/sci/ - Science & Math

>>11553666
>>book recs?

~UNANSWERED~

Math
>>11541589
>>11541591
>>11543513
>>11545615
>>11549098

Physics
>>11547809 (Another anon and myself both seem to think there is not enough information given. I think the best you can do is find dV/V, but I could be wrong. Help this anon.)
>>11549774
>>11551032
>>11551832
>>11552272

Bio+Medicine
>>11551023

Stupid
>>11542479
>>11542483
>>11542657
>>11542664
>>11543405 (Did you have a question?)
>>11550225 :3
>>11551710
>>11551968
>>11552940

>>11547809
Maxwell relation gives [math]-(\frac{\partial S}{\partial P})_T=(\frac{\partial V}{\partial T})_P[/math], so sub that in to get:
[math]\alpha=\frac{1}{V}(\frac{\partial V}{\partial T})_P[/math]
Rearrange to give [math]\alpha \, \partial T=-\frac{1}{V}\partial V[/math], integrate both sides, then calculate V for 293K and 330K

Express the answer as some constant times the initial [math]V_0[/math], I don't think you'll actually be able to solve [math]V_0[/math]

How cold can the average human cell get before dying?

I'm aware that our whole body experiences hypothermia at like 95F, but i mean if you take a human cell out, say a skin cell, how cold could you chill it before warming it back up didn't revive it? I'm guessing there is probably a range here, but i'm just looking for a ballpark answer.

>>11553675
You just copy and pasted the furry's unanswered post, so now you've responded :3 to the guy complimenting the furshit and you included several posts that do not have a question or were answered.
How hard can this be?

I don't know where to begin.

>>11553666
nice satan trips
>>11541589
First, read this carefully: https://en.wikipedia.org/wiki/Frobenius_method
Multiplying by [math]\frac 1 x[/math] on the DE we get:
[eqn]3y'' + \frac 2 x y' + \frac 1 x y = 0,[/eqn]
which has a singularity at [math]x=0[/math]. Suppose there exists a power series solution [math]y(x)=\sum_{k=0}^\infty A_k x^{k+r}[/math] for some [math]r[/math]. Then [math]y'(x)=\sum _{{k=0}}^{\infty }(k+r)A_{k}x^{{k+r-1}}[/math] and [math]y''(x)=\sum _{{k=0}}^{\infty }(k+r-1)(k+r)A_{k}x^{{k+r-2}}[/math]. We replace in the DE to obtain:
[eqn]3 \sum_{k=0}^\infty (k+r)(k+r-1)A_k x^{k+r-2} + \frac 2 x \sum_{k=0}^\infty (k+r)A_kx^{k+r-1} + \frac 1 x \sum_{k=0}^\infty A_k x^{k+r} = 0,[/eqn]
[eqn]\implies ~ \sum_{k=0}^\infty (k+r)[3(k+r-1)+2]A_k x^{k+r-2} + \sum_{k=0}^\infty A_k x^{k+r-1} = 0,[/eqn]
[eqn]\implies ~ r(3r-1)A_0x^{r-2} + \sum_{k=1}^\infty (k+r)[3(k+r-1)+2]A_k x^{k+r-2} + \sum_{k=1}^\infty A_{k-1} x^{k+r-2} = 0,[/eqn]
[eqn]\implies ~ \underbrace{3r(r-\frac 1 3)A_0x^{r-2}}_{(\ast)} + \sum_{k=1}^\infty [(k+r)[3(k+r-1)+2]A_k+A_{k-1}]x^{k+r-2} = 0.[/eqn]
Note that [math](\ast)[/math] has roots at [math]r=0[/math] and [math]r = \frac 1 3[/math]. Since the difference between the roots is not an integer (see Wiki article), we get the coefficients of two linearly independent solutions by setting [math]r=0[/math] or [math]r = \frac 1 3[/math] in the recurrence relation:
[eqn](k+r)[3(k+r-1)+2]A_k+A_{k-1} = 0,[/eqn]
which you should be able to solve by yourself.

>>11554771
goddammit, the math looked fine in the preview fuck you hiroyuki

can someone explain how I'm supposed to use gauss-jordan elimination to solve this? I just keep getting 0 = 0 and I can't come to an answer

looking at it, they're all either equal to zero or equal to 1, 1 and 2 (or -1, -1 and -2) but I can't figure out how to work to it

>>11554793
Remember that a system either has no solutions, one solution, or infinitely many. You can't have 3.

When you do Gauss-Jordan you should end up with the matrix
1 1 -1 | 0
0 0 0 | 0
0 0 0 | 0
Because the second and third equations are just multiples of the first one.
So x2 and x3 are free variables, and you set x1 = x3-x2.

>>11554809
>When you do Gauss-Jordan you should end up with the matrix
>1 1 -1 | 0
>0 0 0 | 0
>0 0 0 | 0
>Because the second and third equations are just multiples of the first one.
>So x2 and x3 are free variables, and you set x1 = x3-x2.

Yeah I ended up with that but do I just leave it as that? I don't really get the concept of free variables so I'm unsure if 'x1 = x3 - x2' is the final answer or not.

>>11554816
Yes, that's the final answer, although your prof may want you to write it slightly differently. Sometimes classes write it as a vector; your notes probably have the correct way for you.

"Free" variables show up when you're left with more unknowns than equations after you eliminate.
When this happens, what it means is that some of the unknowns (the ones that aren't pivots) are basically superfluous; you can _freely_ choose them to be anything, with no restrictions, and the system is still solvable. Like here; you can select any number at all to be x2, and any number to be x3, and there's still a solution.
By comparison x1 is NOT free, because there's a restriction on it; it has to equal x3-x2.

>>11554771
>satan trips
You know Serre will deliver!

graduated in december, starting grad school in the fall for amo physics. should i brush up on general physics and math during the long wait, or maybe just look ahead to courses i will take and research papers in the field?
reposting because new thread

What do I need to know in order to make fat stacks of dolla dolla bills y'all

What does the See Saw mechanism say about the hypercharge of right handed neutrinos? I'm 87% sure it's zero, but I'm not sure

>>11555049
Yes it is, silly me [math] Q = T_3 + \frac{Y}{2} [/ math]

Both [math]Q[/math] and [math]T_3[/math] are zero for neutrinos, so [math] Y [/math] must be zero too.

The isotropy group stuff is fucking me. Any help?

I'm dumb:
List all the orders of elements
which are guaranteed by Cauchy’s theorem for the group [math]SL_2(\mathbb{Z}_7)[/math].

>>11555073
>SL2(a_7)
Sounds like that's just a small set of matrices, write a short script to list them. Then think about that theorem and how it works out for it.

>>11555096
Quickly gave it a shot myself (although I'm not sure if I understood SL2(a7) right)

det[{a_,b_,c_,d_}]:=a*d-b*c

Select[
Flatten[Table[{a,b,c,d},{a,0,6},{b,0,6},{c,0,6},{d,0,6}],3]
, det[#]==1&]

returns

> {1, 0, 0, 1}, {1, 0, 1, 1}, {1, 0, 2, 1}, {1, 0, 3, 1},
> {1, 0, 4, 1}, {1, 0, 5, 1}, {1, 0, 6, 1}, {1, 1, 0, 1}, {1, 1, 1, 2},
> {1, 1, 2, 3}, {1, 1, 3, 4}, {1, 1, 4, 5}, {1, 1, 5, 6}, {1, 2, 0, 1},
> {1, 2, 1, 3}, {1, 2, 2, 5}, {1, 3, 0, 1}, {1, 3, 1, 4}, {1, 4, 0, 1},
> {1, 4, 1, 5}, {1, 5, 0, 1}, {1, 5, 1, 6}, {1, 6, 0, 1}, {2, 1, 1, 1},
> {2, 1, 3, 2}, {2, 1, 5, 3}, {2, 3, 1, 2}, {2, 3, 3, 5}, {2, 5, 1, 3},
> {3, 1, 2, 1}, {3, 1, 5, 2}, {3, 2, 1, 1}, {3, 2, 4, 3}, {3, 4, 2, 3},
> {3, 5, 1, 2}, {4, 1, 3, 1}, {4, 3, 1, 1}, {4, 3, 5, 4}, {4, 5, 3, 4},
> {5, 1, 4, 1}, {5, 2, 2, 1}, {5, 3, 3, 2}, {5, 4, 1, 1}, {5, 4, 6, 5},
> {5, 6, 4, 5}, {6, 1, 5, 1}, {6, 5, 1, 1}

>>11553666
Let 6x=0 for all x in A, a ring. I'm having trouble showing that h(x) = 3x is a ring homomorphism.

h(x+y) = 3(x+y) = 3x + 3y = h(x) + h(y)

but h(xy) = 3(xy) which is not equal to (3x)(3y). I'm just not seeing how this is a ring homomorphism. pls help.

can anyone explain how to use row reduction to find the inverse of this matrix?
like how does row reduction even work? is it just trial and error?

>>11555196
Set up the matrix as follows.

