Differential Forms | The exterior derivative and vector calculus.
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- Опубликовано: 1 авг 2024
- We describe the operators from classical vector calculus in terms of the exterior derivative, the Hodge operator, and differential forms.
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Books I like:
Abstract Algebra:
Judson(online): abstract.ups.edu/
Judson(print): amzn.to/2Xg92wD
Dummit and Foote: amzn.to/2zYOrok
Gallian: amzn.to/2zg4YEo
Artin: amzn.to/2LQ8l7C
Differential Forms:
Bachman: amzn.to/2z9wljH
Number Theory:
Crisman(online): math.gordon.edu/ntic/
Strayer: amzn.to/3bXwLah
Andrews: amzn.to/2zWlOZ0
Analysis:
Abbot: amzn.to/3cwYtuF
How to think about Analysis: amzn.to/2AIhwVm
Calculus:
OpenStax(online): openstax.org/subjects/math
OpenStax Vol 1: amzn.to/2zlreN8
OpenStax Vol 2: amzn.to/2TtwoxH
OpenStax Vol 3: amzn.to/3bPJ3Bn
Please don't abandon this series. I watched all videos with the excitement a kid has watching a movie. I'm checking often your channel just to see if you posted the next video. Thanks for the great content!
it's all coming together now, this is all very cool
20:15
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
I really loved this playlist about differential forms. It made me remember a lot of things I studied in the mathematics degree and now I have understood them more deeply. Your explanations are so clear. Thanks a lot for your work.
I was kind of expecting to find a video about the General Stoke's Theorem at the end of the playlist, after the definition of the exterior derivative and its relation with the gradient, curl and divergence. If someday you have time to do it, I'm sure a lot of random people for the internet like me would appreciate it.
Best regards.
It always gives me pleasure to see different mathematical concepts getting united in a general theory. Great video I'm loving it! I watch this as if I'm watching my favourite anime!
Loving the differential form series
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
this insert is the climax of the theory of differential forms and why we started this: ie it unifies different derivatives that vector calculus had arbitrarily defined. exterior derivative though arbitrary , it is a deeper definition in that it unites different things. This is an example of good definition. all mathematical definitions are arbitrary , but there are definitions that unifies, that brings out beautiful mathematics. stoke theorem is proof of the superiority of exterior derivative over alternatives.
I can't imagine how anyone could come up with that. I love algebra, but figuring out all those relations seems like a whole other level of dedication.
Thank you so much Michael, this is the clearest explanation I've ever seen about the differential forms.
Great series of videos. Easy to understand. Many thanks
Loving this series
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
i really enjoyed this entire series a lot, thank you very much :D
A really great informatve series, like oliver I would love some more please! Always wanted to understand the Generalised Stokes theorem.
This is happening. My semester recently started and I am catching up on other stuff. I should get back into these videos very soon. My goal will be to investigate the generalized Stoke's theorem and the differential forms version of Maxwell's equations.
Hi Mickael,
I love your videos, and hope you never reach the "good place to stop"!
I begin to understand. God bless you.
This series is great
I've learned so much from this channel
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
Please continue this series! :)
Finally! This is clear to me
Hi I binge watched this series, I've watched 19 videos of you over night, so informative. also I like the differential form text book you suggest in description
As always 🔥🔥🔥
Note definition of curl at the beginning should be dR/dy - dQ/dz in case you missed the correction.
jeeez! Elegant video
Magnificent !
what i found suprising in this series is realizing dx isn't necessarily a infitesmal and open sets does not neccessarily mean infinitely small.
it should be grad(f)=(df)^#, where # is the sharp map (inverse of the flat map). similarly for the curl
@Michael Penn Is this the last video of the series? I thought the goal was to go over the generalized stokes theorem.
24 karat gold as always
Oddly, this def of the curl is - the one I remember using, with the pseudo determinant computation. Any idea where that comes from?
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
At about 3:24 minutes, it says that grad(f)=df. I completely disagree: the gradient grad(f) is a vector field, whereas the differential form df is a covector field. They transform differently and also yield different results in curved spaces (their relation involving the metric and its inverse).
dF is just the jacobian applied to a vector. If the function is a scalar field, then is the directional derivative.
You are absolutely right. It should be df=grad(f)^b, where b is the flat isomorphism that maps a vector to covector. The div and curl here also lack the transformation from vector to covector.
5:20, he kind of mentioned that.... no wonder something was fishy when i saw that (i couldnt tell what) and than i saw your comment and i was like ....of course lol
Great vid! Just one caveat - can you make sure to write all the plus signs? I thought dш was a three element vector for a minute
I had the same misconception, and was scratching my head for why dw is a 3-vector. :-) Writing the "+" would help me.
How can ** NOT be the identity? The set of m dx_i plus the set of (n-m) dx_i is all of the dx_i's. Complementing any subset twice always returns the original subset...
whoa...
I got mind-fucked, thank you.
ruclips.net/video/nJpONHO_X5o/видео.html
An excellent explanation of the correspondence between del and d can be found over on eigenchris's channel.
Please solve for all x and n for which 2n²+1 is perfect square
Please
@@sujalsagtani6868 Look up Pell equation. It gives all solutions.
First!
That’s a lot sexier than nabla.
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
20:15: "good place to stop"