/sci/ - Science & Math

What's a good book to learn the basics foundations of physics? I'm looking for something like Lang's basic mathematics for physics.

I am still struggling to understand a concept i am learning in linear algebra. My textbook says that complex numbers can be represented in the polar coordinate form re^(iθ)=r(cos(θ)+i*sin(θ)), where θ is the angle between the vector representing the complex number and the real axis. How do get from e to the power of an imaginary number to trig functions?

>>10210745
Im in a thermo dynamics class right now and I keep mixing up enthalpy and internal energy. I understand the difference conceptually, but when it comes to using them in equations I always use the wrong one.

Can someone give me a quick guide to when to use each one?

>>10210836
>How do get from e to the power of an imaginary number to trig functions?
Use [eqn]e^x = \sum_{i=0}^{\infty} {x^i \over i!}[/eqn] Now put in [math]x=i\vartheta[/math] and watch the magic happen.

>>10210836
Taylor series.
e^x = sum x^n/n!
cos(x) = sum (-1)^n*x^(2n)/(2n)!
sin(x) = sum (-1)^n*x^(2n+1)/(2n+1)!
e^ix = cos(x)+i.sin(x)

Using DeMorgan's theorem, express the function as a Boolean expression with only OR and complement operands.

F = ABC + A'B + ABC'

I simplified the expression and got F = B but this isn't what they're asking for. What do they mean?

>>10210846
>he uses i to simultaneously index the sum and represent the imaginary unit

>>10210905
Probably ABC = (A' + B' + C')' etc.

>>10210905
Thinking more about it, should it be this?
(A'B'C')' + A'(B')' + (A'B')'C'?

>>10210913
Thanks

>>10210910
It takes real courage to do something like that, don't you think?

>>10210846

I remember my professor saying that it was related to the power series but he never explained the details or proved it.

wait so kirchoffs law, critical to basically all of astrophysics, does not have a valid theoretical proof? and it can be disproven by a retard in 2 seconds with a perfect reflector [ e/0 = f(T,v) ]
is science completely fake?

>>10210745
Can a fucking scientist explain the miracle of electromagnetism without getting me pissed?

>>10211090
Fuck you

Can someone please explain to me what I'm missing, conceptually, to algebraically solve for a min/max of a sin equation? Here's an example that I was just working through on khan academy

5-2sin ((2pi(t+1))/7)

They explain that the minimum height is achieved sin = -pi/2 + 2pi(n)
And go on to (in my opinion) poorly explain showing

(2pi(t+1))/7 = -pi/2 + 2pi(n)
t+1 = -7/4 + 7n
t = -11/4 + 7n

my issue is the lack of clarity between the first and second steps. What is the order and how are the terms being moved around? How does multiplying by 7 turn 2pi(n) into 7n and how does pi/ 2 turn into 7/4. Shit is making no sense to me

>>10211213
sin(x) has a maximum of 1 when x=2nπ+π/2 and a minimum of -1 when x=2nπ-π/2.

5-2sin(x) has a minimum of 3 when x=2nπ+π/2 and a maximum of 7 when x=2nπ-π/2.

2π(t+1)/7=2nπ+π/2
=> 2(t+1)/7=2n+1/2
=> (t+1)/7=n+1/4
=> t+1=7n+7/4
=> t=7n+3/4

2π(t+1)/7=2nπ-π/2
=> 2(t+1)/7=2n-1/2
=> (t+1)/7=n-1/4
=> t+1=7n-7/4
=> t=7n-11/4

> How does multiplying by 7 turn 2pi(n) into 7n and how does pi/ 2 turn into 7/4. Shit is making no sense to me
They're multiplying by 7/2π. In the above, I've multiplied by 1/π, 1/2, and 7, in that order.

>>10210777
How basic are we talking? There's likely no one stop shop, but if you're comfortable with calculus you could try walter lewin's lectures or the feynman lectures. All bullshit aside they do cover the basics pretty nicely.

>>10210777
Arnol'd's classical mechanics and Von Neumann's quantum mechanics.
>>10211084
Kirchoff's laws are provable from elementary graph theory.

What piezoelectric material is used to make basic 40kHz ultrasound transducers?

>>10210777
most state schools (in the united states) use the big introductory physics texts like halliday and resnick or young and friedman or whatever. Those are pretty readable and comprehensive if you're familiar with basic calculus.

Is this circuit moore?

>>10210777
>Lang's basic mathematics
Lang is a meme.

>>10211285
Thank you so much anon, that helps out a lot

Is this a valid diagram for a mealey machine?
Circuit in question is >>10211361

>>10211524
Next State | Output
0 1
1 1
1 1
1 0

Can someone tell me if my negation of this statement is correct?
Statement:
If x is a rational number and x != 0, then tan(x) is not a rational number
Negation
There exists a rational number x that is not 0 which satisfies the condition tan(x) is rational

What exactly am I calculating during surface and line integrals for some random function?

>>10211606
Correct.

>>10211364
Brainlet, stop repeating everything you read on this board. Maybe actually read a fucking textbook.

>sin(pi) = 0
How does that make you feel?

>>10210969
the courage to use shitty notation

>>10212133
wrong

>>10211704
Imagine you have a real valued function along a surface. So picture it's value as an orthogonal vector, and you're measuring the volume between the surface and the vectors.
>>10212143
Literally the quintessence of engineering.

>>10212150
>Literally the quintessence of engineering.
nah. an engineer would tell you that sin(pi) = pi

What's the name given to the phenomenon which makes a material contract when applied an electrical current?

How many ways can we tile a 2xn rectangle with 2x1 or 1x1 tiles? (Extra points for explaining how did you derive the recurrence relation.)

>>10212282
I offer [eqn]T_n = 2T_{n-1} + 3T_{n-2} + 2T_{n-3}[/eqn]

>>10212143
Show how sin and pi are both defined

>>10212294
Thanks anon-kun. I derived that as well. But the real answer was:
$\ a_n = 3a_{n-1} + \ a_{n-2}\ - \ a_{n-3}$

I am pretty confused right now.

>>10212304
\[$\ a_n = 3a_{n-1} + \ a_{n-2}\ - \ a_{n-3}$\]

>>10212315
[math]\ a_n = 3a_{n-1} + \ a_{n-2}\ - \ a_{n-3}[/math]

>>10212297
pi is defined as the 64 bit floating point number that is closest to [math] \pi [/math]
sin is probably defined by a rational function approximation of the sine function

>>10212304
We probably both overlooked the cases where the sequence parts are not split at a straight line, like for n=4, with the top row like o==o. I‘ll look into it more after having something to eat.

>>10212355
Thanks yet again. But got my answer a few minutes ago. Here you go:

https://math.stackexchange.com/questions/3038311/in-how-many-ways-can-a-2-times-n-rectangle-be-tiled-by-2-times-1-or/3038366#3038366

>>10212326
Then why would it be expected to be 0 since an error of O(10^-16) is reasonable for your float

Ok, here's my question. Rubinstein's bargaining game has been extended by Herrero (1985) and Haller (1986) to an n person game. In particular Haller proves that any allocation of the cake is an SPE. My questions are:
1) Would this hold if players had outside options?
2) Would this hold if the discount factor was 1?

Please tell me if these questions are too long and I should consult /mg/ or any other place, really.

>>10212390
>would this hold if the players had outside options
Not really. Consider player A wants to buy, player B wants to sell, and player C is the third option.
Consider the situation where player B is willing to sell for less than player C. However, he'd still rather sell for more than for less, so his price either gets arbitrarily close to C's, or he sells for less than B would be willing to because bargaining sucks.
I'm not sure what exactly the discount factor being one implied, but if there was no discount the game would go on forever.

