/sci/ - Science & Math

2+2=4

>>9680429
hold my beer buddy

Nice b8, besides that a better DEFINITION is https://en.m.wikipedia.org/wiki/Fréchet_derivative.

>>9680431
-1 that's 3

>>9680429
I got your math right here
*unzips dick*

>>9680429
>I defy you to name a more elegant piece of math.

>>9680429
*rigorizes your math*
[math] \displaystyle f'(c)=\frac{f(c+n)-f(c-m)}{m+n} [/math]

>>9680429
> neigh

that’s what horses say you fucking donut

>>9680696
>assuming his species

>>9680696
>assuming his pastry

>>9680429
>neigh

>>9680429

>>9680429

i wish more authors would use something like [math] x =_{def} y [/math] when they're just defining symbols.

it took me a while to stop thinking of lim as some kind of function and retrain myself to think of the epsilon-delta definition. i think calc 1 should be more like real analysis so students don't have to re-organize how they think about things.

>>9680435
this is the function that literally makes the modern world work

>>9681268
why, whats special about it?
t. never read fourier shit

>>9680429
>name a more elegant piece of math.
[math]\dfrac{dy}{dx}\,=\,\dfrac{f(x)-f(x-h)}{h}[/math]

>>9680525
Mein neger

>>9681058
kys

>>9681354
Heavily used in Electric Engineering and (I think) Physics

>>9680525
Why do millennials write Stokes' theorem without associating a measure to the integral they use?

>>9680435
Pls explain, no bully

Tupper's self referential formula

>>9681463
>being this much of a brainlet

>>9681669
Seriously though, why do you millennials do that? Did not a single topologist learn Lebesgue's theory?

>>9681461
thats an understatement buddy
>physics, partial differential equations, number theory, combinatorics, signal processing, digital image processing, probability theory, statistics, forensics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry, protein structure analysis, and other areas

>>9681479
a very powerful mathematical tool for approximating periodic functions which has many usages >>9681695
basically on the same level as multiplication and division as an operation (fourier transform)

>>9681695
>forensics
???

>>9680435
>defined from 0 to T
as a guy who likes signals i like this

>>9680492
The proof of this one was pretty hot iirc

When is being a dumb undergrad going to become a bannable offence

>>9681058

The five constants!

>>9681684
your derogative tone is ironic, as you're the one who happens to not know your math here. The omega is the differential, it has all the dx's etc. Writing \int\omega amounts to an integral \int\mu.
As an aside, it has certainly nothing to do with millennials, it's plain differential geometry and has been written like that for decades.

>>9681747
spectroscopy
>>9681752
its clearly the superior notation.
thats why i picked it

>>9681811
agreed, it pissed me off so much when i was first learning it and all the sources used to list it from -T/2 like what the fuck do i need to define on the negative axis for brah

>>9681058
i prefer [math]e^{i\pi(0+1+2+3+4+5+6+7+8+9+10)}=-1[/math].
it even hides the distributive law somewhere deep inside

>>9680429
>neigh

>>9680429
e^i = pi
the most beuatiful equation

here u go

x = x

>>9681641
that is black magic, burn the witch!

>>9682441
[look at the vertical axis]

>>9682445
it's all french to me

>>9681695
How's it used in options? Never looked at solving black Scholes -is the fourier transform done to the BS pde or something?

>>9680696
>assuming his onomatopoeia

>tfw you dont understand nearly any of the equations in this thread
>>9681641
How does this work?

>>9682803
levy models and all dat shit

>>9682848
It's a cheat. The formula produces every possible arrangement of pixels in the region shown for different values of y.

So for some (ridiculously high) value y=k, it produces that specific pattern.

v-e+f=2

>>9680429
Literally can't beat that.

>>9681463
>>9681684
fucking brainlet, integral of a measurable function and integral of a differential forms are two different concepts (even though the latter ultimately reduces to the former). pick up a book next time you try to be smart

>>9681695
also the backbone of most quantitative finance processes

>>9680431
fobp

>>9682931
>in matter

>>9680429
>>9680693
>>9681360
so close guys, but wrong! Symmetric difference is best difference.

[eqn]f'(x) = \lim_{h \to 0} \frac{f\left(x+\frac{h}{2}\right) - f\left(x-\frac{h}{2}\right)}{h}[/eqn]

check this out
[eqn]f''(x) = \lim_{h \to 0} \frac{2}{h^2}\left(\frac{f\left(x+h\right) + f\left(x-h\right)}{2}- f(x) \right)[/eqn]

this makes it obvious that the second derivative is basically just the difference between the value of a function at a point and the average of the nearby points. you know, so if you were going to make a differential equation describing how heat or waves flow in or out of a point over time you could do that.

>>9680429
op=faggot

>>9681641
wait what the actual fuck

i have to try this

>>9682441
>>9682848
>>9684239
relax, it spits out all the possible combinations for some nxm grid next to eachother along some axis, so you just need to find the right area to look
still pretty cool

>>9681075
Don't they?

>>9681641
Better yet, Dual of a Hyperset:
B* = { B*, B}

>>9682931
You could if you just wrote down the QED lagrangian

Smh

>>9681766
What even is there to prove? Weren't integrals defined to work this way?

