/sci/ - Science & Math

it looks like a possible sum, but there are better ways to write it

pic related

You in medicine?

you can clean it up a little:
letting <span class="math">\Delta x = \frac{b-a}{n} [/spoiler] and <span class="math">x_i = a+i \Delta x [/spoiler] it is
<div class="math">\alpha (f(x), a, b)=\lim_{n\rightarrow \infty} \Delta x\sum_{k=0}^{n-1}f\left ( x_k \right ) </div>
usualy writen as
<div class="math">\alpha (f(x), a, b)=\lim_{n\rightarrow \infty} \sum_{k=0}^{n-1}f\left ( x_k \right )\Delta x </div>

I suspect a lot of poeple will want to use this, so why dont we introduce a new symbol thats easyer to write I propose rewriting
<div class="math"> \lim_{n\rightarrow \infty} \sum_{k=0}^{n-1}f( x_k )\Delta x </div>
as
<div class="math"> \int f\left ( x \right ) dx</div>

Look up 'Riemann sums'

>>2177622
Thanks. So isn't that exactly what the Riemann sum does?

How do you guys write mathematical symbols like that? is there a program to download. would make taking notes easier

>>2177626
>>2177622
I tested that limit and I calculatd that the area ander the curve x^2 from 0 to 1 is 1/3 or
<div class="math"> \int_0^1 x^2 dx = \frac{1}{3} </div>
I used the trapesium rule to check the answer and got 0.33466
0.333 is only about 0.4% of from that value

>>2177644
jsMath is what to forums use. And if you're using a laptop (not a tablet) to take notes in a math class, you're retarded.

since you've never formally studied calculus, I doubt you even know the meaning of the symbol lim(n->inf) (I'm not gonna start using jmath for this trivial shit, fuck you.)

Or what the real numbers are, or functions defined on those.

And yes, finding approximating rectangles under the curve is motherfucking easy, way to go.

But again, since you don't know anything about limits, you can't really write down a limit, since, well, you're kind of talking out of your ass.

>>2177644
double click on equations to see the source, write that between [ eqn] and [ /eqn] (leaving out the space inside the brackets)
o, and it uses latex notation

>>2177651
>http://www4a.wolframalpha.com/input/?i=(1/5000)(sum+(k/5000)^2,+k%3D0+to+5000-1)
And that's with n = 5000.

>>2177653
If you can't type faster than you can write with a pen or pencil, you are retarded.

>>2177671
typing is one thing, latex another. But you wouldn't know, since you obviously never used it and also obviously never been to a real math lecture.

fucktard

>>2177674
I can typeset in latex faster than I can write. You jelly, retard?

>>2177679
I am the king of Poland. You jelly, fucktard?

>>2177691
Oooh, someone is mad because they suck at latex.

>>2177644
>>2177644
I just noticed something,
<div class="math"> \int x^2 dx = \frac{1}{3} x^3 </div>
but
<div class="math"> \frac{d}{dx}\frac{1}{3} x^3 = x^2 </div>
maybe it was just a coincidence, can someone else try some other functions and see if it also works? maybe the area under a curve is the opposite of the derivative, almost like addition is the opposite of subtraction. thoughts?

>>2177697
It's not like this is the fundamental theorem of calculus or anything, right?

I have NEVER studied thermodynamics formally but I just discovered an interesting relation

<div class="math">\Delta U=Q-W</div>

Is that correct

>>2177679
Ok, prove it: please give me the latex-source for the butterfly lemma.

I needed 20 seconds to write it down with my hands. The clock is ticking, go for it.

pic most certainly related.

>>2177697
You just blew my mind. Publish that shit, you'll make millions.

>>2177700
thats a good name!
I went trough the math and got this, ill steal your name and name it the fundamental theorem of calculus:
if <span class="math"> f(x) = g'(x) [/spoiler]
then
<div class="math"> \int_a^b f(x)\,dx\, = g(b) - g(a) </div>
can someone check if its correct?

>>2177711
>graphs

Oh, sorry, I thought we were talking real mathematics! My mistake.

>>2177679
>still talking out of his ass
>he's the only one that doesn't know
>we all pity him

Unless you're a brain hooked up to a computer with no hands then you're provably wrong.

>>2177730
have you ever considered that mayby he just realy sucks at writing?

>>2177711
please, feel free to submit the latex source for the above graphic. Since you're faster in typing latex than with your handwriting, finding the source for the shown graphic shouldn't take you more than 1 minute, tops.


If you don't deliver very soon, I'm afraid I have to call bullshit.

Also, give me the latex source of the image to the right. It's a commutative diagram. I needed approx 1 and a half minutes to write that down with my bare hands and a pencil.

Assuming your handwriting is approximately as fast as mine, you should be able to give me the latex source for it very shortly.

I'm looking forward to it.

>>2177722
The butterfly lemma is on the solvability of finite groups (I think it's about finite groups, anyway), it most certainly is "real" mathematics.

Of course you don't even know what a group is, let alone a solvable group.

And visualizing proofs is always preferable to not visualizing them. If it's in any way possible. But again, you obviously never been to any kind of math lecture, so it's rather pointless talking to you about that..

also nb4 >commutative diagrams aren't real mathematics

hahaha, fucking high school noob. just die.

>>2177743
You are just mad because you are in a pointless branch of mathematics.

Also
>implying I don't know group theory
>implying visualizing proofs isn't worthless, seeing how formulas are way more clear

>>2177722
>>2177748
10/10flamingeyes.h

>>2177748
started saging because your fail was beginning to be obvious to even the most retarded idiot on /sci/, huh?

Here, have a little exposure. Idiot.

And btw, please write down all the equations contained in the commutative diagram I gave in my last post. I mean, you're the idiot claiming equations are easier to read than diagrams, so please, feel free to give us an example of your awesome latex skills.

Since you claim to know group theory I'll just assume you know what a commutative diagram is.

ITT: The theory of retardtivity

Well, this thread turned to shit.

why does no one want to recreate the 16 - 18 century with me?

>>2177784
this thread was shit from the very beginning. No one gives a fuck that some pathetic tripfag knows how to calculate the area of a rectangle.

Funny how the idiot suddenly started to shut the fuck up when it became obvious he was talking shit.

Here, have another bump, fucktard. Also, I'm still waiting for the latex-source on the Zassenhaus lemma and the given commutative diagram.