I want to know everything about the application of vector calculus.

Electromagnetism.

>>8187058
Maxwell's Equations?

learn about forms and differential geometry, then you'll be able to write the general version of Stokes' theorem.

>>8187079
The applications of vector calculus, dude.

>>8187046
Fluid Dynamics

>>8187777
Great, where do I start?

>>8187046
[math] ∫_Ω dω = ∫_{∂Ω} ω [/math]

>>8187790
We've only learned:

[eqn] \int_{ \partial S } F \dot \mathrm{d} s = \iint_S \mathrm{curl}(F) \dot \mathrm{d} \Omega [/eqn]

>>8187810
What the fuck is wrong with LaTeX here

>>8187811
It has issues parsing commands, basically put whitespace everywhere. So I think the problem is \int_{ \partial s } and others where there's no gap between command and option, so we'll write them as \int _{ \partial s } notice the space after \int

[eqn] \int_{ \partial S } [/eqn]
[eqn] \int _{ \partial S } [/eqn]
[eqn] \mathrm{d} [/eqn]
[eqn] \mathrm { d } [/eqn]
[eqn] \int _{ \partial S } F \dot \mathrm {d} s = \iint _S \mathrm {curl} (F) \dot \mathrm {d} \Omega [/eqn]

Hopefully that should work.

>>8187843
Does LaTeX here even know the \mathrm command?

Testing:

[eqn] \int _{ \partial S } F \dot ds = \iint _S curl (F) \dot d \Omega [/eqn]

>>8187046
Transport phenomena in general

>>8187811
>>8187863
Don't try to understand why, LaTeX here is just completely fucked.

>>8188293
Why doesn't hiro fix that instead of adding a gazillion new boards nobody cares about?

I remember learning vector calculus completely divorced from application
I passed, but I didn't learn shit
it wasn't until we used it in electromagnetism and fluid dynamics that I 'got it'
even the 'physics proofs' were easier to understand than the autistic reasoning of pure math

>>8189062
>Implying he knows how to do anything other than copy-pasting markup and changing a name.

>>8187046
there is this whole field called fluid dynamics which can take up a good share of your time,
>if your interested that is

>>8187066
yup

[eqn]\oint_{\partial D} P\ \mathrm{d} x + Q\ \mathrm{d} y = \iint_{D} \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) \mathrm{d} A[/eqn]
[eqn]\int_{C} \mathbf{F} \cdot \mathrm{d} \mathbf{r} = \iint_{S} (\mathrm{curl}\ \mathbf{F}) \cdot \mathrm{d}\mathbf{S}[/eqn]
[eqn]\iint_{S} \mathbf{F} \cdot \mathrm{d}\mathbf{S} = \iiint_{E} \mathrm{div}\ \mathbf{F}\ \mathrm{d}V[/eqn]

test

>>8187863
>>8187843
>>8187810
holy shit, you guys know you can preview the latex to make sure it works before posting right?

>>8189506
Where do I start? Assumming I already know a good deal about vector calculus.

>>8189608
Do you never write relatively complicated LaTeX here? The preview isn't as broken. I've had preview work and post broken several times.

>>8189675
same

>>8189608
>I have literally never used LaTeX on /sci/ before

It's been broken from day one, right now it's better than it was but it's still broken as >>8187843 points out.

>>8189432
Interesting. When I see the treatment of Mathematics in Physics contexts I find it harder to follow because it is far too loose. For me, when proper rigor is used, the steps are clear cut and logical instead of hand wavy and ad hoc.

>>8189675
post something that works in the preview but not on the post

o, wait, you cant, because there isnt such a thing

>>8189432
OP here, we also took a very mathematical approach to vector calculus, and I have no fucking clue what the applications are, or what a "curl" of a vector field represents in the real world.

[math]{{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}_{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}}^{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}}}_{{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}_{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}}^{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}}}}^{{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}_{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}}^{{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}_{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}^{{{x_{x}^{x}}_{{x_{x}^{x}}}^{{x_{x}^{x}}}}}}}}}}[/math]

test

>>8187843
It renders correctly without that space on my end. Also, it isn't an "option", latex is a macro language. It doesn't work like that.

\int_{\partial s}
[eqn]\int_{\partial s}[/eqn]

\int_{\partial S}F \cdot\mathrm{d}s = \int_S\mathrm{curl}(F) \cdot\mathrm{d}\Omega
[eqn]\int_{\partial S}F \cdot\mathrm{d}s = \int_S\mathrm{curl}(F) \cdot\mathrm{d}\Omega[/eqn]

>>8187810
>>8187811
>>8188293
You are fucking idiots.
>\iint
should be \int
>\dot
should be \cdot

There isn't any problem with mathJaX. There's just a bunch of people who only know LaTeX at a basic level and aren't used to writing a line of LaTeX without it live-rendering as they type.

You guys should all learn how LaTeX actually works and use an editor where you aren't being hand held through it as you type.

>>8189737
\iint is double integral, dummy

>>8189737
>>\iint
>should be \int

\iint is for the double integrals DUDE.

>>8189743
You win this round, anon.

\int_{\partial S}F \cdot\mathrm{d}s = \iint_S\mathrm{curl}(F) \cdot\mathrm{d}\Omega
[eqn]\int_{\partial S}F \cdot\mathrm{d}s = \iint_S\mathrm{curl}(F) \cdot\mathrm{d}\Omega[/eqn]

That does raise a more interesting question though. I thought iint and oint were part of esint.
http://muug.ca/mirror/ctan/macros/latex/contrib/esint/esint.pdf

I wonder if MathJaX has a list somewhere of all the packages it loads.

>>8189757
Please be nicer next time, "fucking idiots" is not a very friendly thing to say. Remember, /sci/ is a board of peace.

>>8189757

http://docs.mathjax.org/en/latest/tex.html#amsmath-and-amssymbols

Not having any luck getting any of these things working. I'm assuming the dev's didn't load the plugins?