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Anonymous Sat 11 Sep 15:10:02 2021 No.13628834 View Reply Original Report

Quoted By: >>13628856 >>13629332 >>13629398 >>13629918

How do physicists and engineers learn about differential forms?

I take it they don't learn about cotangent spaces, graded algebras, exterior bundles and such.

So what is the "physical" way they learn it?

Anonymous

Anonymous Sat 11 Sep 2021 15:14:43 No.13628856 Report

Quoted By: >>13628867

>>13628834
You'll learn about cotangent spaces - even that name, although a name is just a name.
You don't need graded algebras or exterior bundles to compute with differential forms, really - just like you don't need to learn the theory of semirings to learn the naturals.

Anonymous

Anonymous Sat 11 Sep 2021 15:17:55 No.13628867 Report

Quoted By: >>13628935

>>13628856
Okay, so they just learn how to compute with them? Not really about forms themselves? Not saying thats a bad thing BTW obviously physicists shouldnt bother with too much formalism im just curious.

Anonymous

Anonymous Sat 11 Sep 2021 15:37:07 No.13628935 Report

Quoted By: >>13628952

>>13628867
>Not really about forms themselves?
Not sure it that means much.
But yes, it can probably be said that physics students get introduced to ${\mathrm d}$ for scalar functions and then inductively on differential forms, not that this ties to deRham cohomology and quotients or rings. Even if feats of those theories pop up in the form of Stokes theorem and all the differential operator identities.

I'm a bit opposed to the phrasing since you can also say the same thing about mathematicians. You learn how to construct the integers (and rationals) using the naturals and pairs and eqivalences, but it's not worth pointing out that this "is" a special case of the Grothendieck construction in K-theory.

Anonymous

Anonymous Sat 11 Sep 2021 15:41:17 No.13628952 Report

Quoted By: >>13628964

>>13628935
Yeah thats fair. I guess you could say they (and we mathematicians) are first exposed and learn at the level of whats essential, mostly.

Anonymous

Anonymous Sat 11 Sep 2021 15:44:57 No.13628964 Report

Quoted By:

>>13628952
Yes I guess.

There's a phrasing of thermodynamics in terms of contact geometry
https://en.wikipedia.org/wiki/Contact_geometry

Anonymous

Anonymous Sat 11 Sep 2021 15:47:30 No.13628968 Report

Quoted By:

They just learn how to do the computation with the hodge star , basically work out the algebra and simplify. Same thing with tensors. The abstractions are kinda swept under the rug, and are not needed for solving problems for exams. There might be some theorems that they use to simplify the solution etc, but they use it as is they dont prove it.

Anonymous

Anonymous Sat 11 Sep 2021 18:06:39 No.13629332 Report

Quoted By: >>13629601

>>13628834
>I take it they don't learn about cotangent spaces, graded algebras, exterior bundles and such.
At least at all the Institutes I know of, you learn about all those things if you specialize in theoretical physics.

Anonymous

Anonymous Sat 11 Sep 2021 18:29:26 No.13629398 Report

Quoted By:

>>13628834
https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS
i learned about them here recently. not everything is well motivated, but with some thought you can fill in the gaps. over all an excellent lecture series

Anonymous

Anonymous Sat 11 Sep 2021 19:17:24 No.13629548 Report

Quoted By: >>13629601

Whatever Walther Rudin's princliples of analysis teaches them. If i reckon correctly, it was just dy= f dx /\ dy /\ dz with operations and rules. For example, flipping dx and dy is possible if you multiply with -1 afterwards the whole deal.

t. applied physicists boy with multiple analysis courses done

Anonymous

Anonymous Sat 11 Sep 2021 19:31:06 No.13629601 Report

Quoted By: >>13629642

>>13629332
Ah yeah, the more theoretical one goes the more sophisticated the mathematical treatment i suppose.
>>13629548
Okay, that sounds decent enough for applied physics purposes.

Anonymous

Anonymous Sat 11 Sep 2021 19:43:04 No.13629642 Report

Quoted By:

>>13629601
Yup and for all other scientifical purposes. More is just mathematical circlejerk. The faggot theoretical physicist doesn't actually need these things but for sake of esoerism, they use them.

Anonymous

Anonymous Sat 11 Sep 2021 20:27:34 No.13629736 Report

Quoted By: >>13629821

not even going to bother with the bait.

For everyone else, as a continuation of the op I wonder now how engineers and applied physicists go about learning variational calculus?

I really doubt you need to go deep into the functional analysis (not that it really is that deep for physics purposes), but is it really just doing problems until you get used to it?

Anonymous

Anonymous Sat 11 Sep 2021 20:59:24 No.13629821 Report

Quoted By: >>13629859 >>13629981

>>13629736
Thornton and Marion, dynamics of particles and systems, faggot. We learn the necessary math. Not the esoteric math.

Anonymous

Anonymous Sat 11 Sep 2021 21:08:28 No.13629859 Report

Quoted By: >>13629883 >>13629892

>>13629821
Why are you so aggressive to someone over the internet? A literal electronic nigger is what you are: feral, retarded, just a plain nigger. By the way its "esoteric math" that has made the only progress in physics for the past 120 years now. The only problems left in classical mechanics are what you call "esoteric" but will likely prove crucial to understanding the motion of complex systems. Nigger.

Anonymous

Anonymous Sat 11 Sep 2021 21:17:54 No.13629883 Report

Quoted By:

>>13629859
Yes im a nigger. 4chan made me a nigger. Leave until it makes you. I compensate the lack of higher math knowledge with 4chan nigger tier insults. Welcome to the nigger club.

Anonymous

Anonymous Sat 11 Sep 2021 21:20:16 No.13629892 Report

Quoted By:

>>13629859
So, you admit that modern physics advance is indeed just mathematical bibbelbabbel. Nothing is invented, vut just rewritten in weird mathematical way that even the writer struggles to comprehend.

Anonymous

Anonymous Sat 11 Sep 2021 21:34:06 No.13629918 Report

Quoted By:

>>13628834
I wish they taught them in calc 3.
The jacobian comes for free.

Instead of integrating and writing dx*dy, write dx^dy.
Changing coordinates to x = f(u,v), y = g(u,v) gives:
dx = (f_u)*du + (f_v)*dv, dy = (g_u)*du + (g_v)*dv.

The dumb way of multiplying gives:
dx*dy = (f_u)*(g_u)*du*du + (f_u)*(g_v)*du*dv + (f_v)*(g_u)*dv*du + (f_v)*(g_v)*dv*dv
= (f_u)*(g_v)*du*dv + (f_v)*g_u)*dv*du = [(f_u)*(g_v) + (f_v)*(g_u)]*du*dv
which is wrong.

The smart way of multiplying gives:
dx^dy = (f_u)*(g_v)*du^dv + (f_v)*(g_u)*dv^du = [(f_u)*(g_v) - (f_v)*(g_u)]*du^dv
which is correct.

Anonymous

Anonymous Sat 11 Sep 2021 22:06:37 No.13629981 Report

Quoted By:

>>13629821
>Thornton and Marion
what a dog shit mechanics book. i've never seen so many concepts explained in such a convoluted manner

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