[2 1; -1 4 | 1 0; 0 1]

Then use row reduction on the entire 2x4 matrix. You should get the identity matrix on the LHS side of the matrix (to the left of the |) and the matrix on the RHS (to the right of the | ) is your inverse.

I don't really know what you mean by "how does row reduction even work". It's just gaussian elimination i.e. an algorithm that you follow step-by-step.

>gee bill two threads?
>>11554687
Total reluctance in the circuit is [math] \mathfrak{R}=\mathfrak{R}_\text{core}+\mathfrak{R}_\text{gap}=L_c/(\mu A)+L_g/(\mu_0 A) [/math]. Then [math] B=\Phi/A=NI/\mathfrak{R}A=...=1.118\text{ tesla} [/math]. Let [math] u=B^2/(2\mu_0) [/math]. Energy stored is just u*volume*relative permeability. So for gap and core we got [math] E_g=Axu [/math] and [math] E_c=A\ell u\mu [/math] with ell being the corrected length of the core.
>force
>Nm
[math] F=Au=...=1792\ \text{N} [/math] with less rounding.
>ii
I'm getting a different number for a) but I think the idea is to find the impedance of the wire at 60 Hz.
>>11555196
>write down a 2 by 4 augmented matrix, with the LHS being the matrix you want to invert and the RHS being identity
>take row 2 and add to row 1
>add row 1 to row 2
>multiply row two by 1/9
>you should now have identity on the LHS and
you get [math] \begin{pmatrix} 4/9 & -1/9 \\ 1/9 & 2/9 \end{pmatrix} [/math] as the inverse on the RHS
>is it just trial and error
not really

>>11555196
>like how does row reduction even work? is it just trial and error?
There's actually just an algorithm for it if you're finding it too complicated.
So, set it up as the above anon stated, with the identity on the right.
Then your first step, using the algorithm, would be to get a one in the top left corner, so you'd divide the top row by 1/2 and we'd have
[1 1/2; -1 4 | 1/2 0; 1 0].
Then add the second row to the first to get a zero below the first leading one yielding:
[1 1/2; 0 9/2 | 1/2 0; 1/2 1].
Then just continue until the LHS is the identity. Again just look up the algorithm, it's not hard. And there are a million ways to check your answers.

>>11555214
>Set up the matrix as follows.
>
>[2 1; -1 4 | 1 0; 0 1]
Yes I did this
>>11555214
>Then use row reduction on the entire 2x4 matrix
I don't get how I'm supposed to figure out which scalars to use on each row in each step and which I should add/subtract.
I know what I'm supposed to end up with but as far as I can tell the steps are just a process of trial and error.

I've tried a of different things but heres
the latest I did

r2 = r1/2 + r2

[2 1; 0 9/2 | 1 0; 1/2 1]

r1 = -2r2/9 + r1

[2 0; 0 9/2 | 8/9 -2/9; 1/2 1]

r1 = r1/2

[1 0; 0 9/2 | 4/9 -1/9; 1/2 1]

r2 = 2r2/9

[1 0; 0 1 | 4/9 -1/9; 1/9 2/9]

This was my fifth try and obviously I got the answer this time around but I went into each attemp with the same mindset (the only thing different was that I opted to not use the same operations as previous attempts) and unless my addition/subtraction and multiplaction were off in the previous attempt I feel like it was a trial and error thing but whatever. I'll keep trying since I have like 35 more questions to do.

>>11555062
Express [math]D_n[/math] in terms of its generators, i.e. rotations and inversions. Note that we can send a vertex [math]x[/math] to itself by rotating to [math]-x[/math] then invert back; the ability to do this depends on what [math]n[/math] is.

>>11555183
[math] h(xy)=h(x)h(y)=3x3y=9xy=(6+3)xy=6xy+3xy=3xy [/math]

>>11553666
Are Physics Bachelors really unemployable? If I got a Physics Bachelor and didn't go for a masters would I be fucked? Is this true even if you go to a school that's ranked 40 nationally?

>>11555453
you might be employed but probably not in something related to physics

>>11555453
>unemployable
No! In fact fast food/cafe chains would LOVE to have physics grads as part of their team!

I really love science & math.

>>11555487
As long as it can help me pay for grad school, I don't really care if its related to physics
>>11555544
Don't scare me like this bro

>>11555453
>>11555636
You can always jump into finance or ML later. If you ace Physics, there's no reason you can't.

Can someone provide me a counter example for this?

Let f : X -> Y, g : Y -> X. If g(f(x)) is bijective, show that f must be bijective.

>>11555772
(samefag)
How's this?:

X = 0
Y = 0
Z = 0

f(x) = 0, g(y) = 0.

so g(f(x)) is bijective, but f is not.

>>11555792
wait i meant X = all reals

>>11555800
Not sure if I completely understand the question. Is it asking about bijectivity of f or f(g(x))?
Because if it's the later, I think f(g(x)) = f(0) = 0, so it's still bijective?

This one is probably a stupid one, and I'm ready to get roasted. I'm a studying theologian soon to become a priest. I had physics and some hard math at high school, but I wasn't really that good. It would be nice to start again with maths as a hobby, even though my brain is pretty number-dumb (if that's even a thing). Either way, is it worth it? Or should I just stay ignorant?

If any of you are american, have your universities initiated a universal pass/fail?
I'm trying to figure out if I should take a class as pass/fail as my university has opt-in. Will grad schools think I'm a fucking bitch if I pass/fail? Or can I push some solidarity angle in interviews?

>>11555807
g o f is bijective, show that f isn't necassarily bijective, so just show f isn't bijective.


this is what i have now:
X = {0, 1}, Y=Z={0}.
f(x)=x, g(y)=0.

is g o f a bijection and f not?

>>11555841
wait, this is wrong, x isn't well defined :(

>>11555841
the X and the Z should be swapped here
>t. samefag

What's the best book on learning relativity?

>>11555835
my university got rid of the deadline for pass/fail this semester so you can switch to it even after finals. i would say if you think the course might be heavily related to your grad school specialization then it wouldnt be great to do pass/fail, but if you are stellar apart from this one semester of all pass/fail i dont think they will care much, especially given the pandemic situation

>>11556197

No such book. Take a university course on GR. I did and I put in ~20 hours a week for that one course alone. It's tough, and you're going to need an instructor to guide you and answer questions.

That being said, Spacetime and Geometry by Carroll is the gold standard for GR. It is rigorous, so learn the math and other physics foundations before diving in. It's also available online for free:

https://arxiv.org/pdf/gr-qc/9712019.pdf

https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html

I just finished basic highschool algebra, I moved on to Spivak Calculus because that is the next topic, but when I got to first set of problems everything is "Prove..."
I thought I was going to get exercises, how do I learn about proofs? I understand the math but I can't prove anything yet

hello can somebody who knows statistics share his thoughts on this?
https://youtu.be/LIkz4Kcb6Cs?t=78

I'm currently writing a (non-/sci/) paper, but this is probably the best place to ask.
When referring to the work of a tranny done before they changed their name, how should I refer to them without everyone getting really angry at me?

Is a basic grasp of chemistry, say high school to beginning college level, reasonably achievable for brainlet autodidacts?

Chemistry's relevant to what I want to major in (not in college, never been to college, just thinking of getting a head start with the extra time) but it seems complicated/liable to bite me in the ass. Not sure how to proceed. If it's doable, what's most essential to learn at a beginner level so I can filter the massive amount of information?

How do I set the boundary?
My first guess was, for the x coordinate
y goes from -2 to 2 and x goes from -1 to [math](y^2-4)/4[/math] multiply that integral by 2 and sum 2* integral where y goes from -2 to 2 and x goes from 0 to [math](y^2-4)/-2[/math]

But that doesn't seem to work

>>11557365
>so I can filter the massive amount of information?
with complex topics, it's best to pick a real world example that's close to your heart, which you can tie your (boring) fundamentals lessons. A muse, so to speak. An inspiration.

Perhaps a loved one's life was saved by a life-saving medicine - learn how it's synthesized. Perhaps you have background as an artist - learn how resin, epoxy, glues, paints, and ceramics work, or how photo developing works. If you're more of a mechanical type, learn what all goes in paint strippers, lubricants, vulcanized rubber, etc. Learn some metallurgy.

so, a function may be defined and continuous everywhere (e.g., t^2) but its laplace transform (2/s^3) will have discontinuities.
These discontinuities are called "poles" and are indicative of possibly unstable solutions if used to solve a differential equation.

Am I understanding that right?

>>11550181
are you sure? I don't want to mess it up. it's the notes the teacher made, and he continued to use 4 throughout the problem and even in other problems.

>>11555815
If you have the time for it, almost everything is worth it.

>>11557114
It's just like solving other problems. Just show the thing it's asking you to show like you'd show anything else.

>>11557221
When you set out looking for things you're likely to find it and it'll look important if you only point out the places where you did.

The variance in the percent daily change is going to go down as the absolute number goes up if your errors stay the same absolute magnitude. If there's a sudden change in the variance then it means something is probably up but it could be a change in how the data is generated or a change in how the phenomenon is measured. The guy says that that date was when there was a significant change in how the pandemic was being handled and that could just as easily have come from instating better reporting requirements as from making data up. I don't know shit about New York though.