>>10212412
Keep in mind that I am talking about the divide-the-dollar game and in particular to the n-players extension in which a consensus has to be reached. Since the game with 3 players has a well-defined solution, consider the case in which there are 4 players instead: A, B, C and D. Whoever the offeror is, he must convince the other three players to accept the split.

Does an inner product space necessarily have an orthogonal basis? For instance, can you have an inner product space where no vector (but the zero vector) is orthogonal to any other vector than the zero vector?

>>10212431
Yes. Let <a, b>=c, and <a, a>=d, where a and b are linearly independent. We take [math]\lambda[/math] such that [math]<a,~\lambda a>=c[/math]. Then [math]<a, b- \lambda a>=0[/math], and [math]b- \lambda a \neq 0[/math], by linear independence.
https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process

>>10212431
if you have two vectors u and v, you can always construct a vector that is orthogonal to u, namely
[eqn]
v - \frac{\left \langle v,u \right \rangle}{\left \langle u,u \right \rangle}
[/eqn]

>>10212431
if you have two vectors u and v, you can always construct a vector that is orthogonal to u, namely
[eqn]
v - \frac{\left \langle v,u \right \rangle}{\left \langle u,u \right \rangle}u
[/eqn]

>>10212451
* [math]v-u\frac{<v,u>}{<u, u>}[/math].
Otherwise you're subtracting a scalar from a vector.

>>10212451
>>10212450
Oh, that's right! Thanks

>>10212431
You need two things for an orthonormal basis
1. A basis
2. Graham-Schmidt
You can do #2 whenever you have an inner product (non-degenerate bilinear/sesquilinear from), for 1 you have to accept axiom of choice.

>>10212495
>linear combinations of uncountable amounts of objects

>>10212495
Delete. This.

So this is wrong because I forgot p^2 sin(phi)?
If I used that, i end up with 9sin^4(phi) dp dtheta.
Is it possible to switch the order of integration so I can avoid integrating sin^4(phi)?

>>10213060
dphi dtheta*

In the linear equation:

(z/3 -4) = (2z - 9)/6

If I were to attempt to isolate the z on the left side first by multiplying both sides by three, then would I need to multiply the -4 on the left side by 3 while canceling out the three under the z which would yield z - 12 = (6z - 27)/6

Or would I not multiply the -4 on the left side by 3 to yield z - 4 = (6z - 27)/6 ?

Or am I just totally doing this problem ass backwards anyways and should move the six in the denominator on the right side over to the left first? I understand that there's no solution, but I am just trying to solve basic linear equations in multiple ways to improve my comprehension of the material.

>>10213161
You multiply all terms by 3. An easier solution would just add 4 to the right side then multiply both sides by 6.
It is possible to have no solution

I need help guys. My combinatorics professor does this Naruto thing where you get +5(~2% of total) on each question that you leave blank. (Meaning if he thinks you're bullshitting you'll actually lose more points than doing nothing at all. If he's impressed by your bullshit, he'll give more than 2%) I need a 55% to pass the class. Do you think it's smarter to use the omission points to reach 55% or should I go all out and pray he's impressed with my logic?

>>10213214
Just study. 55% is not that hard to get, unless youre a retard. What class is this even? Please don’t tell me it’s something easy.

>>10213060
yeah, you forgot to include the jacobian. In this case (spherical coordinates) you need to indeed multiply the intergand by p^2 sin(phi).
Can I ask what the convention you guys use in class is? Is phi the azimuth or the altitude in your coordinate system?
sin^4 is definitely integrable, although you might be tempted to use some standard integration tricks for powers of sines or cosines.

I was recommended to take more math classes after all the undergrad stuff, but there are so many to take.
Which ones should i be looking for if I’m interested in wave propogation/signal processing?

>>10213241
Yeah, phi is azimuthal angle.

>>10213254
yeah then you just need to integrate the sin^4
good luck

>>10213240
Combinatorics taught by a dude from Harvard. Everything is all about logic and philosophy. The numbers aren't hard to calculate, but he purposefully makes bloated questions to make sure you understand what you're looking at. Everything has to be reasoned properly or he gives it nothing. (A passing score in his class is 50% and 1/4 of the class this semester were repeats)

>>10213254
Same guy here, answer should be [math] 6\frac{3}{4}\pi^2 [/math]

F = qvB sin theta

I know all of the values except theta, which I must find. I know that for protons, I'd just plug in the values, but in the question, it's asking about an electron. I'm guessing I just have to reverse something. Any help?

>>10213305
If you know all the values except theta, what exactly is the problem. Just so some algebraic work.

>>10213326
I think I was confused because I thought the angle would be different depending on if it was a proton or an electron. But I realize now that it doesn't matter, right? Since the only thing that's different is the direction of the force and not the angle between the velocity and the magnetic field.

[/math]
(1 - x)y{}'' + (x)y{}' - y = 0.

y = \sum_{n = 0}^{\infty}a_{n}x^{n}.
y{}' = \sum_{n = 0}^{\infty}(n + 1)a_{n}x^{n}.
y{}'' = \sum_{n = 0}^{\infty}(n + 1)(n + 2)a_{n}x^{n}.
xy{}'' = \sum_{n = 0}^{\infty}n(n + 1)a_{n - 1}x^{n}.
xy{}' = \sum_{n = 0}^{\infty}na_{n - 1}x^{n}.

\sum_{n = 0}^{\infty}[(n + 1)(n + 2)a_{n} - n(n + 1)a_{n - 1} + na_{n - 1} - a_{n}]x^{n} = 0.
(n^{2} + 3n + 1)a_{n} = n^{2}a_{n - 1}.
a_{n} \frac{n^{2}}{n^{2} + 3n + 1}a_{n - 1}.
[/math]
Where am I going wrong?

And no this is 100% totally not a homework question.

>>10213394
[math]
(1 - x)y{}'' + (x)y{}' - y = 0.

y = \sum_{n = 0}^{\infty}a_{n}x^{n}.
y{}' = \sum_{n = 0}^{\infty}(n + 1)a_{n}x^{n}.
y{}'' = \sum_{n = 0}^{\infty}(n + 1)(n + 2)a_{n}x^{n}.
xy{}'' = \sum_{n = 0}^{\infty}n(n + 1)a_{n - 1}x^{n}.
xy{}' = \sum_{n = 0}^{\infty}na_{n - 1}x^{n}.

\sum_{n = 0}^{\infty}[(n + 1)(n + 2)a_{n} - n(n + 1)a_{n - 1} + na_{n - 1} - a_{n}]x^{n} = 0.
(n^{2} + 3n + 1)a_{n} = n^{2}a_{n - 1}.
a_{n} \frac{n^{2}}{n^{2} + 3n + 1}a_{n - 1}.
[/math]

>>10213396
[math]

(1 - x)y{}'' + (x)y{}' - y = 0\\
y = \sum_{n = 0}^{\infty}a_{n}x^{n}\\
y{}' = \sum_{n = 0}^{\infty}(n + 1)a_{n}x^{n}\\
y{}'' = \sum_{n = 0}^{\infty}(n + 1)(n + 2)a_{n}x^{n}\\
xy{}'' = \sum_{n = 0}^{\infty}n(n + 1)a_{n - 1}x^{n}\\
xy{}' = \sum_{n = 0}^{\infty}na_{n - 1}x^{n}\\
\sum_{n = 0}^{\infty}[(n + 1)(n + 2)a_{n} - n(n + 1)a_{n - 1} + na_{n - 1} - a_{n}]x^{n} = 0\\
(n^{2} + 3n + 1)a_{n} = n^{2}a_{n - 1}\\
a_{n} \frac{n^{2}}{n^{2} + 3n + 1}a_{n - 1}.

[/math]

do you mean this?

