Differential Forms: PART 2- COVECTORS AND ONE FORMS

Hi, this is just a short video outlining some of the motivation behind one forms, and it will help us understand k-forms as well. We skip over a lot of the details at this point. I hope to return to that. In particular, the questions at the top of your mind should be: "how do we weave tangent and cotangent spaces together?" and "how do we actually compute integrals like this?"

CREDITS:

--ANIMATION--

I used 3Blue1Brown's library "manim". He's honestly an icon.

--REFERENCE--

L.W. Tu, An introduction to manifolds

--MUSIC--

•Music By: "KaizanBlu"
•Track Name: "Remember (Extended Version)"
•Licence: Creative Commons CC BY-SA 4.0

[Aleph]

This is incredible! The way you've explained forms without going taking the typical red-army approach (i.e: without plodding through definitions about tensors and tensor products and wedge products, and so on) is really refreshing. You've brilliantly explained the intuition behind forms / how they're a natural extension of the integrals that we've always been doing. Keep it up -- looking forward to your future content!

[IntegralMoon]

I really like these videos. I hope you keep making more. Although I'd really like to see you work through some simple examples - I find your videos a little abstract in general. That seems like it's just your style, but a simple vector field on a simple manifold would really help me make sense of everything you're saying. Thanks for making this :)

[williamturner]

Is \gamma really from M to TM? I'm not sure that makes sense.

[lukalomtatidze]

Can't watch because of music. Pls remove.