P.S. I just went looking for reasons he might be wrong and I obviously found some.

>>11554793
[math] \displaystyle

\left [
\left .
\begin{matrix}
1 & 3 & 1 \\
1 & 1 & -1 \\
3 & 11 & 5
\end{matrix}
\right |
\begin{matrix}
1 \\
2 \\
3
\end{matrix}
\right ]
\begin{matrix}
\cdot 7 \\
\cdot 8 \\
\cdot 9
\end{matrix}

[/math]

What's the role of male neck strength in attracting females from a darwinian point of view?

>>11555046
I can't tell if the platform is a guillotine or a teleportation device

>>11558042
Forgot photo

>>11558059
Trying to bait me into posting it, eh?

>>11558110
what do you mean?
I didn't know it was a comic,I thought it was just a stand-alone image

>>11558129
I'll post it if you tell me what I need to learn for a mountain of cash chedda chedda

>>11553666
>>11553674
>>11553675
Remiliaanon is actually facing a permanent ban at this point, and so he disabled the mega.nz links in the copypasta. In the post following this one, I'll give the new pasta.

>>11557510
I would break up the region into two parts: the right hand side bounded by x=0 and y^2=4x+4, and the LHS bounded by x=0 and y^2=-2x+4. Now you solve for the mass and center of mass for each region, and you can combine. In general, center of mass (or area) is the ratio of first moment of mass (or area) to total mass. So on the right we get a first moment of area: [eqn] N_R=\int x\ \text{d}A=\int_{-2}^2\int_0^{(4-y^2)/4}x\text{ d}x\text{ d}y=...=64/15 [/eqn] Now compute the mass of the same region: [eqn] D_R=\int\text{d}A=\int_{-2}^2\int_0^{(4-y^2)/4}\text{d}x\text{ d}y=...=16/3 [/eqn] So you have [math] \bar{x}_R=N_R/D_R=12/15 [/math]. Now you may compute [math] N_L=-16/15,\ D_L=8/3,\ \bar{x}_L=-6/15 [/math]. Finally, [eqn] \bar{x}=\frac{\sum\bar{x}_im_i}{\sum m_i}=\frac{D_L\bar{x}_L+D_R\bar{x}_R}{R_R+D_L}=2/5 [/eqn]
>>11557615
Yep. Behavior of a system blows up around a pole.

>>11558287
>R_R
D_R, ofc

~NEW PASTA~

>what is /sqt/ for
Questions relating to math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/diy/ohm , >>>/adv/ , etc.
>pdfs?
libgen.is (Warn me if the link breaks.)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://anonfile.com/Nfxd6do9o0/good_charts_7z
Shitty charts: https://anonfile.com/ney26do2o1/shitty_charts_7z (Post any that I've missed.)
Verbitsky: https://anonfile.com/Hcx06co1o0/verbitsky_7z
Graphing: https://www.desmos.com/
Answer engine:
https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>>11553666
So, Anons, can you please recommend me some book or article about the plasma physics history. I mean, there are a lot of books with just short overview of history, and I haven't seen one that is actually informative

>>11558287
>R_R
D_R, of course

~NEW PASTA~

>what is /sqt/ for
Questions relating to math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/diy/ohm , >>>/adv/ , etc.
>pdfs?
libgen.is (Warn me if the link breaks.)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/1Q1LIMk
Shitty charts: https://imgur.com/a/kAiPAJx (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Answer engine:
https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>>11558287
>Remiliaanon is actually facing a permanent ban at this point
Why is exactly one avatarfag getting permabanned but the rest are allowed to freely shit all over the thread/board?

Can someone point me toward a good resource for solving this?

[eqn]
\lim_{n \to \infty} \tan(\frac{2n \cdot \pi}{1 + 8n})
[/eqn]

Wolfram says it's one, but I don't know how to get there myself.

>>11558384
Just use that [math] \lim_{n\rightarrow \infty} \frac{2n \pi}{1+8n}=\frac{\pi}{4} [/math]

>>11558395
ahhhh ok, I had forgotten tan(pi/4) evaluates to one, thanks a bunch

What's the best book on Classical Mechanics from a mathematical point of view?

Please don't say Taylor.

>>11557615
A physical system is unstable if any of the poles (of the Laplace transform of its transfer function) are in the right half plane (i.e. have a positive real part). This basically corresponds to positive feedback, i.e. the output keeps increasing.

The s-domain function F(s)=a/(s-ω) is the Laplace transform of the time-domain function f(t)=a.e^ωt
f(t) = a.e^ωt
= a.e^(Re(ω)+j.Im(ω))t
= a.e^Re(ω)t.e^j.Im(ω)t
= a.e^Re(ω)t.(cos(Im(ω)t)+j.sin(Im(ω)t))
IOW, this is a complex sinusoid multiplied by an exponential. If Re(ω)<0, it decays exponentially; if Re(ω)>0, it grows exponentially.

>>11557782
if i understand it correctly, basically he had a series of 19 data points which looked suspicious to him, and focused on them. he doesn't explain it like this in the video, but he then noticed that 8 of those data points went up-down-up-down and so on, and he says the probability of that pattern not being a random occurence is 2 out of 2^8 therefore the data could be faked.

is the fault on the reasoning that he made the math only for those 8 data points?

>>11558543
>he says the probability of that pattern not being a random occurence is 2 out of 2^8 therefore the data could be faked.
This is nonsense reasoning. This would only be the real probability of the movement up or down of the data was a completely random 50/50 coinflip each day. You'd have to assume that the data you're charting is literally just random noise.

>>11558346
>Shitty charts: https://imgur.com/a/kAiPAJx (Post any that I've missed.)
Why is Kodaira's Complex Analysis and Sternberg's Advanced Calculus considered shitty?

>>11553666
how the everliving fuck do you end up with the hbar omega there? it's driving me fucking insane

anyone got any ideas on how to approach this?

>>11558747
not looking for an answer fyi, just something that i should look into. I've considered all the tools in my toolbox and I am not seeing anything.

>>11558735
Just distribute the hbar omega into the three terms on the left side, then add the negative middle term to both sides.

My uni makes me take 3 social science classes to give me a certificate to teach math. Now I gotta do a 5000 word essay on school bullying to pass one of them. I haven't written 5000 words with no math/code since 6 years ago. What the fuck do I do? I'm an autist, pls help, guidelines, articles, anything.

>>11558761
not science or math
>>>/lit/ >>>/adv/

>>11558493
Arnol'd or Sternberg-Guillemin
>>11558735
Bring the [math]-\hbar\omega a^\dagger[/math] term in Eq. (4.3.13) to the other side. >>11558760 is wrong as it that misses the [math]\frac{1}{2}[/math] factor.
>>11558747
Recall that harmonic maps [math]u[/math] minimizes the energy functional [math]-\frac{1}{2}\int_D |\nabla u|^2[/math] and satisfies the min/max principle. The condition here is "shrunk" to make [math]u[/math] satisfy min/max only in tangent circles [math]C[/math] and hence minimizes the energy functional [math]-\frac{1}{2}\int_{C(z)}|\nabla u|^2[/math] for each [math]z \in \operatorname{int}D[/math]. However, note that as [math]z[/math] is in the interior so you can find [math]z \neq z' \in \operatorname{int}D[/math] such that [math]C(z) \cap C(z') \neq \emptyset[/math], allowing you to analytically extend [math]u[/math] to [math]C(z)\cup C(z')[/math]. Since [math]\bigcup_{z\in D}C(z)[/math] is an open cover of [math]D[/math] and since [math]D[/math] is compact, you're done.

>>11558810
aaaaaaah holy shit it was that easy, thanks buddy, you saved me hours

>>11558654
Don't confuse "shitty chart" with "chart comprised entirely of shitty books".

>>11558810
>Arnol'd or Sternberg-Guillemin
Bur isn't Arnold a little too advanced for someone who's just getting into CM? Is Sternberg-Guillemin a gentler intro?

why is the distinction drawn almost always across medium and seldom across theme, setting, idea, or characters?

why /tv/, /lit/ and /co/ instead of /superheros/, /indie/ and /horror/ for example? this happens not only with boards and places where people discuss and enjoy things in general, but also with specialties (people tend to specialize in a field, be it books film music films whatever),

>>11558895
For boards, it's because genres are very ill-defined, blurry things, which makes it virtually impossible to decide what belongs where. You can argue endlessly about what does and doesn't count as "horror"; you can't argue that a movie isn't a movie. If I want to talk about a movie, I immediately know exactly where to go, and I know that everybody else there watches movies too.
I think specialists tend to specialize in _both_ of the ways you're talking about. You won't find many professors at universities who specialize in "books"; they have a very specific type of book they specialize in.

