Manifolds #5: Tangent Space (part 1)

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Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.

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Great clarity. Thanks for creating this. Hoping you will continue the series

ikechukwumichael

Thanks for the explanation, I was stuck on some concepts, now its clarified.

rudypieplenbosch

Fantastic explanation of a very complex topic! You're a natural.

Huffer

Thank you as always! I keep learning so much in these videos :)

iamtraditi

You are a really good teacher. ❤ your videos

kingassassin

Really excellent. Thank you.
But where is the follow-up where you construct the basis? I don't see it on YouTube.

johnspivack

This is such a nice lecture. I've been going through Nakahara's "Geometry, Topology, Physics", and your lectures have helped me get started on the Manifolds section.

One question: how would you attempt to connect a student's knowledge of multivariable/vector calculus, and relate what was learned in those courses back to manifolds and differential geometry?

monadic_monastic

Hi, your video is great! Will you upload next set of Tangent space video?

daveh

Really helpful videos, thank you very much 🐙

lugalek

Yo I’ll be honest I’m not that good of a mathematician but I find this super interesting

bobjohn

A tangent space is a vector space. Well understood. Thanks.

simbarashebepete

Is it correct that the only notion of "direction" we have on the manifold is "along the curve"? As we don't know about distances and angles yet.
So for a manifold of dim n, do I need at least n curves to fully define (a basis for) the tangent space?
Can we already define linear independence for the gamma curves?

narfwhals

Really well explained! I'm currently reading "introduction to smooth manifolds" by Lee (chapter 12, tensors) and I must say I find these topics very interesting. Can't wait to see the riemann manifold - related content!

danielesantospirito

Is it just me or does this seem like an unreasonably complicated way to say something which is actually unreasonably simple.

APaleDot

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