/sci/ - Science & Math

>>8005282
>3 hours
>10 Calculus problems from stewart

hello brainlet

>>8005282
I'll give you an interesting problem (assuming you haven't seen it before).

Let [math]{\mathbf{F}}[/math] be a vector field on any bounded subset of [math] {\mathbb{R}^3}[/math].

Prove that you can decompose [math]{\mathbf{F}}[/math] into a curl-free and a divergence-free component.

[math] {\mathbf{F}} = - \nabla \varphi + \nabla \times {\mathbf{A}}[/math]


This decomposition is related to a much more complicated theory.

>still doing calculus
>having the temerity to call anyone a brainlet
what a brainlet

>>8005305
Your reading comprehension is beyond comprehension.

>Go through the FIRST 10 problems

I wonder what do words mean and also what does it mean when I put words with other words that effect the meaning of the overall sentence DURRRR

>>8005308
nigga what

>>8005317
>I was born a few years before you
>That means that I am a better person

Yeah, keep stroking it faggot. You sure are showing how you don't have an inferiority complex.

>>8005308
Ayy lmao this is p. cool anon. Didn't cover this at my school. Thanks for the exposure to new shit.

>>8005354
>nigga what
Have you taken Calc 3?
>>8005357
Yeah I am surprised it isn't covered in more vector calculus classes. It is (sort of) a special case of Hodge Decomposition. And well Hodge Theory is pretty damn important.

>>8005354
>>I was born a few years before you
>>That means that I am a better person
Missed the point completely. I am explaining to you that you don't know shit yet so calling someone a brainlet as though you're not one is plainly stupid. Even if you blast your way though calculus it still doesn't mean shit. Fuck, I self taught calculus when I was 15 and I'm still here shitposting with the rest of you brainlets.


>Yeah, keep stroking it faggot. You sure are showing how you don't have an inferiority complex.
I may have an inferiority complex but it certainly doesn't involve a simpleton like you.

>>8005282
>stewart calculus book
found the brainlet

>calculus
>wonderful

it's like a watered down version of real analysis, which itself is fucking disgusting

>>8005308
This follows from the fact that all closed forms are exact on [math]\mathbb{R}^n[/math].

>>8005359
He might be in highschool doing basic shit for all we know. This guy already said he's a superior intellectual, yet didn't care about the "small mistakes" he was making.

He's confirmed for being a 16 year old that thinks he knows it all.

>>8005475
This is a theorem of classical vector analysis and should be proved using methods of an equivalent level.

If the theory of differential forms was fair game, I would have instead proposed the following problem:

Let M be an oriented closed Riemannian manifold. Prove the following. [math]{\Omega ^k}M = \operatorname{d} {\Omega ^{k - 1}}M \oplus \delta {\Omega ^{k + 1}}M \oplus {\mathcal{H}^k}M[/math]

>>8005507
Let [math]\Delta = d\delta + \delta d[/math] be the Laplace operator, and let [math]\omega \in \Lambda^{k}(M)[/math] be a [math]k[/math] form. Consider the vector space of cochains [math]C^{k}(M,\mathbb{R}) \equiv \mathbb{C}^{k}(M)[/math] with real coefficients equipped with the norm induced by the non-degenerate pairing [math](\cdotp,\cdotp): \Lambda^{k}(M) \rightarrow \mathbb{R}[/math] defined by
[eqn]
(\omega,\sigma) = \int_{M}\omega *\sigma,
[/eqn]
then the derivative [math]d: \mathbb{C}^{k-1}(M) \rightarrow \mathbb{C}^{k}(M)[/math], the coderivative [math]\delta: \mathbb{C}^{n-k}(M) \rightarrow \mathbb{C}^{k}(M) [/math] and the Laplacian operator [math]\Delta: \mathbb{C}^{k}(M) \rightarrow \mathbb{C}^{k}(M)[/math] define projections (due to nilpotency) onto [math]\mathbb{C}^{k}(M)[/math], this gives a decomposition [math]\Lambda^{k}(M) = \operatorname{img}d + \operatorname{img}\delta + \operatorname{img}\Delta[/math]. Uniqueness is left as an exercise.

>>8005282
>stewart
>recommended by /sci/

if you weren't illiterate you would realize it's recommended as the best book for the weakest students

/sci/ endorses apostol and spivak for strong students

>>8005539
>left as an exercise for the reader

>>8005539
>Uniqueness is left as an exercise.
Yeah, nice try. Better than what the majority of /sci/ could do.

>>8005282
>pure Math major
>taking Calculus

Either you're a faggot in high school posting on /sci/ or you're a brainlet taking Calc in college.

Sage, you're trolling/faggotry won't get a bump from me.