>>11558867
You'll be fine with a strong mathematical background.

sorry I'm stupid and I don't go to /sci/ often, can someone answer this >>11558933 please?
>>11558867
Arnol'd is really great, go for it.

can someone point me to a good source to learn highschool electromagnetism?
preferably one that gets to the point without any unnecessary bullshit, I learn fast

>>11558980
get Serway-Jewett or Sears-Semansky off libgen and only read the summaries at the end of each chapter, then try to do the exercises.

>>11558354
Remifag isn't banned for avatar shit.
>>11557313
Use the name they used at the time and gender neutral pronouns.
>>11558654
I realize I got good and shit mixed up. Feel free to fix.
>>11558493
Goldstein
>>11558980
>highschool
http://hyperphysics.phy-astr.gsu.edu/hbase/index.html
>>11558747
There's a harmonic function which agrees with your function on the border. Since harmonic functions satisfy medium value, the difference of your original function and the harmonic one does too. Mess around with Weierstrass's theorems on extrema

>>11555263
Notice that if you had a 1 directly on the top left entry, you could make the rest of the first column be 0's. Then you could repeat this idea on the second entry of the second row, etc. So you'd like this 1 to appear first of all.

>>11559002
you're talking about these, right?
https://www.amazon.com/Physics-Scientists-Engineers-Raymond-Serway/dp/1133947271
https://www.amazon.com/University-Physics-Modern-Chs-1-20/dp/0133978044
no preference over any?
>>11559027
>http://hyperphysics.phy-astr.gsu.edu/hbase/index.html
sadly no exercises which will make me forget crucial stuff quickly

>>11559041
>sadly no exercises which will make me forget crucial stuff quickly
I see.
I'm not the anon who recc'd it, but university physics has lots and lots of examples for basic electrostatics and covers Maxwell's equations.

can someone help me understand how a brainlet such as myself would reasonably derive [math]\frac{1 + \sqrt{5}}{2}[/math] from pic related?

I've since read a lot of proofs and such but it still seems like a major asspull that I wouldn't come up with by just trying to find the limit of a recursive function like this.

in other words eli5 pls

>>11559084
forgot pic

>>11558789
>what is /sqt/ for
>Questions relating to math and science, plus appropriate advice requests.

>>11559084
Suppose the sequence converges to [math]a[/math]. By recursivity, we have [math]a = 1 + \frac{1}{a} \Leftrightarrow a^2 = a + 1 \Leftrightarrow a^2 - a - 1 = 0[/math]. This gives us [math] a = \frac{1 \pm \sqrt{5}}{2}[/math], and the necessary positivity of [math]a[/math] eliminates the other option.

>>11559093
i thought it was just a_n = a_n-1 + a_n-2
use this to then derive the ratio by solving a simultaneous equation(?)

I already gave up on studying on my own, I simply can't defeat procrastination or internet addiction, so I decided to take some meds, what do you guys recommend me? Ritalin is pretty famous, but can it fuck my memory or some shit?

>>11559124
but anon, 0.99.. is not equal to 1

>>11559147
Barbiturics are relatively efficient. Learned this from a vet.

>>11559158
>namefag
>and a schizo

>>11559147
when i was at university i would do all my homework stoned. you can really zone in and focus on a thing when high but your working memory goes to fuck. on the other hand one is definitely more curious and creative with your conceptual thinking. i managed to pass my courses just fine.

>>11559167
it was a joke anon, but seriously, it is a bit funky to imply strict equality in this case.

>>11559158
Prove it.

>>11559167
>>11559177
I actually have done the BEST proof that 0.99.. = 1 on /sci/ this week

>>11559177
0.999... has the number 0, the number 9 and 4 dots

1 has the number 1

Therefore they're are not the same number.

>>11559185
I liked the topology proof more, even though it assumed what it was to prove. You were supposed to prove they are not equal. Don't waste my time ever again.

>>11559189
This is a valid proof. Thanks.

>>11559145
the a_n terms are the elements of the series produced by the function f_n, so it's basically the same thing. I know there are other ways to solve it but I'd like to do the method suggested by the text.

>>11559124
this example is like everything else I've read, I still struggle to intuitively understand the limit approach. Here is my work so far:

Given [math] \{a_n\} = \frac{f_{n+1}}{f_n} [/math] and [math]f_{n+1} = f_n + f_{n-1}[/math], let [math] \phi = \lim_{n \to \infty} \{a_n\}[/math].

[eqn]
= \lim_{n \to \infty} \frac{f_{n+1}}{f_n}\\
= \lim_{n \to \infty} \frac{f_{n} + f_{n-1}}{f_n} \\
= \lim_{n \to \infty} 1+ \frac{f_{n-1}}{f_n} \\
[/eqn]

I feel like I already fucked up. I don't see how to continue the division. apologies in advance for being a turbo brainlet.

>>11559251
Note that you have lim a_n = 1 + lim a_{n-1} there, just like in >>11559124

>>11559262
[math]a_{n-1}[/math] is [math]\frac{f_n}{f_{n-1}}[/math], right? what I have is the recpricol of [math]a_{n-1}[/math], so [math] a_n = 1 + \lim_{n \to \infty} a_{n-1}^{-1}[/math] unless I'm being stupid (likely)

>>11559262
more like a_n = 1 + 1/lim a_(n-1)

>>11559278
>>11559279
Ah yes a typo. But yeah, it leads to a = 1 + 1/a as in the anime poster's post.

>>11559196
this is the best you will get from me.

>>11559292
sure. but >>11559278 is a bit lost with figuring that these stuff are not that complicated, so it's better to clarify. Also, >>11559278, in general it is better to use the limit only "at the end". Like here, you would have a_n = 1 + 1/a_(n-1), leading to a_n*a_(n-1) = a_(n-1) + 1. Now, definitely, the sequences (a_n) and (a_(n-1)) have the same limit (if they converge) so the limit a satisfies a^2 - a - 1 = 0 and u done brah.

>>11559292
ok, thanks, taking note of the recipricol was just what i needed to be able to see the continuous division. but im unsure how to make the leap from a repeating fraction to [math]a^2 -a -1[/math].

as in, do I just call the repeating a variable, say u, of udetermined value since n goes to infinity.. and..

So where I'm at now is essentially fully understanding
[eqn]
a_n = 1+ \frac{1}{a_{n-1}} \\
= 1 + \frac{1}{1 + \frac{1}{a_{n-2}}}
[/eqn]

etc etc but i don't get how to go from here to arriving at a limit

>>11559307
i know it's not that complicated but im not getting it completely so im forced to go into detail and over complicate until i get my long awaited a-hah moment then it's all super simple and obvious brainlet material forever after

>>11559321
bruh. youre missing the point. a_n and a_n+1 are members of the same set, which has the same limit, so you just say that at infinity a_n = a_n+1, because the set is convergent. therefore you sub both of them in for general limit a, giving you the polynomial a^2 -a - 1=0

>>11559327
I apologize if I sounded pedantic or condescending.
>>11559321
I don't see why you want to go to a repeating fraction.

Could someone clear up the concept of rate of change for me? Instantaneous one that is. I'm doing calculus and I don't think I understand the concept that clearly, at least when it doesn't come to velocity, which is kind of what we're used to.

What would a rate of change of say area dependent on say radius at a certain radius mean?

>>11559349
it is very trivial. For example, 1$ is 100 yen. This is the rate of change: if you change x dollar, you would get 100x yen. But it becomes very complicated when you start paying taxes, unforntunately.

>>11559338
>>11559345
so as n approaches infinity, [math] a = \lim {a_n} = \lim {a_{n-1}} [/math] obv. this i get with no hesitation, so I guess from this I go, noting also that [math] a_n = 1 + \frac{1}{a_{n-1}}[/math] (as stated in the original problem):
[eqn]
a = \lim a_{n-1} = \lim a_n = \lim (1 + \frac{1}{a_{n-1}})\\
[/eqn]
But [math] a = \lim a_{n-1} [/math], so [math] \lim a_n = 1+ \frac{1}{a}[/math], so
[math]
a = 1 + \frac{1}{a}\\
a^2 - a - 1 = 0
[/math]

i think i get it now, you were rght i was just glossing over a = lim a_n = lim a_{n-1}, i think. i haven't done the quadratic yet but that will be easy, i see im on the right trcak unless something above was conceptually wrong

>>11559371
>so as n approaches infinity, a=liman=liman−1a=liman=liman−1 obv. this i get with no hesitation, so I guess from this I go, noting also that an=1+1an−1an=1+1an−1 (as stated in the original problem):
yeah it does in this case, only because it is convergent mind you.

I'm doing CS, in a shit uni so I admit I'll have to do a lot of studying by myself to be a good professional, but I still have this question: even though I want to learn calculus, how do I know I'm not gonna forget it eventually if I don't use it in my job? If I'm not a neet I'll have more important things to do in my time at home, including working on job related abilities, than managing upkeep of a specific knowledge set for the sake of it.

>>11559388
calculus is like taking apart a car. no matter how much you do it you or how long there will always be that finnikey bit you have to go to the user manual for. once you learn the basic gestalt though in its breadth it will not easily leave you.

