Riemann geometry -- covariant derivative

In this video I attempt to explain what a covariant derivative is and why it is useful in the mathematics of curved surfaces. I try to do this using as many visual arguments as possible; however, some knowledge of differential calculus on the part of the viewer is necessary.

[GovernmentAcid]

love this! blown away by the fact that someone can so clearly and concisely convey info about such a potentially difficult-to-convey subject as riemann geometry

[mnazaal]

If Tarantino made a math lecture series he'd use this intro

[davidwright]

If only there had been the internet in my undergrad days - and grad student! I always knew that my questions had answers. It was finding good guides that was the problem! Many thanks & I look forward to more.

[LydellAaron]

I found this video while listening to Leonard Susskind's lectures on General Relativity (Lecture 3) after realizing I was unfamiliar with Riemann geometry. Your explanations and illustrations were very clear and easy to follow. I had to pause, rewind, re-listen, section by section, so that I could slowly follow your arithmetic but you kept a good pace. Thank you so much for your time and explanation.

[jennariseley]

Thank you so much, this is the only place where I have found an actual explanation of the metric tensor g. The wikipedia article has paragraphs and paragraphs describing what it is used for but doesn't actually tell you what it is in a straightforward way!!

[chasr]

WoW - Very Nice
This is the first time I ever saw the covariant derivative and gammas derived without explicitly using the metric tensor. Working through this has strengthened my understanding a lot. I look forward to more.
Thank You :)

[rockapedra]

This is the first time I understood the covariant derivative fully. You make it so obvious. I’ve looked in many places for this and it is always so confused ! And your explanation is obviously correct from the simple identification of the covariant derivate term in the full partial derivative formula. Sheesh! I spent a lot of time on something that is now so simple!

Thank

[christophergreeley]

As a programmer who learned C++ one ten minute tutorial at a time who was good at explaining things from the fundamentals upwards and didn't wave their hand and say "poof you do X and get Y" this is EXACTLY what I needed in order to learn this. Thank you so much these are some of the best physics tutorials I have ever seen, I am studying general relativity ahead of time as a physics student because I am very interested in it! Thank you so much!

[paulhinrichsen]

BRILLIANTLY EXPLAINED !! So CLEAR ! Thank you for this beautifully clear explanation.

[biagiodevivo]

While taking a tensor analysis course I had a hard time finding these concepts explained concisely. Great video

[aadika]

Youtube recommended me this video after 2 years I learned general relativity. And now I have a little idea about covariant derivatives. I wish you were my GR lecturer.

[Therfgd]

Thanks a lot, I did really make progress in my math by understanding the covariant derivative with your explanation.

[atzuras]

That's why the Flat Earth society do exists: they never got a grip on covariant derivatives and made parallel transport wromg all the way.

[ginosuinoilporcoinvasivo]

my god, finally a good explanation, as a high school student who is trying to learn the math of general relativity by himself is really hard to find good material.

[satyareddy]

Thanks for the great video. If you run out of explaining these complicated concepts, please make a video of simpler stuff. I am doing my undergrad in Physics and i am very sure i will be searching for this video in couple of years as i look forward and try to understand General Relativity. GREAT VIDEO!

[pinodomenico]

Truly excellent video. I watched this twice then I decided to stop it down and make a copy of the notes in full detail - that's when it really started to sink in. I also love your theatrical style of including an entertaining introduction and trailer. Brilliant. ♥
Now a sample problem where we might use the covariant derivative to calculate a result would make an interesting video. Nothing makes math as concrete as an applied problem...with real numbers and values.
All the Best !

[jackwilliams]

This explanation of a metric tensor is incredible.

[juleskurianmathew]

Really nailed it explaining what exactly are the covariant derivative and the christoffel symbol...

[Saki]

fuck man this is one of the best videos ever made for covariant derivative, linear algebra, and Einstein Summation. WELL DONE. This is better that google+Wikipedia+topology textbooks.

[davidprice]

This is a terrific description of the Covariant Derivative. Thoughtful, well constructed and easy to understand for a seemingly complex topic.