/math/ general
pic related
sorry not gonna do ur hw for you
>>7937243
use complex numbers to factor out terms, creating a convergent series in the function of the argument, then cite Euler saying the magnitude of the product is trivial and left as an exercise to the reader.
Just got my Complex Analysis grades, aced the course. Thanks /sci/
what do i ask him?
>>7938037
>PIMS 2012
You're a bit late.
>>7938052
that's a room number
>>7937243
You take tan of the whole thing, then solve using the tan addition formula.
Alternatively draw right angled trianges which give those angles and solve graphically.
>>7938033
or type 16arctan(1/5)-4arctan(1/239) into your calculator
nobody who works in stem actually does the math on paper all that matters is you know what to put in the calc/code
Just plug it into wolfram alpha or a calculator genius... How hard is finding answers these days
>>7937243
It's Pi. But why?
>>7937243
is this not machin's formula for pi?
given that you are using the infinite series approximation for arctan
Code monkey here. Is there a quick way to solve where x=y for y = alogb(x) ? Needs to be computationally light. The function would take x,the base, and the factor and return the number for which x and y are equivalent.
>Tfw going to fail calc II
Kill me
>>7938663
You're looking for fixed points of a function, and you should just google this. There are many very simple algorithms that do this well, such as simply iterating the function (start with some guess and keep inputting the result into your function until it stops changing by a lot).
>>7937243
180
>>7938686
Thanks.
>>7938883
or pi
Hey /Sci/
Borderline retard here.
Really cant wrap my mind around this.
What equation did this madman use to get a 21$ shipping cost out of a 7.2.
Its so simple and i just cannot wrap my mind around it, the image is the information we were given.
We needed to write a program and this is the only thing i cannot figure out.
>>7940138
Here is the image, been up too long.
>>7940138
Every 10 kg or part thereof costs $11, maybe?
>>7940146
I mean $10 + $11 for every 10 kg or part thereof. It's the only way I can see a $21 as the output.
>>7940148
Yeah i suppose that might be what he means.
Sorry for the stupid question, you guys can go back to the real problems
Bump
Out of the famous "easy to describe" open problems, which one do mathematicians usually consider the hardest?
For an example, we already reached some pretty good bounds for the twin prime conjecture, and the weak version of Goldbach's conjecture has been proved. But there's hardly been any progression on the Collatz conjecture, and Erdős even said that "Mathematics may not be ready for such problems"
>>7940808
hard to say if you don't have experience in them
im familiar with the Jacobian Conjecture and it looks slippery as fuck
My PDE book asked as an exercise to find all the solutions to the 2d laplace equations in polar form that are angle independent. This is the laplace equation in polar coordinates: [math] U_{rr} + \frac{1}{r}U_r+\frac{1}{r^2}U_{\theta\theta } = 0[/math]. Then, I just solved it when the last term is zero.
Is it actually expected of me to find one? Because I found none.
[math] rU_{rr} + U_r = 0[/math]
>>7940841
>all the solutions to the 2d laplace equations in polar form that are angle independent
Are you familiar with conformal maps?
>>7937243
No parenthesis makes this a guess mess.
>>7940150
this is the first actual math /sci/ has done since its inception
>>7937243
Using
arctan(x)+arctan(y) = arctan((x+y)/(1-xy))
arctan(x)-arctan(y) = arctan((x-y)/(1+xy))
16arctan(1/5)-4arctan(1/239)
12arctan(1/5)+4arctan(9/46)
8arctan(1/5)+4arctan(7/17)
4arctan(1/5)+4arctan(2/3)
4arctan(1)
pi
Can someone explain to me how he's gone from the last third line to the last second?
Above it I can understand. From the constraints of the problem, U(x,0) = f(x) and that is equal to the series which must be the fourier sine series of f(x). But U(x,b)=g(x) is not clear at all how he's made g(x) into a fourier sine series. Why and how did he do it? Where did the sum from the previous line go?
>>7941323
Forgot pic.
>>7940939
>implying /sci/ didn't definitively prove 1+1=2
>>7941327
He "inner product-ed" the third to last line with sin(npi x/a) which killed each term, except the nth one
>>7937243
MATH THRAD
>>7937267
>ur
You know what, this shit pisses me off. WHAT ARE YOU DOING WITH THE EXTRA 2 SECONDS IT TAKES TO WRITE YOUR YOUR?
>>7942073
That's a stupid exercise. You don't need a Hilbert space condition - it works on Banachspaces aswell. And Lambda is even an element of the approximative point spectre.
>>7943151
You should use the fact that the norm is defined by an bilinear inner product
>>7943158
Wait I think I had an error in reasoning.
But if that equivalence is right it would mean that the approximate spectrum is the whole spectrum in Hilbert spaces. Is that really true?
>>7943214
approximate point spectrum*
>>7942996
You type a letter per second?
>>7943220
i sometimes forget that people actually use the hunt-and-peck method of typing, and that some people have less than 90 words per minute
>>7938667
Heeyyyy, that's pretty good. Makes me feel funny.
Why do we care so much about sections of maps (i.e. right inverses)?
>>7938674
calc 2 is the easiest one wtf you doing
>>7943594
The section pullback [math]\mathcal{A}_\alpha = s_{\alpha}^*\omega[/math] of the connection 1-form [math]\omega \in \Lambda^{1}(P) \otimes \operatorname{Lie}G[/math] on a principal bundle [math]P =(P,G,M)[/math] is the Yang-Mills gauge field in physics.
Also the existence of a continuous (or smooth) section is equivalent to the triviality of the principal bundle.
>>7943655
>Also the existence of a continuous (or smooth) section is equivalent to the triviality of the principal bundle.
Why?
>>7943657
A very rough picture is that you can extend local sections to a global one if they're smooth, and since the projection of the section is the identity on P we get a trivial action of the group G on M, so [math] P = M \times G [/math].
>>7943594
I'm a physicist and so I will also think of field theories on spaces with more complicated topologies first.
However, in topology you can always argue with "because it's a tool for classifying stuff"