>>11559388
>how do I know I'm not gonna forget it eventually if I don't use it in my job?
You will absolutely forget it eventually, if you never use it. Even professional mathematicians forget some undergrad-level stuff if they never use it in their research or teach it.
However anything you forget you'll be able to pick back up again very quickly. Relearning stuff you've forgotten the details of is many times faster than learning stuff from scratch.

>>11559385
what the rest of what i said correct? thanks a bunch for dealing with me

now that i understand at long last it's trivial as shit

>>11559395
oh eh, i think the other guy really got you there. i just jumped in with>>11559338
>>11559385

but yeah its a tad confusing first time looking. dont assume your instructor would have you calculate an infinite fraction lol.

>>11558810
>>>11558760 (You) is wrong as it that misses the 1/2 factor.
How so? That factor stays on the left, where it belongs. You and I both said the same thing.

>>11559388
ok i have some semantic questions now, here is my proof:
[eqn]
a = \lim_{n \to \infty} a_n = \lim_{n \to \infty} a_{n -1} \\
= \lim_{n \to \infty} (1 + \frac{1}{a_{n-1}}) \\
= \lim_{n \to \infty} (1 + \frac{1}{a})
[/eqn]

How do i close this out so I can solve the quadratic equation for a? I need to properly drop the limit so I can do normal algebra but im honestly not sure what's correct

>>11559415
Then the last line just equals 1+1/a. Solve the quadratic.

>>11559422
thanks!

>>11559415
take the lim off the bottom one.

>>11559422
>>11559444
are they equal or is the last line wrong?

>>11559453
the second line = bottom line without limits.

think about it. the lim of a is just a

lmao so you're putting jean-pierre serre as the pic rel of a thread where you help each other doing limits of sequences?

>>11559463
its unlikely OP is even here.

Let [math]\operatorname{FiveBrane}(n) \rightarrow \operatorname{String}(n) \rightarrow \operatorname{Spin}(n) \rightarrow SO(n) \rightarrow O(n) [/math] be the Whitehead tower of [math]O(n)[/math], I wish to find the cohomology ring of [math]\operatorname{FiveBrane}(n)[/math]. This can be done by noting that [math]\pi_k(\operatorname{FiveBrane}(n)) = \begin{cases}0 &; k \leq 7 \\ \pi_k(O(n)) &; \text{otherwise}\end{cases}[/math] whence [math]\operatorname{FiveBrane}(n)[/math] is the 7-connected cover of [math]O(n)[/math], hence the fibration sequence [math]F \rightarrow \operatorname{FiveBrane}(n)\rightarrow O(n)[/math] has fibre [math]\pi_k (F) \cong \pi_k(O(n))[/math] for all [math]k \leq 7[/math], and is a CW complex with known cohomogloy. Using this fibration sequence, I construct the Leray-Serre spectral sequence [math]E^{p,q}_r[/math] whose second page reads [math]E^{p,q}_2 \cong H^p(O(n),H^p(F,\mathbb{Z}))[/math].
How do I show that the sequence [math]\{E^{p,q}_r\}_r[/math] converges/collapses and [math]\lim\limits_{r\rightarrow\infty}\bigoplus_{p}E^{n,p}_r \cong H^n(\operatorname{FiveBrane}(n),\mathbb{Z})[/math]?
>>11559463
There, a question on limits of sequences. You like?

>>11559460
>>11559460
no i understand, but saying lim(1 + 1/a) = 1 + 1/a technically isn't wrong, right?

i have removed it from my actual proof of course

anyway, what the hell is going on in this pic? in particular the middle equality with the two fractions being multiplied by a limit? must be a mistake right?

>>11559504
nvm i see what's going on, 4chin won't let me delete tho

What's a good anatomy program? Also why isn't sci-hub in the op?

>>11559521
by program I mean piece of software

What are the alternatives to the paradigm for units of min/sec/hour?

Fuck jannies, gotta ask this:

Are any of you late bloomers when it comes to attending college? I've been getting an online bachelors completely out of pocket starting when I was in the mutt army, I'm graduating at 25 yo, and I'm hopefully heading to grad school next year on gibillbux. Gotta say, I'm feeling a little existential angst about it, but I have a passion to learn my desired field, and I'd rather do that and attend a brick-and-mortal school for fucking once than become a career contractor who updates excel spreadsheets all day

>>11559657
yeah 25 is not old for university

I'm doing my homework and it says to show that some equation is true. I substituted some numbers and the equation is definitely true. Is that what they want me to do?

>>11553666
Freshman biochem major registering for next year’s classes. I have the option of taking bio or diff eq next fall. I have two questions that would be great to have answers to:

>1: how dependent is diff eq on the material covered in calc 2?

>2: is there any advantage to taking bio alongside orgo?

Thanks

>>11559682
you’re going to fail diff eq, you type and think like a retarded nigger.
>is there any advantage to taking bio with orgo
you should kys you dumb fucking monkey

>>11559657
25-26 is not particularly old to be starting grad school at all. You're only a few years older than the folks who blitzed straight through undergrad and then immediately went to grad school the following semester.
Many people graduate undergrad, work for a few years, and then come back to grad school. You may have done it backwards, but that won't make you any older.

>>11559695
damn anon, what are you so worked up about? Just doing the best I can with the one hand that doesn’t have neuropathy right now. lmao happy easter goatfucker

>>11559682
I can't answer the second one (math major) but differential equations rely fairly heavily on your ability to do integrals quickly; pretty much every solution to a DE involves integrating at some point along the way to the final answer.

>>11555073
Recall that if [math]\mathbb F[/math] is a field with [math]q[/math] elements, then [math]GL(2, \mathbb F)[/math] has [math](q^2-1)(q^2-q)[/math] elements, by an easy combinatorial argument. The group homomorphism [math]M \mapsto \det(M) \in \mathbb F^\ast[/math] has [math]SL(2, \mathbb F)[/math] as it's kernel, and by the first isomorphism theorem we have [math]GL(2, \mathbb F) / SL(2, \mathbb F) \cong \mathbb F^\ast[/math]. If [math]\mathbb F = \mathbb F_7[/math], then [math]|GL(2, \mathbb F)| / |SL(2, \mathbb F)| = |\mathbb F^\ast| = 7-1 = 6[/math] (since the groups involved are finite). Then [math]SL(2, \mathbb F_7)[/math] has order [math](7^2-1)(7^2-7)/6=48\cdot 7=2^4 \cdot 3 \cdot 7[/math]. Hence by Cauchy's theorem, there exist elements of orders 2, 3 and 7 in [math]SL(2, \mathbb F_7)[/math].

I'm in week one of linear algebra. I'm trying to understand a basic question:

>There are two neurons, and each has an output (y1 and y2). Each neuron has two inputs (x1 and x2 for the first neuron, and x3 and x4 for the second neuron). Each input has its own weight, meaning there are four weights total (w11, w12, w21, w22).

>Represent this system using matrices.

Obviously the output vector Y needs to be 2x1. But how do I represent X and W? The only thing I can think of is making X a 2x4 matrix, of [x1 x2 0 0; x3 x4 0 0], and W is a 4x1 vector of [w11; w12; w21; w22].

HELP

>>11559657
You're fine. I'm graduating this year, at 24 y/o in pure maths — I did two years of a BSc in natural sciences before that. If you are sure of your passion then follow it by all means; if you become competent at it then most certainly you'll end up with marketable skills of some sort (e.g. in case you don't end up in academia after grad school).

>>11559521
>why isn't sci-hub in the op
because it's illegal, see e.g. >>11558287:
>Remiliaanon is actually facing a permanent ban at this point, and so he disabled the mega.nz links in the copypasta.

>>11559923
You are on the right track, but shouldn't X be [x1 x2 0 0; 0 0 x3 x4]?
This way w11 and w12 will only multiply with x1 x2, and w21 w22 will only multiply with x3 x4.

>>11559996
Thank you, yes that was a typo, what you wrote is correct. Is that really the answer? It seems fucked

>>11559998
>It seems fucked
Why is that? Inserting 0 and 1 to make your matrices work how you like is okay.

>>11560004
Oh OK. Thanks that puts me at ease since that's normal

>>11559923
W a 4x2 (or 2x4??) matrix X a "4x1" vector.
W= (w11, w12, 0,0;0,0, w21.w22)

The question seems very confusing to be honest and I don't get what the point of it would be...

>>11559975
>facing a permanent ban
There is no such thing. Just reset your router to get a different IP.
Yes, ban me mods, but all I "circumvented" was me getting some absurd Ukrainian IP...

>>11558927
kinda makes sense thanks

>>11559665
no you have to do it for ALL numbers.

>>11559665
>Is that what they want me to do?
No.
Take the equation x^2=x.

Is this equation always true?
If we plug in x=1, we get 1=1, which is certainly true.
But for x=2 we get 4=2, which is definitely false.

So it is NOT enough to show that the equation is true for one number, you have to show that the equality holds for ALL numbers.

>>11559757
Solving DE's by hand is an absolute meme.

