On Vector Analysis Notations

Let us settle it once and for all. Which notation should be the only used notation in vector analysis?

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

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

That would be Germany, and therefore European notation.

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

Samma här

t Winland

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

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 :^)

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

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

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

Seriously why?

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

x is a vector though...

what is V you fucking moron

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

a vector space?
i'm not following.

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.

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

yes, thats it

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]

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

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

I prefer the French notation.

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

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

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.

Ameritard absolutely btfo RIGHT HERE