Differential Forms | The Hodge operator.

[@meneiroh]

Dude, you're helping me a lot on my General Relativity classes!

[@youtubeuser8232]

I love your videos on differential forms! I really hope you'll continue them indefinitely... there is so much stuff to talk about... like De Rham cohomology...

[@lyrafiddle]

This is such a wonderful mini-course and especially for anyone who wants to understand the deeper foundations behind some of the modern trends in computational geometry. Thank you for creating and sharing this course!!

[@jmafoko]

the way calculate that hodge star is ridiculously amazing. my book made this mysterious, but there you are with a simple permutation rule with aim to get the right pattern(dx^dy^dz). you is a gread teacher hands down. i believe all advanced maths can be taught like this. with simple examples, using software and practicing on real applications.

[@xshortguy]

Every college should have a second "multivariable" calculus that explains this stuff. One thing I regret not doing in my undergrad (which is all I have done) is exterior forms and tensors. And it turns out that the leap in graduate school if I went there would have been too great for me. And this was even with a wedge product appearing in my vector calculus course, but it was treated poorly and without generality.

[@twistedsector]

Awesome explanation! The wiki page on this is notoriously abstruse.

[@stevelam5898]

Yes, it only makes sense after watching the full series on Differential Forms.

[@mastershooter64]

math wiki pages are usually not for learning stuff, they're only good for like reviewing what you already know, like using it as a reference yk?

[@madlarch]

Great! I finally managed to get the basic hang of what the Hodge star is doing !!! Many thanks for all your videos.

[@AdrienLegendre]

A good related topic is application of Hodge operator to Lorenz metric as it has nice applications to physics. Thanks for a great video, you are a excellent teacher!

[@stevelam5898]

God bless you Sir for making me understand what the Hodge star is, after two years of effort.

[@byronwatkins2565]

At 4:00, depending on the ordering, dx_I^dx_J might produce plus or minus the all-inclusive wedge product...

[@forheuristiclifeksh7836]

13:08 wedge

[@Ferolii]

Damnn I follow you since some years ago and it's the first time I really needed your videos for something of university or my studies instead of curiosity and stuff. Thanks very much, you helped me a lot with this!!!!

[@jeffin05]

Wow. Great video and class! Thank you so much!

[@rafaelles5063]

Thank you for the series. You could continue into differential geometry after that :)

[@goodplacetostop2973]

15:50

[@azhakabad4229]

Are you Martian?

[@theartisticactuary]

Michael - in the final answer, shouldn’t the 2 and 7 coefficients in *w be 1/2 and 1/7 to cancel out the 2 and 7 coefficients in w when you wedge w and *w together?

[@jeromemalenfant6622]

No; the condition is only that dx_I ^ *dx_I equals the volume element dx_1 ^ ... ^ dx_n, not that w ^*w is the volume element. The coeffcients are the same (up to sign) since the Hodge operator is a linear operator.

[@theartisticactuary]

Jerome Malenfant Thanks for taking the time to reply. Making more sense now.

[@__8474]

I know I’m late, but the hodge dual is also dependant on the metric chosen :) eg: *x^y = g(x,y)z where z is the elementary n form

[@abcabc-dl1ke]

super cool

[@the1111code]

You had me at dx *STAR* dy

[@gaganaut06]

Hi can you guide on how to solve semi explicit differential algebraic equations of index 3, I am not able to find any place to refer... It will be a great help thanks

[@raymondchou9550]

How do you draw such round circles

[@felipetavares7454]

this looks a bit like grassmann algebra

[@md2perpe]

It *is* the Grassman algebra. "The exterior algebra, or Grassmann algebra after Hermann Grassmann, is the algebraic system whose product is the exterior product." en.wikipedia.org/wiki/Exterior_algebra

[@twistedsector]

Physicists worship the mysterious exterior algebra too, but they call them grassman numbers

[@obaidurrehman2464]

Next video !??

[@arvindsrinivasan424]

🔥🔥🔥

[@eldattackkrossa9886]

cool!

[@eldattackkrossa9886]

nvm this is so far beyond me that my head exploded

[@stevenwilson5556]

@@eldattackkrossa9886 made perfect sense to me, but I have an undergruaduate degree in mathematics. How much mathematical training have you had?

[@eldattackkrossa9886]

@@stevenwilson5556 oh, not enough. i'm not sure of the correct english word for it, but i usually manage to understand his other videos. it's just that there were a lot of new concepts i think i'd need to understand this one

[@Rbaronii]

@@eldattackkrossa9886 this is part of a playlist, I'm sure you'd understand it if you'd watch the other videos on the subject.

[@eldattackkrossa9886]

@@Rbaronii oh, that makes sense, thank you

[@seanannigan7914]

Some days I wake up and think rotF= (*dF^b)#. God did calculus traumatize me.