Why you don't understand GREEN'S THEOREM -- Geometric Algebra, Calculus 3, Vector Calculus
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- เผยแพร่เมื่อ 3 ก.ค. 2021
- In this video, we discuss the link between the fundamental theorem of calculus and Green's theorem. This offers an introduction to the exterior algebra, specifically, the wedge product. We discuss, albeit not explicitly, the de Rham pairing, which offers an enlightening interpretation of the fundamental theorem of calculus, bridging this theory with the theory of vector calculus. We discuss Stokes' theorem, verify properties of the wedge product, and more. This is part of a series on Geometric Algebra (c.f., • A Swift Introduction t... ).
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Hi, my name is Kyle and I'm currently doing my doctoral mathematics degree in complex differential geometry under the supervision of Professor Gang Tian and Professor Ben Andrews.
This audio is terrible....
You sure went to a special kindergarten!
@Kyle Broder can you please stop saying things like "you learned in kindergarten" or "kindergarten level". It makes you come across as quite dismissive and arrogant and turns people off. None of this material is necessarily obvious or intuitive and to pretend that it is (even if it has become second-nature to you personally) is not the right attitude for an educator to have. Otherwise good video
I don;t think the title is any good.
Before watching the video, I just want to say that I don't understand Green's theorem because it's always taught at the end of the semester when you are trying to scramble to study for all your tests and get everything else done.
In my undergraduate years at UNSW, I took courses in Vector Algebra, but the theorems seemed ad hoc. I never became aware of any deep insight in these theorems. Geometric Algebra is what I should have been taught. Thank you. There are right ways and wrong ways to present mathematical concepts. I think Geometic Algebra will take us into the next millenium.
This is brilliantly concise. Edward Frenkel gave lectures for a semester of UC Berkeley's Math 53 (multivar calc) that were videotaped and put on YT, but only hints at this development without mentioning any defined concept (such as wedge product). Robert Ghrist even gives his online Calc 1 students a peek at the concept of boundaries, but doesn't note the next steps, not even in the Calc Blue series. It's not that I expect material offered openly to elaborate these next steps, but to come so close and then retreat seems a shame. And here you are with this wonderful presentation! I don't have enough math to go all the way there, but this is more than enough for me to see the outline of the advanced concepts. Beautifully done!
All names are made up, but Peter Petersen looks like is a made up kind of The Sims' NPC.
Then you go to study about spaces without an orientation and realize that everything actually comes from Stokes' theorem for *pseudo*forms. It never ends, really.
One question: why is a wedge implied between dx and dy?
What a clear cut presentation!! You made as clear as possible man...I am glad that I found your videos !!
Great video, best explanation of Green’s theorem I’ve seen so far
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Nice Video man! You deserve a Million subs. As a Computer science student, I found this very useful!
this was so simple yet so accurate and elegant I cant believe it!
Thanks for posting this video 👍
This was so cool!! Thank you
That was so deep. Brilliant.
And thank you for this video
This is gold.