On Vector Analysis Notations

>>8812339
Never was a fan of nabla notation, usually it makes no sense in everything else but cartesian coordinates.

>>8812339
The notation from the country that has put men on the moon, I'd say

>>8812457
That would be Germany, and therefore European notation.

>>8812339

We use nabla in Norway. Had no idea that wasn't the norm.

>>8812490
Samma här

t Winland

>>8812480
And that's why we have a German flag on the moon, right?

No disrespect tho, most white Americans are of German ancestry, and hamburgers are practically our national food

>>8812510
It was essentially V2 that took people on the moon for the first time. On the other hand, it was mostly V2 that took the Soviets to the space earlier.

And don't forget the moon nazis :^)

>>8812339
less writing == better, theres nothing wrong with the american notation.
its just aliases for the words.

>>8812339
[math] \mathscr{D}_a f(\mathbf{x}) [/math]
what's dat tho?

>>8812339
>Be American
>Call analysis: """calculus"""
>Call vector calculus: vector """analysis"""

Seriously why?

>>8812519
partial derivative of (f) with respect to (x)
[math]\mathscr{D}_a (f)(\mathbf{x})[/math]

>>8812528
x is a vector though...

>>8812564
what is V you fucking moron

>>8812384
Only if you define your dot and cross products with Cartesian coordinates...

its fucking vector calculus of course x is a vector what do you think? youre taking the PARTIAL you FUCKING RETARD

>>8812568
a vector space?
i'm not following.

>>8812570
You mean its the vector composed of partial derivatives of f with respect to components of x?
I didn't think you generally needed a basis to define grad, div and curl.

Or am I still missing something?
Calm down btw. You don't have to answer everyone on the internet. Some of us haven't seen this in more than a decade.

>>8812339
Nabla notation is the standard here in the Netherlands
Also, the nabla was introduced by Hamilton, which makes it a European notation

>>8812581
yes, thats it

>>8812519
Directional derivative.
[eqn]\mathscr D_{\mathbf a} \left(f\right)\left(\mathbf x\right) \,=\, \lim_{h \,\to\, 0} \frac{1}{h}\left[ f\left( \mathbf x \,+\, h\, \mathbf a \right) \,-\, f\left( \mathbf x\right)\right][/eqn]

>>8812339
I object to the line in your inner product. Also your D is foppish.

>>8812339
The solution is to get rid of vectors in vector analysis, instead work with differential forms.

>>8812339
I prefer the French notation.

American notation
>because I'm not gunna fuckin' hand write grad and curl in bold

>>8812339
Writing stuff in plain words is much clearer and less prone to error, especially in this case.

>>8812520
Calculus is what high schoolers and engineers take so they can do calculations. Analysis is the rigorous version for math majors, after they take calculus.

>>8812457
>>8812480
Ameritard absolutely btfo RIGHT HERE