Self-Study Geometric Algebra!
Вставка
- Опубліковано 29 чер 2024
- Just listing books for learning GA!
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// Patreon
patreon.com/Eccentric282
// Timestamps
00:00 - Intro
01:04 - Bivector.net Discord
01:29 - Books for Beginners
02:41 - Books on Geometric Calculus
03:34 - Extra Books
04:30 - Good Papers
04:45 - Outro
04:52 - Extra
//Music
Music by Vincent Rubinetti
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/playlist/3zN...
Definitely agree that GA for physicists is a fabulous and well written book. It's a tough slog though, and I've had to teach myself a lot of physics to read it.
Your narration bloopers at the end was awesome. Why is it so hard to speak to a prepared video? I can do a live screen recording where I am also doing the mathematics, and don't have any trouble speaking to that, but might have to take 7 tries to get through plain spoken text.
Yeah, the topics in more advanced rotational physics were hard at first because I didn't learn much about that in my undergrad. Lots of supplemental sidework was needed for sure!
I honestly don't know 😂
Recording while scripted is so weird! I'd guess that it clashes with what we'd like to say if we were just freeflowing.
I couldn’t find any solutions to the problems at the end of each chapter. Does anyone know where I can find them?
Geometric for Electrical Engineers - Peter Joot (also has a blog and youtube channel) is a good one, too
I agree with this. The book gives you all the necessary Geometric Algebra concepts you need to apply to problems (Super Engineering friendly). The author also gives you examples problems solved with and without Geometric Algebra to get an idea of how to apply it. Currently reading which supplements my Electrical Engineering classes. The concept of phasors, and the complex plane became so intuitive. Also, will come in handy for Electromagnetics class.
There's a very recent book that came out by Michael Taylor on geometric calculus too called "An Introduction to Geometric Algebra and Geometric Calculus'' that you may be interested in checking out too! I've heard it attempts to delve through the subject with a bit more rigor, but I can't speak to that in great detail as I'm waiting for my copy myself. He did previously write a book with someone else on multivariable calculus, where it was written in such a way to prepare the reader for manifolds (by not doing the thing were we jump immediately to topological manifolds, charts, atlases, etc.. all in the guise of not requiring an embedding, but instead see manifold theory through the lens of an embedding just to start out.. A similar book which is out for free, which doesn't delve into exterior algebra let alone geometric algebra sadly - at least not yet - on manifolds that goes with the embedding approach is Boumal's "An Intro. to Optimization on Smooth Manifolds", and has much more of an applied flavor/that's the audience it's catering mainly to).
Michael does fwiw have crash course notes on geometric calc. for free online as well that you might find interesting too!
Your videos are worth watching
This made my day :)
personally, coming from a less physics heavy background has also really hampered my ability to put GA into application & I had to breeze past a lot of nomenclature I'd never needed to encounter as a CS undergrad. I'd say for students of that side, a list of more remedial texts to study foundational physics subjects like spinors at an undergrad level would go a long way into making a broader spectrum of applications more accessible too. to merit studying GA with that as common core, a lot of the language will probably make the pursuit feel a lot less overwhelming.
Spacetime Algebra as a Powerful Tool for Electromagnetism is a great paper too
Very true, I should've included it as well!
I get stuck trying to learn geometric calculus. The d[] operator, implicit diff; seems to assume commutativity; and for scalars, seems to do ALL of calculus. But I get stuck every time I see a gradient operator, with non-commutative arguments.
Noncommutative arguments are one of the initially most confusing topics in my opinion too!
@@EccentricTuber Specifically: define d[] over "+","*","^", and "log" binary operators. For implicit differentiation
d[a+b] = da + db
d[a*b] = da b + a db
d[a^b] = (b/a)(a^b) da + log_e[a] (a^b) db
d[log_a[b]] = ... (its complicated)
For addition and multiplication, it is clear that a and b can be multi-vectors. I have no idea what d[] is for ^ and log though. It is THIS that confuses me when I see the gradient operator applied to an object.
what do you think about Eric Lengyel? I really like his books,
The name sounds somewhat familiar, but I couldn't name any of his works. I'll look into him!
What software should we use?
My area of expertise is definitely not software: I'm more of a pen and paper guy! But there's something called ganja.js made by Enki. If you join the Bivector discord, there are channels for discussing this too :)