2. Introduction to tensors.

MIT 8.962 General Relativity, Spring 2020
Instructor: Scott Hughes

The notion of 'coordinate' bases.  Several important 4-vectors for physics: 4-velocity, 4-momentum, 4-acceleration, and their properties.  1-forms, and tensors more generally.  Using the metric and its inverse to raise and lower tensor indices. Introduction to tensor fields. The number flux 4-vector, and its use in defining a conservation law.

License: Creative Commons BY-NC-SA

[mingshey]

A high school physics teacher, I want to follow up GR so many years after my graduation, and this open courses lecture is greatly helpful. Thanks a great lot!

[tzachs_]

Great initiative from the side of MIT to share such valuable and prestigious sessions to common people while some universities are not willing to share.Please do similar for econ classes.Hats off to you MIT.

[gurunandhaelamezhagan]

1:19 Recap
4:20 Basis vectors
8:54 Transformation of basis vectors
24:01 Operations using four vectors.
59:44 conservation of 4momentum

[SpokoSpoko]

Regular guy would say I will drink water, the professor will hydrate himself.

[hariszachariades]

Making these courses available to everyone makes the world a better place.

[coffeeguy.]

When he said "That's the damn vector", I felt that.

[g.v.]

I’ve begun learning General Relativity using Bernard Schutz’s book. These lectures (so far) match the notation and topics of the textbook. This is truly a gold mine of information! Thanks many times!

[qbtc]

As with any of these advanced and technical courses, the views drop off exponentially with each successive lecture. Kudos to those who kept with it all the way to the end.

[KakashiChidori]

Finally after so many years.
The general relativity.

[meowwwww]

MIT ocw is just the right way to learn in quarantine

[MrJesuswebes]

AT LAST, general relativity from MIT with videos. GREAT DAY FOR ME!

[andrewfeng]

I'm taking a math course in calculus on manifolds which covered tensors and it seems like the physicists use a pretty different language...

[aadika]

6 February 2020 : "My daughter has some kind of a virus"😅

Great lecture btw. Keep it up MIT!

[calebjimmysmith]

Correction at 47 min for spherical coordinates: the "dφ" is missing on the final term.
It should be something like this:
vec{dr} = dr vec{r} + r dΘ vec{Θ} + r sin Θ dφ vec{φ}

[abdulsamadkhan]

myyyy i have never commented on any video in my 10+ years of youtube but i wanna say that
THANK YOU MIT i really needed this ive watched all three semesters of quantum by prof Zwiebach and im thankfull to the ocw team
ps a little QFT would be nice

[vednarsekar]

oh thanks MIT OCW now i understand tensor calculus

[rishabhkaushik]

00:51 When he said virus, only corona came in my mind.

[johng]

This is what I want for years, my university won't allow selecting courses from other majors, I'm in computer engineering btw:-)
Finally I can try to understand GR

[gso.astrowe]

Just starting this series (and watching Stanford's Leonard Susskind's series on GR concurrently). At the beginning of this video, Prof. Hughes is drinking water and mentions that his "daughter has some kind of virus." This was recorded in Jan. 2020 -- just as COVID was appearing on the radar. The first recorded case in the US was January 20, 2020 (and that was in Washington state, on the opposite side of the country from MIT). So I presume this was just an "ordinary bug" his daughter contracted. Still, knowing what was to come in the next few weeks and months; it was enough to give me pause. In fact, I will be interested to see if this becomes an issue in the course later on.

[tetbundy]

I like how this guy is moving relatively fast!