What are the practical applications for the generalized Stokes'

Shit, wrong board, janny pls delete

Explain this.

>>66160749
It allows you to simplify the analysis of inviscid, irrotational potential flows

>>66160814
no, we are all greek here

>what is interpretation of the curl of a vector field as a measure of swirling about an axis

>>66160749
math without numbers...
how terrifying.

>>66161068
That's just a very long 5. A chilean 5, if you will.

>>66160985
Thanks, that's exactly what I was after.

>>66161031
Isn't that exactly what the kelvin-stokes says though? The modern version doesn't even mention curl, just the exterior derivative over the manifold

When mathfags generalize things and remove disgusting c*ordinates, they aren't thinking of applications.

In general some versions of that theorem appear in weak formulations of PDEs, I assume if the dimensionality is high enough and the approach is abstract enough you might see it used. I had a course on this shit but the dimension of the problems was always low enough to use the more well known R^3 specific formulas.

It's always good to keep in mind though.

File: 1474771303221.png (108KB, 357x368px) Image search: [Google]

108KB, 357x368px

>>66161266
no problem lad

>tfw too intelligent to post on the correct board

>>66161266
Is this relevant for Calculus 2? Cause that's how far I was required to go, but I don't understand what you're talking about (I'm a filthy CS major).

Should I know this? I don't like falling behind on maths.

>>66161455
>Is this relevant for Calculus 2?
No. Only 3 courses in Porto use it, perhaps a couple more in Lisbon, and none of them are CS.

>>66161332
Yeah, I've always wondered what it was for since KS, Green and Gauss always did the job for me.

>>66161266
>Isn't that exactly what the kelvin-stokes says though? The modern version doesn't even mention curl, just the exterior derivative over the manifold
the exterior derivative operates on differential forms, and because of how the differential operates in coordinates, in low dimensions and in cartesian coordinates there's a natural correspondence with the curl of the associate vector field(associate through the inner product)

so if you have a 1-form with coordinates w^i, you'll see that the coordinates of the 2-form obtained by differentiation look like the coordinates of the curl of w^i thought as a vector field

as you go up in dimensionality and as you move away from standard coordinates a lot of the intuition goes away

>>66162030
This is actually a pretty good explanation. I haven't had a PDE class (yet) so I can only imagine how this would apply to high order ones. Does it enable you to "drop" the order of the PDE you're solving by some process?

>>66163025
pretty much, it lowers the degree of smoothness required to take a pointwise derivative by using integral equalities, interpreting those as equalities between inner products and linear functionals in properly chosen functional spaces

then by using some theorems like the lax-milgram theorem, you can have some interesting existence and uniqueness results
so by increasing the size of the spaces of possible functions you have a larger degree of freedom to find solutions

moreover, working in those spaces usually comes with nice properties like completeness and various density results
and computationally there are nice results as well

the theory in general is fairly though as you need a strong grip on functional analysis

>>66163463
That sounds really interesting and actually intuitive but I'm willing to bet the autistic professor that will teach me the class will find a way to complicate what is simple.

Just out of curiosity, what's your field of study?

>>66163682
Mathematical engineering, which is pretty much an even more applied version of standard applied maths.

>>66163747
So it's basically the field I'm in just with a different designation. Nice knowing I'll take this class too.

IN ENGLISH, DOC

>>66160749
>intelectugal

My head hurts reading this.

Worst thread ever

>>66161455
>Calculus 2
Stokes theorem is relevant in vector calculus. If by calculus 2 you mean vector calculus, then yes.

>>66166489
CS/Engineering Calculus 2, not Maths calculus 2. We use the American programme, I think. Either way I was asking the Portuguese guy who definitely followed the same program, except with a different major.