>>10213407
yes
help please

>>10213428
\\ is a newline in the math /math code

you also want to check the indices, if you take the derivative of the first term in
[math]
\sum_{n = 0}^{\infty}a_{n}x^{n}
[/math]

thats [math]
a_0 + a_1*x+...
[/math]

so the derivative shouldn't have an a_0 term since its just a constant

>>10213446
I was taught that for series solutions to be added together they had to have the same index, so in this case they all have to start at 0

>>10213470
yeah, but for the derivative to still be ok you need to shift the index over

[math]
y= \sum_{n = 0}^{\infty}a_{n}x^{n}\\
y=a_0+a_1x+a_2x^2+...\\
y'=a_1+2a_2x+3a_3x^2+...\\
y'= \sum_{n = 0}^{\infty}(n+1)a_{n+1}x^{n}

[/math]
you didnt change the index on the a to shift it

>Mentally dropped out of school in 8th grade
>Actually dropped out my sophomore year of high school

Are there any guides or books I can read to not be a complete retard? I pretty much don't know anything beyond basic algebra as far as math goes and I don't remember a single thing from any of my science classes.

I'm sick of feeling retarded.

>>10213305
You reverse the sign of q. Electrons have negative charge.

>>10213161
> (z/3 -4) = (2z - 9)/6
Has no solution. Expand the RHS:
=> z/3 - 4 = 2z/6 - 9/6
=> z/3 - 4 = z/3 - 3/2
=> -4 = -3/2
If you graph the two sides, they have the same slope (1/3) but different offsets (-4 and -3/2), so they'll never intersect.

>>10213486
>Are there any guides or books I can read to not be a complete retard?
Obviously there are. Just go back to school. I doubt you’ll be able to apply what you’ve learned through selfstudy to real life if thats what your goal is.

>>10212522
Yes, it's called integration

>>10212431
It's not very interesting, but there is a class of examples fitting the description in your second question: any one-dimensional space with a nontrivial inner product.

>>10213486
Well you seem to have good grammar and spelling. And you speak in an articulate way. So that's a start. It shows that you have the potential to learn.

But the fact that you're unable to find resources on the internet is alarming. Or maybe you're lazy and want us to find them for you. Or maybe you just want to vent your frustration and guilt in a safe space.

Figure out your motive first.

What is this symbol surrounding x?

>>10210745
What is the distance at which the neck should be broken? or is it recommended that it be by asphyxia?
How long must pass to find the corpse and not be completely disgusting?

>>10214026
Just turn yourself in anon

Did I do this right? It doesn’t look right to me. 1/2

>>10214054
2/2

>>10214019
Double brackets, https://en.m.wikipedia.org/wiki/Floor_and_ceiling_functions
Check the notation section

>>10214054
>>10214061
Ah nevermind, I see now I can't use a distance of 0.3 meters for the y-component.

>>10210852
I really wish someone would have told me how core Taylor Series is to so many proofs instead of telling me that it can be used to approximate functions. I honestly wish all my math classes were taught based on axioms and proofs (not necessarily walking through every proof just showing how they compound on each other) instead of hurr durr you can calculate how many pennies you will get back. May have been less interesting, but I sure as hell would be better at math.

Haent taken the WPJ or writing placement for juniors. Is it hard?
Haven’t done any real writing in sometime. Do lab reports count? Am I supposed to do well in this? I only have major classes to take care of now.

>>10214054
v_y = a_y*t
d_x = v_x * t
t = .3 m / v_x

v_y = a_y * .3 m / 5*10^6 m/s = 3*10^5 m/s

What's the difference between convection and advection?

>>10213538
>sets g(0)=2f(0), g(x)=f(x) otherwise
>watches the integral's value not change
So much for linearity.

Am I correct in assuming that the currents i1 and i3 are the same for these 2 circuits? Is there anything I'm missing here?

Does pic related converge in R for a > 1? My guess is that it doesnt but I cant show it

imgur dot com slash a slash cDejzz8

is steam technology still used to produce energy from the heat provided from coal and nuclear sources? we still rely on steam turbines?

Does sqt have a patron waifu-tier god of grades that I can pray to before a test?

>>10214054
>>10214061
>>10214084
You're in the right direction, just go back to your basic kinematics from chapter 1 of physics 1. Some for time in x then solve for v_fy.

the order of an element's cyclic subgroup, |(a)| is the same as element's order, o(a), right? this seems obvious but the text i'm reading does not point it out explicitly and i find that weird

>>10214582
> is steam technology still used to produce energy from the heat provided from coal and nuclear sources? we still rely on steam turbines?
Yes. At least, that's the case for all large-scale electricity production.

>>10214638
If I had to nominate the dumbest post in 2018 you'd win with a large margin>>10214638

>>10210745

What would the electric field in space look like if there was everywhere a uniform and constantly increasing magnetic field?

>>10210745
fucking gram-schmidt process that takes me back bro damn
I can't wait to get back on that math grind

Honestly even though I'm a more I enjoy math

>>10211084
Science doesn't actually need valid theoretical proof, buddy. It's nice when it happens, but it's not a prerequisite.

>>10214662

just tell me what i'm getting wrong. the cyclic subgroup of a is {a^i | i non-negative integer}. the order of a, o(a), as defined in my text, is the least integer m s.t. a^m = e. if we're talking about finite groups, then {e, a, a^2, ... a^(m-1)} is a subgroup and as far as i can tell, the same thing as the cyclic subgroup (a).

>>10210846
>>10211007
[math] \displaystyle
e=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\cdots
\\ \\
e^x=\frac{x^0}{0!}+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\cdots
\\ \\
sin(x)=\frac{x^1}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-\cdots
\\ \\
cos(x)=\frac{x^0}{0!}-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}-\cdots
\\ \\
cos(x)+sin(x)=1+x-\frac{x^2}{2!}-\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}-\frac{x^6}{6!}-\frac{x^7}{7!}+\frac{x^8}{8!}+\frac{x^9}{9!}-\cdots
\\ \\
e^{ix}=\frac{(ix)^0}{0!}+\frac{(ix)^1}{1!}+\frac{(ix)^2}{2!}+\frac{(ix)^3}{3!}+\frac{(ix)^4}{4!}+\cdots
\\ \\
e^{ix}=1+ix-\frac{x^2}{2!}-\frac{ix^3}{3!}+\frac{x^4}{4!}+\frac{ix^5}{5!}-\frac{x^6}{6!}-\frac{ix^7}{7!}+\frac{x^8}{8!}+\frac{ix^9}{9!}-\cdots
\\ \\
e^{ix}=\left ( 1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}-\cdots \right )
+i \left ( x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-\cdots \right )
\\ \\
e^{ix}=cos(x)+i \, sin(x)
[/math]

>>10213407
[math] \displaystyle (1 - x)y{}'' + (x)y{}' - y = 0\\ y = \sum_{n = 0}^{\infty}a_{n}x^{n}\\ y{}' = \sum_{n = 0}^{\infty}(n + 1)a_{n}x^{n}\\ y{}'' = \sum_{n = 0}^{\infty}(n + 1)(n + 2)a_{n}x^{n}\\ xy{}'' = \sum_{n = 0}^{\infty}n(n + 1)a_{n - 1}x^{n}\\ xy{}' = \sum_{n = 0}^{\infty}na_{n - 1}x^{n}\\ \sum_{n = 0}^{\infty}[(n + 1)(n + 2)a_{n} - n(n + 1)a_{n - 1} + na_{n - 1} - a_{n}]x^{n} = 0\\ (n^{2} + 3n + 1)a_{n} = n^{2}a_{n - 1}\\ a_{n} \frac{n^{2}}{n^{2} + 3n + 1}a_{n - 1}.
[/math]
Optimized.

>>10214638
Yes, yes it is.
The proof is two-limes long.

>>10214732

sorry for asking a stupid question in the stupid questions thread.

>>10214805
You’re mistaken. This is a thread for smol questions. Questions in this thread will vary in size

>>10214830

it was also a small question.