Is it allright to have "verify seminal paper results" as a bachelor thesis or a master thesis subject?

>>11559975
Isn't ligben too?

If the variable "x" is indeterminate, doesn't that make it equal to 0/0?

Does anyone know the mathematical argument as to why you are allowed to reduce a 4x4 matrix containing 1x zero row and 1x zero column into a 2x2 matrix by deleting the zero row and zero column?

>>11560432
Sorry I meant 2x zero rows and 2x zero columns

>>11558042
muscle

>>11560432
because they're dependent

>>11560432
There's no information in those rown and columns, why would you need to keep them?
It would be like keeping blocks that always equal zero in an equation.

>>11560451
Thanks
Do you know if there is a specific rule that says dependent zero rows and zero columns can be removed if it doesn’t affect symmetry?

As in deleting both the zero rows and zero columns we go from 4x4 -> 2x2 so we maintain an equal amount of rows to an equal amount of columns before and after

I assume this is an important condition to allow the removal of the zero rows/columns

>>11560452
Yes but I was wondering if anyone knew about a specific rule or statement that says it is allowed to remove them if certain conditions are met

If $A$ is a non (Lebesgue) measurable sub-set of the real line and $B\supseteq A$ is a measurable superset of $A$, does there exist a measurable $C$ so that $C\supseteq A$ and $B - B\cap C$ has non-zero measure?

If not, is there a theory of a "measurable closure" (up to zero sets) of non-measurable sets?

Looks like I fucked the math boxes, here is the question again:

>>11560509

If A is a non (Lebesgue) measurable sub-set of the real line and [math]B\supseteq A[\math] is a measurable superset of A, does there exist a measurable C so that [math]C\supseteq A[\math] and [math]B - B\cap C[\math] has non-zero measure?

If not, is there a theory of a "measurable closure" (up to zero sets) of non-measurable sets?

>>11560513
>>11560509
well that didn't work

>>11560517
use the latex viewer/tester at top left of reply box popup

>>11558042
keeps your neck from breaking as easily?

>>11558042
oh and there is also the traps which make for a bigger neck, I think that's where you have more androgen receptors so with higher androgen you get a bigger neck

>>11560459
zero in a cell means they're completely independent of each other. zero in all cells means they're completely independent of anything you're trying to calculate, and therefore mathematically irrelevant.

>>11559975
What exactly am I meant to see there, it doesn't say why he was banned

>>11560554
You could have a 1x zero row in your matrix you cannot just delete that in any case as it wouldn’t allow you to calculate the determinant if the number of rows and columns don’t match AFAIK

>>11559491
I was joking no need to get upset, but thanks for reminding me how much I hate AT

Dumbfuck here with high school tier question, it seems pretty obvious that both of these balls have the same initial and final kinetic energies just by virtue of starting with the same kinetic and potential energies.

But won't ball 2 experience a larger impulse? I mean it experiences the same force but it's on the incline for longer. Larger impulse ---> larger ∆v ---> larger ∆Ke / work done which is clearly not true? I'm pretty sure my understanding of impulse is flawed. IDK I feel so retarded.

>>11560635
I'm not sure about this but here my 2 cents, it's not how long it spends on the ramp that gives it the impulse, it's not like a boost ramp from mario kart, it's the distance that it falls, and it falls the same amount regardless of it going straight or at an angle.

>>11560635
Don't worry classical mechanics is much harder than it sounds, for me I had much more trouble with freshman mechanics than electromagnetism for instance.

As for your problem it's not how long you're on the incline for, it's not like video game, it's how much height you're losing (ie potential transferred to kinetic energy), ball 2 on the incline gains less speed per second because some of it's speed is not in the direction of losing height so it loses less height per second

>>11560650
wow we had the same exact analogy, that's eerie

I asked for help/guidance with my lab write up some months back. Ended up getting very good grades. In one lab, it seems that I got the highest grade in the entire year. So thanks anime posting anon.

Curvature and torsion are defined on curves. What's the name of these properties on planes? There has to be a way to distinct a plane from a sphere

>>11560661
same ones, it gets more complicated in dimension >2

>>11560662
What exactly is torsion in 2D? How would you distinguish a rectangular carton box vs a cylindrical(somewhat at least) plastic bottle of milk?

>>11560667
I don't know how to define torsion for a carton box though that can be done at least. Mathematically you would distinguish them by saying that one is smooth and the other isn't, for instance the tangent space at an angle of the carton box is three dimensional while the cylinder has a 2 dimension tangent plane at all points

>>11560650
>>11560651
>>11560650
>>11560651
Thanks guys, looking at the actual integral definition it seems like impulse isn't necessarily dependent on time after all. I'm trying to reconcile the problem with the watered down F∆t definition.

Any recommendation to get into Digital Signal Processing?

Is highlighting the text in your book even effective?
I know some people do it in class and their textbooks look like a color vomit.

>>11560742
>Is highlighting the text in your book even effective?
I firmly believe that everyone who does this has sever brain damage.

>>11560742
No but it's sometimes useful to mark a paragraph or two if you need to keep coming back to it.

>>11560432
um you arent? what it depends on is what is working on your matrix? if its a 4vector then reducing the matrix will produce the wrong expression. the reason the zeros could be removed is because when you do the calculation its just adding a bunch of stuff times zero which adds nothing.

>>11560658
thats kind of sad that the best performing student in your class got hand held by 4chan. must be a pleb school.

>>11560789
What do you mean, you know anon is a published scientist, right?

>>11560789
There's some very smart guys on /sci/. I'm not sure why you think it's a negative to ask for clarification from people more experienced and knowledgeable. You come across as a rather petty person, and a bit of an asshole.

>>11560789
2hu anon is love.
2hu anon is life.

>>11560794
which anon? lab report anon? unlikely. i guess its just like getting some one to one with an instructor, but still think of the student who just worked earnestly by himself, ignored by the class and by anons. im sad now.

>>11560817
I'm lab report anon, and no, I am not a published scientist. I'm a first year student. I did not know that anime posting anon was a published scientist (which is what I assume the anon who replied to you meant), but he knows his stuff, so I am not surprised. It's not like he wrote the paper for me, he clarified one or two things. I still ended up writing about 108 pages (for all labs) of work myself.

>>11560826
fair enough, im sure you did a good amount of work. well done. idk why i lashed out like that. this is 4chan though so im not going to dwell on it.

>>11560513
It's [/math], not [\math]. It's stupid.

>>11560635
I have an idea anon, I think it's to do with the velocity of the objects. To make a 1kg object go 5m/s it's 1/2mv^2=12.5 J, but to make it go 10m/s it's 50 J. The first ball gets a smaller increase in it's velocity from the smaller impact, but it's already moving faster than the ball 2 experiment. The second ball will increase speed but it will do as at an angle to what it's current velocity is, so that the resultant velocity should still be the same as the ball A. Both balls gain the same amount of energy since they both fall the same amount of distance.

>>11560867
I mean the speed of the second ball will be the same as the first ball but it will point in a different direction.

>>11560661
I mean you have numbers defined at every point of a surface called the second fundamental form entries and the christoffel symbols which tell you how the surface curves "in the direction of its normal vector" and in "other directions" respectively. No one calls them these but you could call the second fundamental form an object which contains the curvature-like curvature and the christoffel symbols numbers which contain the torsion-like curvature.
For arbitrary vector bundles over a manifold equipped with a connection, one simply decomposes the connection into its indices in a moving frame to get all these symbols, they're just the components of the tensor. So curvaturey ones are ones where you measure components on diagonals and torsiony ones are off diagonal. But torsion is defined differently here so don't use that term. It's all just curvature.

>>11560509
>>11560513
For some set [math] A [/math] and any [math] n \in \mathbb{N} [/math], there is an [math] S_n \in \mathcal{L} [/math] such that [math] \mu(S_n) < inf_{B ~ measurable ~ such ~ that ~ A \subset B} \mu (B) + 2^{-n} [/math], and the intersection [math] S = \cap_n S_n [/math] has measure [math] \mu(S) = inf_{B ~ measurable ~ such ~ that ~ A \subset B} \mu (B) [/math], and thus should be what you want. Finally, for any other [math] A \subseteq C [/math] with [math] C [/math] measurable, it follows from the definition that [math] \mu(C \cap S) \geq inf_{B ~ measurable ~ such ~ that ~ A \subset B} \mu(B) = \mu(S) [/math], which implies that either [math] \mu (C -S) > 0 [/math] or that they are the same except for a set to measure zero.

>>11560635
Impulse is just change in momentum. Does B have a greater change in momentum than A?

>>11560826
Fluid mechanics?

