I want to know everything about the application of vector calculus. Where do I start?

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.

Does LaTeX here even know the \mathrm command?

Testing:

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

Transport phenomena in general

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

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

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

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

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

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

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

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

same

>I have literally never used LaTeX on Veeky Forums before

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

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.

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

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

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

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]

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.

\iint is double integral, dummy

>>\iint
>should be \int

\iint is for the double integrals DUDE.

You win this round, user.

\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.
muug.ca/mirror/ctan/macros/latex/contrib/esint/esint.pdf

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

Please be nicer next time, "fucking idiots" is not a very friendly thing to say. Remember, Veeky Forums is a board of peace.

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?

bump