Please hit me up with your best memorization techniques.

>>10215002
Method of Loci
Peg System
Major System

>>10215006
Thanks, fαm.

Is self-capacitance a thing in conductors? Imagine a long, straight copper wire with voltage applied at one end and ground at other, due to resistive losses any two points in the wire have different voltages, thus these two points have an electric field between them and the field is represented by parallel capacitance? Let's ignore the return path of the current

>>10212136
Dirac must have had massive balls then.

>>10214609
Open your fucking textbook you twat

in my fourth semester of uni at a fairly tough school, will I be okay for grad school if I've gotten 4 C's so far? two of which were in my major (biochemistry), gpa of 3.2 currently

>>10215937
Try not to fall under 3.0

how do i go about writing an equation that always results in a integer?
ie y=(5*x)/3, but with Y being integer always, rounded up

>>10216378
[math]
y=\lceil\frac{(5*x)}{3}\rceil
[/math]

?

>>10216378
y=0

>>10216386
kek

>>10216384
i meant a number without a fractional component

>>10214609
Grothendieck.
>>10216378
There's this symbol that's used like |x| but both | have little turns inwards at the bottom, and that denoted the biggest integer smaller than or equal to the number.

if i understand this bit of QM at least somewhat then when you observe a particle its wave function collapses and its position becomes definite

so what if you had a box of particles w/ mass and you observed just one? how does knowing the position of one particle affect the rest? would it be possible to determine (or at least decrease the number of possible positions) of the other particles in the box by knowing the position of one? it seems like you could, since the other particles cannot occupy the same space as the particle you definitely know the position of

to chemists:
is the name formaldehyde just a convention? is it not pretty stupid to name a pure chemical compound like the substance it makes when deluded with water and dehydrated again?

I guess first they found Formalin and then purified it and called it the "purified" Formalin, Formaldehyde.

Shouldn't they fucking name the pure compound Formalin and the "watered down" substance Formalhydrat?

Am I missing the idea behind the etymology or is this just scientists not giving a fuck about language efficiency?

>>10212388
floats are not reasonable, prone to rounding errors

So why is it that most orbiting systems in space form flat rings/discs as oppose to orbiting the central body in a cloud?

i.e Saturn's rings form a flat 'disc', most of the Solar System orbits on the same plain, and galaxies, on a macroscopic scale, are also 'flat'. Why not a spherical cloud around the central point?

>>10217576
So what would you propose instead? Representations exist for algebraic numbers, but there is no general representation for transcendental numbers (being an uncountably-infinite set and all). The most general representation is computable numbers, but those can't even be compared for equality.

>>10217385
>since the other particles cannot occupy the same space
This is incorrect. Bosons can occupy the same spacce while Fermions can do the same as long as they have distinct labels (e.g. spin, momentum, etc.).
It'd be good for you to learn what "observation" actually means in the context of decoherence.
>>10217675
Because the angular momentum is conserved. In a Keplerian system, the coadjoint orbits of the group of rotational symmetry [math]SO(3)[/math] determines the trajectories and an your symplectic manifold foiliates through these orbits. Since the angular momenta [math]L_{1,2,3}[/math] generate [math]\mathfrak{so}(3)\cong\mathfrak{su}(2)[/math], the coadjoint orbits are labeled by these angular momenta and, as physical trajectories can't leave the leafs of these orbits, they have to have the same value of [math]L_i[/math] throughout. This makes planetary orbits unable to change its direction perpendicular to its orbital plane, since doing so would change the direction of the angular momentum.

Why don't fats/oils break down easily in the environment? They're carbohydrate chains, so I would think microbial life would be well-adapted to breaking them down, but oil run-off is very simple pollutant.

A similar line I was laughed at by a chemistry teacher for asking in high school, how does mayonnaise go bad? Temperature, oxygen, or life? When you leave a sandwich out the mayonnaise becomes clearer and gross, so I was thinking what exactly involves it's process into not-good-food.

>>10212214
Piezoelectricity. Start from there at least.

>>10211524
Yeah that works. Normally we connect the arrows. I say it works because I don't remember if there's a different name where you put the numbers/output in the circle.

>>10211361
Since there's a clock, I'd have to go to the definition. One of them is only dependent on initial input, so having a clock violates that I'd guess.

>>10214491
Draw your circuit better, preferably on graph paper. They make graph paper notebooks and loose sheets. A quick skim, I think your conversion is correct.

>>10210745
How many ways are there of rearranging the letters of WORKED if the letters are taken three at a time?
The book says there is 120 but I honestly thought there would be two:
WORKED
KEDWOR

i guess if you continue, you might be able to arrange all of them freely and thus its 6! or 120, which is the answer.
But then how would you do it at 2 at a time?
Halp

>>10218005
I think it means changing only three letters.

>>10218005
from the sound of it, it seems like you can "take" any three letters at a time. Does it require it to be consecutive groups of three letters (ie each letter follows another) or can you get your set of three letters from anywhere in the word?

Either way, clearly the point of the exercise is to show you that with 6 letters, picking n letters to move will always eventually allow you to form any of the permutations as if you were just considering standard (ie one letter at a time) permutations of 6 letters.

How much time is there between the point when I downloaded Python and when I become a millionaire? I'm guessing like 30 days.

Can someone help me out with these electrolysis questions. I missed the lectures on it due to illness. I can do voltaic cell questions fine but not the electrolysis ones

>>10217970
I might be wrong, but fat are really long carbonic chains and that may be responsible for the less efficient decomposition of the oil.
More so, when the bacteria break the oil, O2 is consumed from the environment, usually a lake or river. Not only that, but the oil form a film on top of the water, reducing the oxygenation and photosynthesis in said lake or river. All of this leads to death of the ichthyofauna. This phenomena alone is enough to demand proper discard of oil.


Mayonnaise goes bad due to oxidation, forming organic acids. This can happen naturally, but it majorly is caused by microorganisms that release acids (butyric acid when it is butter, that's why the name :)). Temperature influences the metabolism of said microorganisms, so cooling the food will give it extra lifetime.

>>10219686
There ya go, dingus.

Can anyone point to me some resources that I can look for further info about this?

>>10220531
This makes me miss the old /sqt/ text with the whole "no universal notation" part.

>>10220539
That should be some sort of fluid dynamic related equation but I am not totally certain about the context either

>>10210745
>The teacher uses molar fluxes (MJ) and mass fluxes (mJ) as
[math]_{M}J_{i}=C_{i}(U_{i}-U^{M})\\
_{m}j_{i}=\rho_{i}(U_{i}-U^{m})\\[/math]
>and he told us to proof these (just transform the right side into the left), asumming only A and B components
[math]_{M}j_{A}+_{M}j_{B}=\rho(U^{m}-U^{M})\\
_{m}J_{A}+_{m}J_{B}=C(U^{M}-U^{m})\\
_{M}J_{A}=-(\frac{\rho^{2}}{cM_{A}M_{B}})D_{AB}\nabla\omega_{A}\\
C(U_{A}-U_{B})=-\frac{cD_{AB}}{x_{A}x_{B}}\nabla x_{A}\\[/math]
I have some problems

>>10220636
[math] _{M}J_{i}=C_{i}(U_{i}-U^{M})\\
_{m}j_{i}=\rho_{i}(U_{i}-U^{m}) [/math]

anyone have good books on sciences of electricity. Beginners all the way up to expert stuff if you dont mind listing it.

>>10220405
Thank you. Oxygenation issues help make sense of oil decomposition, though I'm still displeased as to why if you smeared oil on a surface exposed to air, you'd still expect it to be there a long time later.

>>10219686
What I liked when I did chemistry stuff:

https://www.kentchemistry.com/newRT.pdf

The New York State reference tables were very well organized. I don't think they're online anymore, but the version before that even included battery reaction stuff.