>>11553666
if you run fast enough east would you experience a force upwards from the earths magnetic field

>>11560509
>>11560513
Not necessarily, but the theory of closures is a go.
A is the non-measurable set. We assume it's bounded for convenience. For some set [math]A[/math] and any [math]n \in \mathbb{N}[/math], there is an [math]S_n[/math] measurable with [math]A \subseteq S_n[/math] such that [math]\mu(S_n) < inf_{B ~ measurable ~ such ~ that ~ A \subset B} \mu (B) + 2^{-n}[/math], and the intersection [math]S = \cap_n S_n[/math] is a measurable set(since it's a countable intersection of measurable sets), contains [math]A[/math] and has measure [math]\mu(S) = inf_{B ~ measurable ~ such ~ that ~ A \subset B} \mu (B)[/math], and thus should be the "closure" you want.
Finally, for any other [math]A \subseteq C[/math] with [math]C[/math] measurable, it follows from the definition that [math]\mu(C \cap S) \geq inf_{B ~ measurable ~ such ~ that ~ A \subset B} \mu(B) = \mu(S)[/math], which implies that either [math]\mu (C -S) > 0[/math] or that they are the same except for a set o measure zero.
You then globalize the function through basic axiom of choice abuse.
>>11560635
Impulse is just change in momentum. Does B face a greater change in momentum than A?
>>11561039
Only if you have net charge.

Hello, something like math lamar but physics instead? Thanks!

>>11559027
"agrees with your function", do you mean the function that is only equal to the average on the tangent circles?

>>11558747
[math]u[/math] is continuous on the closed unit disc, and thus [math]u|_{\partial \overline{D_1 (0)}}[/math] is continuous on the unit circle. This means that there's a harmonic function [math]f[/math] defined on the closed unit disc which agrees with [math]u[/math] on the unit circle.
Now, since harmonic functions satisfy the mean value property (for all circles), they in particular satisfy the one for the circles in the problem. It's easy to check that, then, [math]u-f[/math] also satisfies the averaging property given in the problem.
Assuming [math]u[/math] is harmonic for a second, you can notice that what you have to do is show that [math]u-f[/math] is constant zero because it zeroes on the unit circle and satisfies the averaging property given.
The hint is then "Weierstrass theorems on extrema."
The second hint is "every circle that [math]u-f[/math] satisfies the averaging problem for is tangent to the unit circle".

>>11561182
[math]u[/math] is continuous on the closed unit disc, and thus [math]u|_{\partial \overline{D_1 (0)}}[/math] is continuous on the unit circle. This means that there's a harmonic function [math]f[/math] defined on the closed unit disc which agrees with [math]u[/math] on the unit circle.
Now, since harmonic functions satisfy the mean value property (for all circles), they in particular satisfy the one for the circles in the problem. It's easy to check that, then, [math]u-f[/math] also satisfies the averaging property given in the problem.
Assuming [math]u[/math] is harmonic for a second, you can notice that what you have to do is show that [math]u-f[/math] is constant zero because it zeroes on the unit circle and satisfies the averaging property given.
The hint is then "Weierstrass theorems on extrema."
The second hint is "every circle that [math]u-f[/math] satisfies the averaging problem for is tangent to the unit circle".

what the fuck is the nature of the universe?
i ask “what is the universe expanding into?” and the reply is “nothing you fuckin retard lmao it just gets bigger and bigger”
what the fuck is the nature of a piece of “space” before matter/energy from the universe expands into it and occupies it? is the fabric of spacetime itself an infinite 3d space that the matter and energy of the universe is slowly occupying more and more of with its expansion or is spacetime bound to the matter/energy within it?

>>11560661
>There has to be a way to distinct a plane from a sphere
A plane is contractible while a sphere isn't, this is detected by the Euler character: [math]\chi(\mathbb{R}^n) = -1[/math] while [math]\chi(S^n) = -2\delta_{0,n\mod 2}[/math]. In 2D, by Gauss-Bonnet [math]\chi(X) = \int_X K[/math] where [math]K[/math] is the principal curvature of the tangent bundle [math]TX[/math]; this was the main starting point of Thurston's classification of compact closed 2-folds.

>>11554939
.

>>11561234
to believe that theories/models of physics faithfully maps into "the real" is mere wishful thinking and cope not having to bother with German Idealism or any of the sorts.
There's unlikely for us to be explaining of the nature of the universe.

You might not understand this point anyway, and, as described, most scientists and mathematicans will try and stick to their realism as long as they can.
The answer that you'll likely get to your question is one that you'd think of yourself if you learn General Relativity. Expansion is in praxis just a change of measurable distance. At one point, you're 1 meter away from an object. At a much later point, due to the laws stated in that theory, that distance is just becoming more. That's the "expansion". You may measure distance in terms of how many clock ticks you need to get there, the same rate.
Moreover, you're at a fools errand form the start if you try - for whatever reason - to conceptualize space (or spacetime) separated from matter.
All that said, that's just general relativity, not "the nature of the universe."

>>11561224
so it suffices to show that they are equivalent on every circle tangent to the unit circle?

>>11560831
No problem. I like asking for clarification on /sci/ because I can freely ask retarded questions in anonymity during any time of the day, plus I always get helpful answers, which most of the time help me understand things better than my professors or textbooks. As sad as that is. Some of you guys should get into lecturing/teaching as you're very good.
>>11561018
That was one of the labs I had to write up. I did quite a lot of labs, but only had to write up 3.

This is a stupid question. But this is the stupid questions thread, right?
I'm trying to characterize [math]0^n[/math] where [math]n\in \mathbb{R}\cup \{\infty\}[/math]. We all know [math]0^n=0[/math] for positive n, and [math]0^n=\infty[/math] for negative n. A common assumption is [math]0/0=1[/math], rather than simply indeterminate. And my crackpot hypothesis is that [math]0^{\pm\infty}=-1[/math], specifically when the - and + infty are joined in the riemann sphere. Go ahead, laugh.

I found a mobius transform [math]f(z)=\frac{1-z}{1+z}[/math] such that [math]0\mapsto 1, 1\mapsto 0, -1 \mapsto \infty[/math]. If you substitute [math]n=z[/math], these three mappings are consistent with the three results of [math]0^z[/math]. Likewise, you find that [math]\pm \infty \mapsto -1[/math].
Is this sufficient to prove, or even suggest, that [math]0^z\equiv \frac{1-z}{1+z}[/math]? And that therefore, [math]0^{\pm\infty}=-1[/math] in the extended reals? What else is there I can do?

This problem should be so easy but I can't find anything in my notes that pertain to this question.
Anyone know this shit?

>>11561614
>We all know
>And my crackpot hypothesis is that
Math isn't empirical in the sense that those questions have a true/false answer.
You can write down any theory you want. The only condition is, by convention, that people will not accept it if the theory holds a contradition (but even that is just a formal property, a contraditory theory isn't "wrong", it just has the property to contain one or many contraditions, such as 0=1. There's nothing wrong about 0=1 in a formalist sense.)

>>11553666
>Good charts: https://mega.nz/#F!40U0zAja!cmRxsIoiLFZ_Mvu2QCWaZg Shitty charts: https://mega.nz/#F!NoEHnIyT!rE8nWyhqGGO7cSOdad6fRQ (Post any that I've missed.) Verbitsky: https://mega.nz/#F!80cWBKxC!ml8ll_vD2Gbw4I1hSLylCw

All dead

If I'm almost done with my college algebra class and aced it with no real difficulty for the most part, how hard should precalc be for me?

Immensely stupid algebra question here. I'm trying to evaluate [math]e^{By}[\math], with B a square matrix, y a vector. I want to use the matrix exponential, but I'm not sure how exactly it works when there's a vector in the exponent. Can someone please explain?

>>11561743
sorry, should be [math]e^{By}[/math]. I can find examples online for [math]e^{yB}[/math] or obviously [math]e^{B}[/math] but I don't really get the intuition

>>11561761
By is only defined if y is a column vector and yB is only defined if y is a row vector. For two matrices A and B, AB is only defined if A has as many columns as B does rows.

For part a, is this answer correct?
The ball drops from initial height H, so + H to start, then it bounces up and down for 2Hr^n. So to find the distance it travels (the sum of the initial drop and subsequent bounces), let S_n denote the series without the intial drop factored in, so that the total is S_n + H. Let D denote the total distance traveled, S_n + H.
[eqn]

S_n = 2Hr + 2Hr^{r+1} + .. + 2Hr^n = 2(Hr + Hr^{r+1} + .. + Hr^n)\\
rS_n = 2(Hr + Hr + Hr^{r+1} + .. + 2r^{n+1}) \\
S_n - rS_n = 2(Hr - Hr^n)\\
S_n = 2\frac{Hr(1-r^{n-1}}{1-r})\\
D = H + \sum_{n = 1}^{\infty} = H + \frac{2Hr(1 - r^{n-1})}{r-1}
[/eqn]

If this is correct, how do begin part b?
>>11561677
memecharts are only valuable to procrastinators and mental masturbators

>>11561834
Also, for reference my answer differs from the on here: https://www.slader.com/textbook/9780495557425-stewart-calculus-concepts-and-contexts-4th-edition/573/exercises/52a/#

Who's right?

>>11561834
oops, the last line with the summation should be:
[eqn]
D = H + \sum_{n=1}^{\infty} 2Hr^n = H + \frac{2Hr(1-r^{n-1})}{r-1}
[/eqn]

>>11561834
>>11561880
>>11561894
I don't know where r^r comes in and no, the last one can also not be right as your right hand side still depends on n. Drop the r^(n-1) term and then it's probably right.

