Differential Forms | What is an m-form?

We give the formal definition of an m-form, give some examples, and present the general "shape" of m-forms.

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Differential Forms:

Number Theory:

Calculus:

[UndeadFil]

I believe you messed up at 3:58 when you did an odd permutation (1, 2, 3 to 2, 1, 3) and accidentally called it an even permutation. Maybe swap the 1 and 3 there and then you have 2, 3, 1, which is obtained with an even permutation of 1, 2, 3.

[ctanle]

Old Macdonald had a form: e_i /\ e_i = 0

[jdsahr]

at 19:48, the subscripts of the dx's should not be dx_1 ... dx_m, they should be dx_i1 ... dx_im. It's pretty clear from the context that this is what was intended --- it's just a typo.

[drpkmath]

Very interesting m-form development from 20:48. As someone said earlier, this video clarified a lot of interesting facts about DG. Expecting more to come

[StephenMeansMe]

In the "wedge distributes over +" section where you're expanding, the dx-wedge-dy term should be 5, not 4.

I really like this series!

[davidgillies]

Note at 4:10, (u2, u1, u3) has odd signature as well.

[jp-ratsratsrats]

For those who are interested, “introduction to manifolds” by Tu is an approachable book that covers this stuff in satisfying detail.

[malawigw]

I have studied general relativity and differential geometry quite a lot, but never seen this kind of clear and "get to the point" explanation of what differential forms really are.

[SayHelllllo]

15:24 forgot the 2 :( there is -3dxdy - 2dxdy

[Mohammad-twcq]

I haven't gotten around to watching any of this series yet but I am very glad to see some videos on Differential Geometry for when I get around to learning it.

[andyl.]

Awesome videos! Just a small oversight: the "2-forms" vides is missing from the playlist, and this video is in it twice.

[paradigmshift]

At 19:50, shouldn't the wedge product terms on the RHS be dx_{i_1} \wedge dx_{i_2} \wedge .... \wedge dx_{i_m} instead? This confused me a little...

[music_lyrics-niks]

These are so good, thank you so much for sharing these with us

[SigmaChuck]

I absolutely love the elementary approach of this series. Really easy to understand. Thank you.

[rutvij]

Thank you Dr Penn for this video series. It clarified a lot of the difficulties that I had in DG.

[SefJen]

4:06 For the second example, the sign is wrong, it must be w(b, a, c)= - w(a, b, c)
Your videos are great ! ^^

[aras_lebasi]

In the example 3:55, how is that permutation an event element of S3?

[jaeimp]

@19:24 it should be -7 dx wedge dy wedge dz.

[quantabot]

80K yeaaa, million subscribers he deserve

[jonesbetty-zp]

amazing! this is my first time to understand what differential form is, read lots of materials but it doesn't work, great!