>>10220648
That's a vague question. Physical electricity is one thing, circuits another.

I suggested in another thread so I'll suggest it again (you need to sign up though):

https://archive.org/details/basicmathematics00nels

I have the predecessor to that book, and it covered a lot of basic maths and circuits. You'll need some math competency as you progress in electricity, because physical representations quickly need calculus, and circuit representations will get into trig and imaginary numbers, and then integration when it steers towards the physicality of it.

>>10220659
im kind of a moron, but i feel like changing, i really cant take being a dumbass anymore, the only other problem is my memory, but i think i can change. If calculus and trig and other stuff is what i need i want to excel.

>>10210745
If I were to fill my bath tub with water, put a membrane over it such that my head doesn't fall in, and take a nap with my body submerged under the water, would there be any effects on my body aside from being wrinkled and possibly cold when I wake up?

I'm a genuine brainlet, and my working memory is non-existent and I constantly daydream. I cheated throughout the school, I cheated throughout the university. Soon to drop out since I decided what am I able to do by myself. Turns out -- nothing, in particular. What could I do to improve? I remember I couldn't learn a twelve-line poem.

>>10210745
Why does my peepee stink? I wash it every day but at the end of the day it stinks bad

>>10220841
Are you circumcised? If you aren't, try "uncovering" the head of your penis when you pee. Avoid masturbating as well, mine was stinking yesterday due to it.

Americans: Burgerpill me on college algebra.
It looks like it's just the part of high school math that was about functions. Is that so?
And if it is, why do I see people claiming a 50% failure rate and then calling it racist and a civil rights issue?

>>10220952
>college algebra
>this guy has to be memeing me, college algebra is group theory
>google it
>it actually is just high school algebra
Fucking dead.
https://www.mathsisfun.com/algebra/index-college.html

>>10220952
>>10220963

>>10220952
>>10220963
>>10221114
Way back, I heard a story about a Math 001 class at a junior college that I imagine was basically this. It was called "double oh duh".

>>10220963
Group theory can easily be taught in high school desu

>>10210745
Let’s say the entire earth is on fire for some reason and won’t be burned out for a thousand years would we look like a star? If no can someone explain the reason why we wouldn’t?

>>10221188
Fire doesn't usually go up to thousands of degrees like fusion does.
And the earth would still have shit mass.

Let [math]P,Q \in \mathbb{R}[X][/math] such as [math]P(X)^2+Q(X)^2 = (X^2+1)^2[/math]
1°) Show that [math]deg(P) \leq 2[/math] and [math]deg(Q) \leq 2[/math]
2°) Show that [math](X-i)[/math] divides [math]P(X)+iQ(X)[/math] or [math]P(X)-iQ(X)[/math]
3°) We now suppose that[math](X-i)[/math] divides [math]P(X)+iQ(X)[/math]. Show there exists [math] \lambda \in \mathbb{C}[/math] such as [math]P(X)+iQ(X) = \lambda (X+1)^2[/math]
4°) Show that [math]| \lambda | = 1[/math]
5°) Deduce there exists [math] \theta \in ]- \pi ; \pi][/math] such as
[eqn] P(X) = cos( \theta )(X^2-1)+2Xsin( \theta)[/eqn] [eqn] Q(X) = sin( \theta )(X^2-1)-2Xcos( \theta)[/eqn]

I'm kinda stumped on the third question, do you guys have any hint on how to proceed?
I took the derivative [math]P(X)^2+Q(X)^2 = (X^2+1)^2[/math] to show that [math]i[/math] is a multiple root. Then since we know that [math](X-i)[/math] divides [math]P(X)+iQ(X)[/math], we've got [math]P(X)+iQ(X)= (X-i)A(X)[/math] with [math]A(X) = (X-i)[/math] but what about that [math] \lambda[/math], do I just say it's some random number on the unit circle and go next question?

>>10221199
Something something Gauss's lemma.

>>10221199
I fucked up the 3°), it's

3°) We now suppose that[math](X-i)[/math] divides [math]P(X)+iQ(X)[/math]. Show there exists [math] \lambda \in \mathbb{C}[/math] such as [math]P(X)+iQ(X) = \lambda (X-1)^2[/math]

>>10221199
>show that
>we now suppose that

>>10210745
how do AC things even work if they constantly return energy in form of negative voltage/current?

>>10221214
If you want to prove that i is a multiple root, you gotta assume that (X-i) only divides P(X)+iQ(X) and not P(X)-iQ(X) or else you'll end up with a 0/0 when you take the derivative of the first equation. At least that's what I thought the dude that wrote the subject meant

>>10221205
baka senpai [math] \lambda X^2 +1[/math]
Just write down "follows trivially from the complex numbers not being separable over the reals".

>>10221203
I'll look into it tomorrow, thanks.

>>10221226
Ugh, I caught the stupid.
[math]\lambda (X^2+1)[/math].

>>10221190
well I'm not meaning we would turn into a sun I'm meaning if another advanced civilization looking for light across the galaxies would we look like a sun to them or would fires light be too dim to be noticed?

>>10221219
> if they constantly return energy in form of negative voltage/current?
The don't return energy. Power = V*I. For a resistive load, V=I*R. When voltage is positive current is positive so power is positive. When voltage is negative current is negative so power is again positive.

>>10221199
[math][P(X)+iQ(X)][P(X)-iQ(X)]=P(X)^2+Q(X)^2=(X^2+1)^2=(X-i)^2(X+i)^2[/math]

>>10221241
>memegineers
>>10221219
Negative and positive quantities are conventions used. I don't really see what exactly you think doesn't work, it's just changing the direction the current flows.

>>10221226
>>10221230
OOOH I know what you mean. That's neat, I think that could be enough of a justification indeed. Thanks!

>>10221247
Fucking TeX preview not working. I'll try spacing.
[math] [P(X)+iQ(X)][P(X)-iQ(X)]=P(X)^2+Q(X)^2=(X^2+1)^2=(X-i)^2(X+i)^2 [/math]

>>10220641
I fixed the equations, don't know how to use "/math"
>>10220636
Can you help me guys, please?
[math] _{M}J_{i} [/math]
molar fluxes
[math] _{m}j_{i} [/math]
mass fluxes
[math] _{M}j_{A} [/math]
wtf is this? molar or mass flux?
How can I proof these 4? >>10220636

>>10221114
>I've had multiple students that failed the course before take it again, come back and pass the course, often with a B or better. They're only too willing to tell me the difference is they actually studied the second time around.

Well, shit. It actually taught them the life skill of applying themselves.

>>10221199
[math]\mathbb R[X][/math] is a UFD and we have [math]P(X)^2+Q(X)^2=(P+iQ)(P-iQ)=(X^2+1)^2=(X-i)^2(X+i)^2[/math], so if [math]X-i[/math] divides [math]P+iQ[/math], it is enough to show that [math]X+i[/math] also divides [math]P+iQ[/math], so that by part 1 we must have equality (modulo some complex constant).

To show this, just assume otherwise. Then by part 1º (and the fact that [math]P\pm iQ[/math] must have degree 2), we can write [math]P+iQ=a(X-i)^2[/math] and [math]P-iQ=b(X+i)^2[/math] with [math]a,b\in\mathbb C[/math]. Then [math]2P=P+iQ+P-iQ=a(X-i)^2+b(X+i)^2[/math]. Comparing coefficients and since P is a real polynomial, we must have both (a+b) real and (a+b)i real, so a+b=0, which gives us [math]P\equiv 0[/math], a contradiction.
QED

>>10221281
>university is there to learn to apply oneself
if you didn't learn it before high school, then you are braindead anyways

>>10221341
if you needed to apply yourself before uni, then you are braindead anyways

>>10221400
>one can only apply oneself in the school atmosphere

>>10210969
>>Nani?

