Differential Forms | The Hodge operator.

We give the definition of the Hodge (star) operator and give some explicit examples.

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[meneiroh]

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

[youtubeuser]

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!!

[madlarch]

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

[twistedsector]

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

[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.

[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.

[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!

[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!!!! <333

[stevelamprou]

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

[jeffin]

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

[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?

[rafaelles]

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

[byronwatkins]

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

[__]

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

[gaganaut]

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

[felipetavares]

this looks a bit like grassmann algebra

[seanannigan]

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