>>9686383
imagine being this retarded

>>9680429
>posts baby differentiation

move aside, papa's coming through

>>9681463
all measures on R agree with the Lebesgue measure you fucking pleb

>>9686383
>fundamental definition of calculus

kek nope, it's something you definitely have to prove. study more

>>9681776
>no fun allowed
whenever being a pretentious faggot does

>>9686405
>everyone who knows more than me is a pretentious faggot

>>9686407
>everyone who appreciates fundamentals is a dumb undergrad

>>9686414
not really fundamental, more of a neat little package that works out nice, making it easy for freshmen to understand

>>9680435
>not using the more elegant complex coefficients
never gonna make it

>>9680429
>she

>>9680438
quick maths

>>9680429
I really like: [eqn] \int \limits_{t_0}^{t} P dt = w [/eqn] also [eqn] I_2m = \int \limits_{0}^{\frac{\pi}{2}} \sin^{2m}{x} dx = (\frac{2m - 1}{2m})(\frac{2m - 3}{2m - 2})\dots(\frac{5}{6})(\frac{3}{4})(\frac{1}{2})(\frac{\pi}{2}) [\eqn]

>>9688481
Fuck me
[eqn] I_2m = \int \limits_{0}^{\frac{\pi}{2}} \sin^{2m}{x} dx = (\frac{2m - 1}{2m})(\frac{2m - 3}{2m - 2})\dots(\frac{5}{6})(\frac{3}{4})(\frac{1}{2})(\frac{\pi}{2}) [/eqn]

>acausal definition of the derivate
get that disgusting shit out of here

>>9686414
OP doesn't "appreciate fundamentals". He's just looking for a way to appear intelligent with the little material he was available.

*has available

>>9688631
>all functions are [math]\mathbf R\ \longrightarrow\ \mathbf R[/math]

>>9680429
Chain theory proof is nice to read, too, if you like the definition of the derivative.

>>9688682
man I'm in high school I don't even know what you're talking about

>>9680492
>>9681766
>>9686383
You can define integrals that way. For example, an indefinite integral can be defined as:

[eqn]\int f(x)dx = F(x)+C[/eqn]

And a definite integral as:

[eqn]\int_{a}^{b}f(x)dx=F(b)-F(a)[/eqn]

Where [math]f(x)[/math] is some function and [math]F(x)[/math] is the antiderivative, both continuous on the interval of [math](a,b)[/math]. But that's boring since it's just playing with definitions. It's more interesting to derive an understanding of what definite integrals can be interpreted as. Area under the curve is obviously one and can be defined generally as:

[eqn]\lim_{n\rightarrow \infty }\sum_{k=0}^{n} f(c_k) \Delta x_k[/eqn]

where [math]\Delta x_k = b_k-a_k[/math] is the length and some subset interval on [math](a,b)[/math] and [math]c_k[/math] lies in that subset interval.

Putting that to the side, let's look at the Mean Value Theorem. For a continuous function on [math](a,b)[/math], the slope will be equal to the following at some value [math]c[/math]:

[eqn]f'(c) = \frac{f(b)-f(a)}{b-a}[/eqn]

Altering the notation:

[eqn]f(c) = \frac{F(b)-F(a)}{b-a}[/eqn]

A little more...

[eqn]f(c)*(b-a) = F(b)-F(a)[/eqn]

And a little bit more...

[eqn]f(c_k)\Delta x_k = F(b_k)-F(a_k)[/eqn]

Now we can play. Taking the definition for area under the curve and jamming in the line above:

[eqn]\lim_{n\rightarrow \infty }\sum_{k=0}^{n}f(c_k)\Delta x_k = \lim_{n\rightarrow \infty }\sum_{k=0}^{n}F(b_k)-F(a_k)[/eqn]

But the right hand side is a telescoping sum since [math]b_k = b_k = a_{k+1}. This brings us to:

[eqn]\lim_{n\rightarrow \infty }\sum_{k=0}^{n}F(b_k)-F(a_k) = F(b_n)-F(a_0) = F(b) - F(a)[/eqn]

This shows the link between a definite integral of a continuous function and the area under said function. It's simple stuff but I enjoy it. You can do something similar for polar functions as well.

Hopefully the LaTeX doesn't fuck up in posting. If it does, oh well.

>>9686544
>engineer

>>9689433
Drop out immediately. You're mentally deficient.

>>9689710
Your formula is making my screen sick.

>>9689720
lol no trust me

>>9689720
I mean what does he mean with "all functions are R -> R"?
And mostly, what does " ->" mean

>>9689836
The arrow thingy means said function relates any number from R (within its domain) to only one other number also in R, R being the real numbers set.

>>9688682
see
>>9680436

>>9680436
>>9690039
That's called a differential you stupid fucking mongoloid. Also,
>implying all Banach-valued functions are differentiable

>>9690052
>banach valued
What the hell is your point?
>>9688682
You tried to imply something wrong about
>>9688631
This arclenght formula. A general formula can be obtained for an arbitrary riemanian manifold yea but what the hell are you talking about?

>>9690074
>This arclenght formula.
For functions in [math]\mathscr C^1\left(\mathbf R,\,\mathbf R\right)[/math]. The topic is comfy formulas. Particular cases aren't comfy.

>>9690080
Well yea, but it has to do with integration in manifolds, but for rectifible curves you can always look at it as the graph of a function and just add the parts.

>>9690094
As the graph of a function locally*.

>>9680429
>neigh
nay

>>9689836
>I mean what does he mean with "all functions are R -> R"?
He meant that all functions have a real domain and a real codomain, but that's obviously false.
>And mostly, what does " ->" mean
The meaning of -> changes from context to context. Here, the "->" in f: X -> Y tells us that the function maps elements from X to Y, where X is obviously the domain and Y the codomain

>>9680435
HNNNNG

Step aside faggots:

[math]\delta S = 0[/math]

>>9680429
Shit last time I saw that was sophomore year of high school. Back than i didn't understand what it meant but it's just a really small y over a really small x. What's the big deal.