I'm trying to compute a (formal) power series for [math]e^{x^2}[/math].

I tried finding a recurrence for the derivatives and wound up that the polynomials in front have to satisfy [math]P_n(x) = 2xP_{n-1}(x)+\frac{d}{dx}P_{n-1}(x)[/math]
but this doesn't seem easily solvable to me.

Any ideas?

Was wondering in physics graduate school, what are the hardest concentrations to get into in order? (out of hep, cm, amo, astro, biology)

I know experimental is easier to get in than theory, and hep is the hardest. After that I am clueless. CM seems to be the hot stuff right now but faculty sizes for CM is big usually so I guess they admit more students proportionally. Astro and bio are memes.

>>10220636
Look at like chapter 1 of Deen's transport book

>>10220434
Oh great thanks. That's what I did but the copper iron thing threw me off

>>10222222

Trying to find the SI units of viscosity, [math]\eta = -\frac{FR}{2\pi r \ell v}[/math], where F is force, r is a radius, [math]\ell[/math] is length, v is speed, and R is distance. I'm getting [math]\text{kg}\cdot \text{s}^{-1}[/math] but I should be getting [math]\text{kg}\cdot m^{-1}\cdot \text{s}^{-1}[/math].

>>10222533
You're probably forgetting speed.
m from F, m from R, m^-1 from r, l and v.

>>10222540
Found my mistake. Had wrote that a newton was [math]\text{kg}\cdot \text{m}^{2}/\text{s}^{2}[/math]. Thanks anyways.

Any tips to improve memorization?
I need to study for an exam that's a few months a way, but the more I study the more I forgot the older stuff.

>>10222656
spaced repetition.

>>10222710
OK, so I need to go over what I've read every 5 days?
But then I'd need to spend a month just to re-read 10% of what I've studied.
Also good way to study?

I accidentally told my professor that I use sci-hub. He's based so there should be no problem, but do students usually get shit for pirating?

I'm a bit new to tensors and stuff. How does
[math] \delta_{ij}\delta_{jk} = \delta{ik}? [/math]

>>10223478
That's the Kronecker delta function, right?
Anyhow, that's incorrect. Consider literally any example. i=2, j=1 and k=2 works.

>>10223478
Sum over j, it will only be nonzero when i and k are the same.
>>10223496
There is no free index j.

>>10223510
>There is no free index j.
That just makes a new fuction of two variables that's only 1 when i=k=j, fixed earlier.

Why would inertial mass and gravitational mass be different? I know I shouldn't think much of it, but it boggles me why this was (and slightly still is) a point of discussion. Isn't F = ma a general law for motion, so that you could just substitute a with -GM/r2? Or what am I getting wrong here? If I have made what I meant more confusing just tell me why inertial mass and gravitational mass could be different.

>>10223478
Literally write down the definition

[math]\delta_{ij}\delta_{jk} [/math] is 1 if [math]i= j[/math] AND [math]j= k[/math] and 0 otherwise, that is, it is 1 if [math]i=j=k[/math] and 0 otherwise, that is, it is 1 if [math]i=k[/math] and 0 otherwise, that is, it is [math]\delta_{ik}[/math]

Entering 3rd year of EE. How difficult is it to maintain a 3.0 considering current GPA is reset? No more Gen ED and all major classes.

>>10224162
Should also note I’ll be working part time.

How do I solve this? For the first part do I just replace v with 15 and it gets 2% and then on the next just times it with the days of a weekend over total?

>>10225072
for (a) wouldnt you integrate p(v) from 0 to 15, since p(v) is the probability density and not the probability
0 to 15 is the interval where you can practice

for (b) i think it would just be the probability from (a) times the number of weekend days in a year.

Y(x,t)=10sen[π(0,01x-2t)]

With x and t in cm and s.


(a) Determine amplitude, frequency, wavelength, and velocity.

>>10210745
I am trying to clean copper casings from ww1.

I found them in a field with some iron rust on them as well as copper oxidation of course.

I put them in HCl to remove the rust, but then they turned a milky white color. I tried to neutralize them by first drying and then immersing them for a couple of minutes in a baking soda solution.

When I subsequently put them in a tumbler they came out as new.

However, just hours after they came out, they started oxidizing (blue/greenish patina) and after a day they looked worse than they looked after being in the ground for 100 years.

I tried washing them extensively with water, to no avail. What should I do? What is causing the oxidation? How do I prevent it?

>>10225212
pic related.

the oxidation as you can see is both reddish and green

Part (b).Why is the solution [0,9]? I thought it should be [4,9].

What are the prerequisites to understand category theory?

>>10225246
Because f(0)=0.

>>10225249
Basic set theory and autism.

how do you prove associativity for an operation in general?
I know in this case you can say its isomorphic to [math] \mathbb{Z}_2 [/math] which inherits associativity from the integers, but I can't think of a process to do it generally, my only thought would be doing it case by case, which sounds fucking atrocious for any set and totally retarded for infinite ones.

>>10225260
But how did -2 become 0? I see it stating that the range has 2 domains, which in this case would be 2 and -2 and together they equal 0. But why don't I do that to the 3 as well, or any other number?

>>10225295
0 is in between -2 and 3, so its in the domain. and 0 also maps to 0, so 0 is in the range

>>10225294
Light's test.
>>10225295
One of the sad, sad facts of the world is that while some people, like Poincare, have absolutely magical intuition for doing maths, other people will reach the stupidest conclusions and should stick to formalism. I myself have trash intuition.

>>10225329
thanks, but this test is one of the grossest things i think ive ever seen.

>>10223585
pls help

>>10225294
there's no way to prove associativity in general. Most of the time you will be alluding to "inherits it from previous ring", or calculating directly (like matrix associativity), or alluding to "function composition is associative" which is easily provable. In fact, associativity of arbitrary groups tends to be one of the hardest things to prove usually, like for example, in the group law over elliptic curves (and not as much, but composition of homotopies is a pain for example).

>>10223585
>>10225402
Think of it like this, by your logic the electric force has the same form as gravity, so why isn't charge the same as mass? Well, it has no reason to be.

In your equation you can't know that the M is the mass of the earth a priori, it could just be something correlated with the mass, or number of atoms or whatever.

If dark matter exists why do we see its effects only on large scales? Why doesn't it change the orbits in the solar system for example?

>>10225552
>we see its effects only on large scales
is that true?

>>10225552
If gravity exists why do we see its effects only on large scales? Why doesn't it change the orbits in electrons for example?

Can a human swim in a salt brine? and if not what gear would they need?

>>10225558
Well all of the evidence that I'm aware of is on the scale of galaxies at minimum.

https://en.wikipedia.org/wiki/Dark_matter#Observational_evidence

>>10225560
It's not the same, gravity is very weak but there should be more dark matter than ordinary matter. Is it simply distributed in such way that there isn't any near us?

>>10225571
Anyone?

>>10225692
https://en.wikipedia.org/wiki/Brine_pool

>>10225745
It says an animal cant go in there due to not being able to breathe methane but humans underwater have scuba tanks but I want to know if standard scuba gear would allow you to explore around

How does decoupling electronic masses with transformers work?

>>10225212
>what is causing it?
Oxygen in the air in the presence of water, transforming the copper/iron alloy into oxides of those elements.
>how do I prevent it?
You can paint it or put zinc or magnesium plate on the surface of the bullet. However, these plates will corrode and you have to change it.

>>10225755
You would dehydrate very quickly, but it's not toxic or poisonous. Still, Drinking the water will get you a heavy diarrhoea and a rise in blood pressure.

>>10225928
So if you wore a dry suit you would be okay?
I know they are expensive though how well would a wet suit work?

>>10225947
I guess

>>10211879
woah i didn't know serge lang browses /sci/!

