who are NOT AFRAID to dive into the maths of a physics problem. Physics youtube doesn't have a culture of solving random, but challenging physics problems like maths youtube does (Take Blackpenredpen or Flammable Maths for example). Physics youtube instead prioritizes telling us about big mysteries or the heroes of the past, it doesn't TEACH physics or solve interesting problems like "how fast would the sun cool if you submerged it in an infinite fresh water ocean?" Even International Physics Olympiad questions would be interesting to watch you work through. In short, I think you can pioneer these sorts of physics videos on youtube, and you can do it without dumbing your channel down to solving simple rope and pulley questions or staying surface level.

Good video to watch during my (extended) break! ALSO I recently got accepted to the SULI internship at JLab in nuclear physics! I mentioned you and your videos in a couple essays about why I wanted to work there so thanks for the boost :)

By far my favourite lecture series atm

My favourite tensor is the StReSs TeNsOr!

So without watching any tensor calc vids and being a first year in college I wanted to see how long until i got lost. Turns out about 5 seconds feelsbad. I tried. Keep up any content tho man I personally cant enjoy this but im sure many people do.

I understood nothing but your enthusiasm made it fun!

I have been wanting to learn tensors for a long time. Recently I started my masters and I was glad I'd be getting to learn tensors. Lmao cut to my prof starting and finishing the material on tensor calc in a week and I spent the last two days binging this playlist a few times. I just finished a test and I hope I pass. I'm now convinced physics is basically masochism and I'm going to get myself some Tensor Boi merch from Papa Andrew. PS. In all seriousness thank you so much for this playlist! I really liked the motivations behind your derivations (esp this video).

I have waited for this for so long!

Named after Dr. Chris Toffel of Norway who first studied these types of connections in the 1890s while working at University of Oslo.

One more great video 🤘🤩.... this is probably the best channel on youtube for me

Well didn't have time to watch this tensor calculus videos. But my university just cancelled classes because of COVID. Let's go.

It's really *USEFUL* . Thank for sharing knowledge! Thug some concepts are still quite like nightmare for me. I do need to review all the notes taken from your video before. Thank you again! :)

Re the Christoffel symbols related to a curvilinear csys, the superscript on Gamma stands for the components of the displacement vector, whose displacement is a comparison of the original vector (prior to transport) to the vector's new position (after transport). Are these components wrt the A) curvilinear csys or B) wrt to an orthographic csys? I ask because its an easy task to find the components of a vector on an orthographic csys since there are many tick marks. But on most graphic representations of curvilinear csyss, it's just four curves (not broken down into smaller units such that one could measure the change in the displacement vect wrt to said curvilinear csys. To me, that means that the breakdown of a displacement vector must be graphically calculated using an orthograhic cys superimposede under the curvilinear one. Are these components wrt the A) curvilinear csys or B) wrt to an orthographic csys?

Taking a covariant derivative is easy. Take the partial derivative, then place a tittle above the comma (transforming it into a semicolon), and voilà! Seriously, another way to derive the Christoffel symbols is using the calculus of variations to find the equation of a geodesic. It's been a long time since I worked through it, and it'd be hard to describe it in ASCII anyway, but perhaps you could do a future video on it.

Now i understand clearly. Sure it helps me in my maematical physics exam thanks man. Please make videos on Einstein tensor

Thanks for this whole series! You've been a great help! Quick question though: where'd you learn Tensor Calculus? Was it in a specific class or just on your own from the book?

lol im stuck now on something like 9th one gonna watch this in few days probably but i know its awesome

Get a load of THIS guy

Just waiting for your next video....

Hmmm yes I totally understand this while scraping a B+ in calc 2... yes of course. Hmmmmm

Please do next videos on tensors....this off time due to covid,I'm really free to read further on physics & so tensors

Hi Andrew thanks for the superb videos on intro to advanced topics of Tensor Calculus, i was wondering will you cover all the topics of "Tensor Calculus for Physics" in this video series

Our electrodynamics teacher mentioned this covariant derivative very briefly.. I now see why there is no affine connection term for regular E&M since we work with the Minkowski metric tensor!