I'm a physics brainlet. From wikipedia about electric power
>High voltage was of interest to early researchers working on the problem of transmission over distance. They knew from elementary electricity principle that the same amount of power could be transferred on a cable by doubling the voltage and halving the current. Due to Joule's Law, they also knew that the capacity of a wire is proportional to the square of the current traveling on it, regardless the voltage, and so by doubling the voltage, the same cable would be capable of transmitting the same amount of power four times the distance.

I'm reading about DC vs AC and can't understand why AC was much better for longer distances.

>>10227129
>why AC was much better for longer distances
in general, it isn't. There are plenty of other advantages that AC offers, specifically the ease at which voltage is transformed as well as the fact that it can be easily rectified. DC doesn't have to deal with reactive losses, but can't be converted as easily without significant losses as well as making an AC signal from DC is ridiculously difficult. HVDC transmission is a thing and has plenty of real advantages over AC.

>>10227129
>>10227310
He overstated it. AC can run through transformers, so by stepping up lower voltage, you can send high voltage over a cable with low losses. One of the power equations is P = I^2 * R, the easiest way to demonstrate that if you can lower the current, for a given resistance, you have lowered the power lost/consumed in that segment. DC can't be stepped up/down at all in a traditional component (resistance, capacitance, inductance).

>>10225560
Gravity is just that much weaker.

http://www.batesville.k12.in.us/physics/PhyNet/e%26m/electrostatics/michaels_question.htm

Gravity is 10^41 times weaker than electromagnetism. If you had two hydrogen atoms (electron and proton), and separated them by something like sqrt(10^41) times the distance between the electron and the proton in a hydrogen nucleus, the gravitational force would approximately equal their electromagnetic forces (proton+electron look neutral from large distances).

A professor I had in a calculus class wrote down a long ass expression for n!

It had som square roots of pi, e to the power of some integral and other stuff, but now I can't find my notes and I can't find the expression on wikipedia are anywhere else. Does anyone know what I'm talking about?

What's the deal with high voltage transformers?

I am thinking about a project and I noticed that it will require very high tensions. On the order of 100kV to 1000kV. What problems might I run into, aside from commercial availability of such transformers? Why are they so expensive in the first place? I thought you could just append lots of transformers upping the tension in series, with care so you don't go over the ionization tension from the isolating materials and such.

My project will be rated at about 100 to 1000W, thus the discrepancy on the voltage. I haven't decided yet.

>>10227536
https://en.wikipedia.org/wiki/Gamma_function

>>10227606
If the voltage exceeds the wire's insulation rating, the transformer needs to be wound so that points with a large potential difference aren't near to each other. Also, the connectors need to be far enough apart that you don't get an arc across the air gap (~3kV/mm for air).

Also, as V increases so does dV/dt, so inter-winding capacitance becomes more of an issue.

>>10227632
Thanks for the answer. I understand now about the transformer's problems. I was looking a bit more into it, and it seems like a tesla coil is almost exactly what I need. After looking at my calculations and getting the figure of 600kV I almost lost all hope, more so after seeing commercially available transformers rated for that. But people make tesla coils all the fucking time. I will need to rectify it using some high voltage diodes, since I require end terminals to have specific charges, but microwaves use that so they are cheap.
What kind of problems would interwinding capacitance make for me? For the dielectric breakdown, I could just spray something for it, carefully, right? I was looking at some materials, and although air is 3kV/mm, solids have more, some plastics having 17kV/mm. I don't know how that would affect the coil's performance, since they need coupling after all, but I am not interested in sparks.

>>10227536
you mean stirling's approximation?

>>10227778
Stirling's approximation only involves logs and is applicable for large quantities. They were probably thinking of the gamma function.

Best way to learn mathematics outside educational institutions?

Right now just doing practice problems daily that gradually increase in difficulty.

Furthest I got in school was trig, probably need to brush up on geometry before I jump back into that though.

Not really looking for specific recommendations on books though I don’t mind them, more asking about what processes anons think work best.

>>10227879
khan academy, check it out

>>10227879
Khan academy up to pre calc, and then follow this chart.

someone at least tell me what this is called or how to do it or something, i could lose my job over this braille bullshit

>>10228367
isnt that meant to be your phone number

>>10210745
Brainlet? Question.

Why is it that the apparent size of an object changes with distance?

As in why is it that the further away I get from something the smaller it seems?

Is it some inherent characteristic of 3d space or something to do with light?

>>10228369
god

>>10228371
The angular size is what your eyes see, and it depends on distance.

https://en.m.wikipedia.org/wiki/Angular_diameter

>>10228192

why there are anime girls on your math problem web site ? ?

Based on the principle of heat exchange and material properties, what is the optimal material for a chair and a pair of pants to minimize my massive ass sweat? Currently I study on a leather sofa in my shorts, and the sweating is unbearable.

Is the hypothetical Alcubierre warp drive also a machine that technically controls gravity since it is able to warp space time?

Is there any general equivalent of Cayley's theorem for Banach algebras over the complex numbers and maps on the complex plane?

can the (two dimensional) laplace equation [math] \Delta u = 0 [/math] be understood as a formulation for some linear elasticity problem?
If so, what kind of material would be discribed?

What are the best methods of keeping something dry if you are storing it outside?

I keep a few things outside for safekeeping. But I don't how how to keep them safe and in the best condition possible. For example, how would you store the following items outdoors in a rainy climate? 5yrs minimum.

1. A regular Steel house key
2. A note of paper
3. Money
4. Computer thumbdrive, or hard drive

>>10210745
Am I being autistic with standard form or is that the right answer? Put 6.73x10^9 (the stress I calculated from mg/'pi'rsquared) over 203x10^9. Looks alright.

>>10229179
Type in 0.000456 for the jokes.

Anyone here have any experience going to graduate school while working full-time? How did you stay motivated? Did either work or school suffer?

>>10229457
>going to graduate school while working full-time
Are you trying to kill yourself through exhaustion?

>>10210745
Can someone explain how this works

>>10229457
I’m taking one class at Georgia Tech while working full time at intel. They’re paying for it, too.

>>10229457
>not picking up entire other skill sets in your free time

What's the point of being intelligent if you aren't gonna learn new shit?

>>10229485
How do voltmeters work? It's fucking magic, man; nobody knows how voltmeters work.

>>10229485
If you're about to study op-amps and are struggling with voltage dividers, you're going to have a bad time.

>>10229179
The force is 2.43*9.81 = 23.8383 N.

The cross-sectional area is π*(0.339)2 mm2 = π*(0.000339)2 m2.

This makes the cross-sectional stress 23.8383/(π*(0.000339)2) Pa = .0000000238383/(π*(0.000339)2) GPa. That's about .066 GPa, so you're a bit off the mark.

I like to keep my numbers unsimplified until I get to the final formula. You're probably getting things rounded off that don't need to be rounded off. Another way to avoid that is to use Excel as your calculator. It's honestly one of the most powerful calculators you can ever expect to have at hand.

>>10229653
Those were superscript 2 symbols when I typed them. That's a shit.

>>10229653
Thank you anon, did it in the end. Will give Excel greater use in that case, really have been neglecting it. Have a nice drink on me.

>>10228566
>/sci/

>>10228091
>>10228192
Muchas gracias anons

>>10228959
Might be a better question for /diy/ than here

is pic related Z_2?

>>10229878
>4 elements
>is it a 2 element set
....

>>10229878
its isomorphic to [math] \mathbb{Z}_4 [/math] with
f(e)=0
f(a)=1
f(b)=3
f(c)=2

Are there any career fields worth going into without a degree?

How difficult is Calc 1-3?
I haven't been in a math class in 8 years, been putting it off forever because of fear. Everyone says it's hard af.

>taken ochem 1 (soon to take 2)
>gen chem 1-2
>gen bio 1-2
>genetics
>biotech 1-3

>>10230346
It depends on the rigor. If it resembles real analysis then you'll have to put in some effort, if not it's an easy claas

>>10230389

I should just change my major to biology or biomedical science...that way I can finish my degree in 4 years instead of 6...

I'm trying to learn some cosmology and I ran into the concept of distance modulus, basically a number that relates the absolute magnitude of an object to the apparant magnitude we see on earth.

I don't get the numbers involved, you always take 5 times the log10 of the distance, but sometimes add 5 or 25, why?

>>10210745
Where are we at on faster-than-light communications? Is such a thing remotely possible in our lifetime?

>>10230905
It's not only not happening on our lifetime, but it's probably not happening ever.

Hi, I have a question please:

f(x) = cos(x * pi)
f'(x) = -sin(x * pi)
F(x) = sin(x * pi)

Right? (F is the antiderivative of f)

Thank you!

>>10231101
No. Use the chain rule.
[math]Dcos( \pi x)=- \pi sin(\pi x)[/math].
The other one is left as an exercise.

>>10230067
because im stupid and somehow worked out that a=b and c=e
>>10230144
thank you

>>10231123
ok thanks!

what happened to Jon? it's been a while and no arcon posts. what gives? did he dieded?

I slipped on some ice earlier today and bonked my hand, it is now 8 hours later and I'm trying to sleep.
When should I worry?
Any easy way to dull it for sleepy time?

Is it good?

>>10232035
Your hand will stop hurting if you cut it off at the elbow.

If i want to make a latex document with only math, what kind of shit do i need to put in it other than the math itself?
I've googled and all example-templates are for full articles with writing and shit so i don't know what's really necessary to keep.
I should learn this thoroughly by myself later but now when I have a very good flow in my mathematics I don't want to stop to study latex for a couple of days. I just want to have enough to compile the document containing only math.
Now I just use those websites that lets you input math and shows a preview but I want to be able to do it offline.

>>10234036
This is my template file:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\thispagestyle{empty}
% place math here
\end{document}

I have a continous function f and I can get it's density in space by a simple 3D grid. With a grid length of 100 points, I get 1 million values.

Now, I want to approximate the function with a new function g, which should as accurately reproduce the densities from the grid.

Can I use machine learning for something like this? It is basically regression but I'm not sure how to approach the problem.

>>10234152
That should be enough. Maybe microtype for better typography and bm for bold math symbols (not sure if that's covered with the ams packages).

>>10210844
Enthalpy is used for open systems with mass transfer. Internal energy is used for closed systems. For open systems, the possibility of net mass transfer being zero is irrelevant as net energy transfer is likely not.

>>10234036
>what kind of shit do i need to put in it other than the math itself?
Whatever you want, but very little is necessary
>>10234152 ist a good suggestion.

>but I want to be able to do it offline.
If you use sublime, there is an add-on which does that, I think it is also possible with vscode.

>>10234254
I'd anwer properly, but I have absolutely no idea what you're talking about, so I'll just drop a link
https://en.m.wikipedia.org/wiki/Stone–Weierstrass_theorem

>>10234254
>I have a continous function f
From where to where?

>Now, I want to approximate the function with a new function g
Why? You already have f, the optimal choice for g is f.

>Can I use machine learning for something like this?
Yes, but why would you? You need training data, which means you have to evaluate f and if you do that, there is no reason to approximate anything.

If you really want an approximation from R^3 to R you can use a spline. MATLAB for example has the capabilities to do things like this, but you usually want to do approximation in the case you DON'T have the function.

>>10234293
So a bit more information.

In quantum chemistry, we want to evaluate the energy of a molecule. The energy is shown to be a functional of the density (Kohn-Sham theorem). However, the exact form of this functional is unknown and in Density Functional Theory, one tries to approximate it.

For very small systems, the electron density can be calculated exactly within a given basis. For larger systems (bigger than say 20 electrons) you must use an approximate methods.

What I want is:

1) calculate the exact electron density from a lot of very small molecules at different geometries
2) put a grid on top
3) try to make a functional that reproduces the grid

>>10234326
Machine learning has no applkcation to that.

Why is it exactly that we never see, say, Hydrogen atoms with 20 neutrons? What physical principle stops those from happening?

>>10234326
So I literally have no idea about chemistry, but you have a function from R^3 to R^1 which you can calculate at certain points, right?

You can do approximations like that for example with a spline, which basically just means that you connect your data points linearly. For example MATLAB can do this with the interp3 function.

There are also other methods, such as fitting a cubic polynomial through neighbouring points, to get a smooth function.

I highly doubtful machine learning will be any help here.

>>10234337
It’s not a hydrogen atom if it has more than one proton. That’s how atoms are defined.

>>10234346
No both functions are in 3D since it is expanded in 3D basis functions.

>>10234353
That's why I asked you at the beginning, I can't speak chemistry, just math.
But I don't think this matters, just approximate each component individually.

>>10234351
do you know the difference between protons and neutrons anonymous
do you know what the word isotope means

>>10234353
>three-dimensional density
I'm unbelievably lost.

>>10234376
It’s the density at every point in 3D space.

>>10234380
That's a function from three dimensional space to the reals.

>>10234385
Could you elaborate on that?

>>10234380
So it is a function from R^3 to R?
Where you assign every 3D point one number?

I doubt that you are even certain of exactly what you want to do...

>>10234390
It’s a quantum mechanical wavefunction expanded in a 3D basis (atomic orbitals).

And correct, I’m not exactly sure what I want to do. That’s part of why I’m asking here for your thoughts.

>>10234415
how complex is the function to calculate in the first place
is there a reason you need to come up with a regression function instead of just calculating the actual value at a given point and reusing it for every other point within X distance. computers are pretty fast, they can handle that shit

>>10234422
The problem is for larger systems (than 20 electrons), calculating the exact electron density (and getting the exact wave function in the first place) is impossible due to the binomial scaling of the Full Configuration Interaction (FCI).

For small systems however it is possible. I want to see if I can find a good expression for the functional that reproduces (or is sufficiently close, say 95%) to the exact ones and see, if the approximate method, which is linear scaling and super super fast, is also good for larger systems where a FCI calculation is impossible.

>>10234415
>It’s a quantum mechanical wavefunction expanded in a 3D basis (atomic orbitals).
I have no clue what this means.

>That’s part of why I’m asking here for your thoughts.
Try formulating your problem mathematically, that will give you insight into the methods you have at your disposal.

I know a bit about interpolation, which is what you want to do, but you can only interpolate things if they are given mathematically.

New thread
>>10234461
>>10234461
>>10234461

>>10234454
So what you actually have is some formula that takes the the properties of your 20+ electrons as input and PRODUCES a wave function

You don't want to take an already-known wave function and approximate it to an easier to calculate form, you want to approximate the formula that goes from electron properties to wavefunction

Am I understanding this properly?

>>10234481
Correct, I can make a wave function with n electrons no problem. If I want an exact wavefunction (FCI), and hence the energy, the scaling is binomial and explodes around 20 electrons.

There exists a bunch of wave function based methods such as Coupled Cluster that are approximate, but quite acurate, but these scales as O(N^7) or maybe O(N^4) if you are cleaver.

An other approach to quantum chemistry is based on Density Functional Theory. Here, due to the Kohn-Sham theorem, we look at the density. It is proven that if we know a function for the density, we can get the exact energy. However, this "exact functional" is unknown and the best expressions are pretty complicated, ugly and often fit to experimental data.

I want to "make up" a formula for the density.

For a large number of small molecules at different geometries, I calculate the exact density on a grid. The input is just where the atoms are relative to each other.

>>10230905
Think of pointing a laser at one star in the sky, then flicking your wrist a little to point it at another star that's a similar distance from Earth. That same information got to one, then the other, at a rate faster than light. However, the information had to come from a third party, and no such communication can ever be two-way.

Last bamp