Hey Andrew, could you make a video where you explain how you fund your PhD- On the tution, scholarships and daily expenses, etc?

Do you sometimes worry that getting a PhD from NMSU might hurt your chances at post-doc or faculty positions at reputable universities in future?

Please make a video on eponymous transformations(if you can...)

You're the best, keep it up.✊👌

Dear Andrew, please do it regularly on white board with the tip of marker flattened. Also the voice of yours is dim and I usually repeat the video many times to listen you properly. Please improve your mic. Waiting for next video.

Excellent video

YES. This is what I subscribed to this channel for. I'm just kidding I came for the jokes.

Why don't you do basic to advance calculus. That would be soooo awesome.

dirac: general theory of relativity is a good book for this. Cartan approach is mind-blowing, though...

Thank god. My Gen Rel be saveth by thou

Awesome Video, thanks! ⚖︎☯︎

I am in high school, I don’t understand this, I shouldn’t be here, and yet I am. Why? I don’t have the slightest idea, but I’m intrigued

In the first line you wrote T_rho my , but shouldnt ist be T_my rho ,or is it necessarily a symmetrical tensor?

Sir is it complete course of tensor for physics?

I have a questio, what is this all about? When are you gonna use this kind of math?

why all the permutations are anti-cyclic? it's the same in my text book and I wonder about it...

My differential geometry professor said that he broke the spine on his textbook when he was in school learning the "christ these are awful" symbols, fun times

Hey dude, I am 14 yr old and I have finished books like Haliday and Resnick and I want to study GR and Qm . Dude could you tell me which books to start cause I tried to start GR but I couldnt understand the math and the matrices. Could you tell me books or lectures that I could take online?BIg fan man

Where is part 13?

Dr.Dot be out there hearting every comment lol.

Are you still doing online tutoring? I'm looking for someone to help me with QED as well as programming this summer.

At this point i'm questioning whether we even speak the same language.. I understood legit about half of the words you said xD Guess physics isn't quite my area

thanks..are you learning general relativity lately?

Wait... Your university is not closed or have you filmed this prior to the closure?

come on man, can't wait to upgrade to lvl 1 Riemann tensor boi

Take care man.

Hello sir., Wanna be a theoretical physics. Advice please......

Tensor calculus is all about fancy lingo....if understood you're good to go....... Attaboy!! ;)

hey I wanted to ask some advice from you all, planning on starting a physics degree this year and thinking maybe I should extand it to 4 years instead of 3 years because I heared its really busy and there is no much time for yourself, I'm thikning about going for masters in physics/CS so I also need total grade of about 85-89 so this also a factor, any thoughts? (btw a year of uni here is 3K usd and I might get a scholarship for the 4th year also, so consider money not a big problem), ty!

I love tensors

Great job!.... at confusing the shit out of an undergrad physics student 😑

Shameful admission: to this day, I still don't know the difference between contravariant and covariant, but hey that's why im an experimentalist 😅. Also, I don't trust anything with that many indices.

In which part of physics are tensors useful to?

I don't even know what a tensor is... still watched the whole video.

Andrew why am I here? I’m a Junior I’m high school taking chemistry...

Hmm yes I understand some of these words. (I have never studied tensord before, but I get at least some of the language from linear algebra)

I need the next video

Do you check the email in your about section still?

Chalk boards ❤🤘

Presumably you are doing this for extra practice? Why does upstairs get + and downstairs get -?

Although bro you forgot to include Le places extensional frequency as the quadratic function of delta h is not a function of earth time but a function of space time continuum according to greys epsilon function.... did you ever consider this?

I'm in the last year of high school and I have no fuckin clue of what a tensor is, but I find it amazing nonetheless

YES!

Do you have students still

ah fits the rule again subscribe will be given.

ey right when we just learned them

The E Nu and the Metric, so the gamma Ro alpha is the Interchange Mu and Nu. I have no idea why I clicked no this video. I have no idea what this is about.

only 30 seconds in and I’m more lost than a child at Walmart