>>11561905
r^r was a typo, sorry. there were a few typos, think I got them all here though:

[eqn]
\ \ S_n = 2Hr + 2Hr^{r+1} + .. + 2Hr^n \\
\ \ \ \ \ \ = 2(Hr + Hr^{2} + .. + Hr^n)\\
\ rS_n = 2(Hr^2 + Hr^{3} + .. + Hr^n + Hr^{n+1}) \\
S_n - rS_n = 2(Hr - Hr^{n+1})
\\ S_n = 2\frac{Hr(1-r^{n})}{1-r})\\
D = H + \sum_{n = 1}^{\infty} = H + \frac{2Hr(1 - r^{n})}{r-1}

[/eqn]

>>11561905
also, thanks I didn't realize i was being asked to find the lmit in a). we can just assume it goes to 0 but other than that it looks good right?

>>11561772
I think my question wasn't clear. I understand matrix multiplication, but I don't get how we can manipulate [math]e^{Ab}[/math]. Is it something we can separate into [math]e^Ae^b[/math] for example?

>>11561961
If Ay isn't a square matrix but something like a vector in R^3, then I don't know what e^(Ay) except the componentwise exponentiation

>>11561932
>>11561936
actually my answer is now the same after some rearragnement, nvm!

>>11561834
I need help laying the plan for b).

d(t) = 1/2g(t^2)

but i don't know what else to do, D = speed * time?

>>11561998
samefag, why is n outside the square root operator here?: https://www.slader.com/textbook/9780495557425-stewart-calculus-concepts-and-contexts-4th-edition/573/exercises/52b/#

>>11561998
I can't help as I go to bed now. I find it a bit overblown, though, that you use 7 posts for your quest.

>>11561970
Ok, thanks! Does it help if A is a square matrix? It is, in the question I'm dealing with, and obviously y is of the correct size for their product to be defined.

I see that for standard matrices, I can use [math]e^A = \sum_{k=0}^{infty}\frac{1}{k!}A^k[/math]. Does a similar representation exist for [math]e^{Ab}[/math], or is there a way I can separate them?

>>11561721
Just as easy. Those courses were invented to hold you artificially longer in college, and so niggers don't fail their first real math courses.

>>11559657
25 is under the average for grad school students you nigger, i'll be lucky if i get in by 27

anyway, don't worry about it, you can't control your age

>>11559657
I won't finish my bachelor's until I'm 30. But over the past 3 years, my grades have been top 10 in our class and I've built rapport with my professors. From having personal talks with my proffs, they respect me a lot more since I'm a man with a wife and kid, they know I'm not some dumb 18 year old wasting their time.

can i get slick derivation of this series?

>>11562345
Let [math] S [/math] be the thing we are after. Let [math] a=\sin\theta [/math] Notice that if you scale triangle ABC down by a factor of BE/CE, you get S scaled down by the same amount. So [math] S-|CD|-|DE|=(|BE|/|CE|)S [/math]. Trigonometry gives [math] |CD|=ba [/math] and [math] |DE|=ba^2 [/math]. You can compute [math] |BE|=b\tan\theta-ba\cos\theta [/math] and [math] |BC|=b\tan\theta [/math]. Then you have [math] S-ba-ba^2=S\big[(b\tan\theta-ba\tan\cos\theta)/(b\tan\theta)\big]=Sa^2[/math]. Anyway, you can simplify: [eqn]
S=\frac{b(a+a^2)}{(1-a)^2}=\frac{ba}{1-a}=\frac{b\sin\theta}{1-\sin \theta} [/eqn] No need to write out an infinite sum!

>>11562345
Isn't it just [math]b\lim_{n\rightarrow \infty}\sum_{i=1}^n(\sin^i \theta)[/math]

>>11562345
Let [math] S [/math] be the thing we are after. Let [math] a=\sin\theta [/math] Notice that if you scale triangle ABC down by a factor of BE/BC, you get S scaled down by the same amount. So [math] S-|CD|-|DE|=(|BE|/|BC|)S [/math]. Trigonometry gives [math] |CD|=ba [/math] and [math] |DE|=ba^2 [/math]. You can compute [math] |BE|=b\tan\theta-ba\cos\theta [/math] and [math] |BC|=b\tan\theta [/math]. Then you have [math] S-ba-ba^2=S\big[(b\tan\theta-ba\tan\cos\theta)/(b\tan\theta)\big]=Sa^2[/math]. Anyway, you can simplify: [eqn]
S=\frac{b(a+a^2)}{(1-a)^2}=\frac{ba}{1-a}=\frac{b\sin\theta}{1-\sin \theta} [/eqn] No need to write out an infinite sum!
>>11562468
Gross!

>>11562468
>>11562481
thanks frens

How to prove that if f is differentiable, f' is continuous at a, and f(a)>0, then f(a)>0 on (a-d,a+d) for some d>0?

>>11562544
Should say
How to prove that if f is differentiable, f' is continuous at a, and f'(a)>0, then f'(a)>0 on (a-d,a+d) for some d>0?

>>11562468
can you explain why? i dn't get it, but I'd sure like to

>>11562481
right before simplifying, you say 'tancos(theta), did you mean tan(cos(theta))? or tan(theta)*cos(theta)?

sorry, i haven't actually verified all this yet, it's a lot to take in

stuck on c)

relevant:
[eqn]
a)\ D = H + \sum_{n = 1}^{\infty} 2Hr^n = \frac{H(1+r)}{1-r}\\
b)\ t=\sqrt{\frac{2H(1+r)}{g(1-r)}}
[/eqn]

last one for the night luckily thanks

>>11562672
forgot pic, it's this one: >>11561834

>>11562646
Typo, sorry. That whole line should be [math]
S-ba-ba^2=S\big[(b\tan\theta-ba\cos\theta)/(b\tan\theta)\big]=Sa^2 [/math]. There are no nested trig functions, so BE = b.tan t - b.sin t.cos t
>>11562619
Use trig to find CE. You should easily find it is b.sin t. Similarly, DE is b.(sin t)^2 and FE = b.(sin t)^3 and so on.
>>11562545
>>11562544
Pick [math] \epsilon=f'(a)/2 [/math]. Then by continuity of f' at a, we have for any delta [math] |x-a|<\delta\implies |f'(x)-f'(a)|<\epsilon [/math]. So there's [math] f'(x)-f'(a)<f'(a)/2 [/math] and [math] f'(a)-f'(x)<f'(a)/2 [/math]. Then [math] f'(x)>f'(a)/2=\epsilon [/math] which is a positive number.

>>11562696
>use CE
why'd you say that method was gross?

>>11562696
also, b*lim(sin(theta))^n really ends up being identical to [math]\frac{b sin(\theta)}{1-sin(\theta)}[/math]?

>>11562646
Typo, sorry. That whole line should be [math]
S-ba-ba^2=S\big[(b\tan\theta-ba\cos\theta)/(b\tan\theta)\big]=Sa^2 [/math]. There are no nested trig functions, so BE = b.tan t - b.sin t.cos t
>>11562619
Use trig to find CE. You should easily find it is b.sin t. Similarly, DE is b.(sin t)^2 and FE = b.(sin t)^3 and so on.
>>11562545
>>11562544
Pick [math] \epsilon=f'(a)/2 [/math]. Then by continuity of f' at a, we have some delta where [math] |x-a|<\delta\implies |f'(x)-f'(a)|<\epsilon [/math]. So there's [math] f'(x)-f'(a)<f'(a)/2 [/math] and [math] f'(a)-f'(x)<f'(a)/2 [/math]. Then [math] f'(x)>f'(a)/2 [/math] which is a positive number.
>>11562705
I just think the argument without explicitly writing the series is fun. Of course you can write down the inf sum and realize it is a geometric series.

>>11562715
Yes. If you don't believe me, just derive the expression in >>11562468 and use the r/(1-r) thing from high school algebra.

>>11562715
Yes.

>>11562725
>r/(r-1) thing
???

>>11562733
It's the sum of a geometric sequence.
https://www.varsitytutors.com/hotmath/hotmath_help/topics/sum-of-the-first-n-terms-of-a-geometric-sequence
Look at example 4.
Anyway, in your case, [math]a_1 = b\sin \theta, r = \sin \theta[/math] so yeah the infinite sum and the b * sin over 1 - sin thing is the same.

>>11562740
oh ok, yeah. thanks! sum of a geometric series is 1/(r-1) though

>>11562749
Thats if the sum starts at n=0.

>>11562749
If the sum start like this: r + r^2 + r^3...
Then you can take r out: r(1 + r + r^2)...
and it would be r/(1-r).

>>11562751
oh! duh, ok, thanks again

>>11562481
Jesus, I just noticed another typo. Denominator in eqn is supposed to be 1-a^2

>>11562823
Thanks for updating, I'm gonna check all this stuff in the morning when I'm more relaxed, I think like shit when I'm stressed out.

Anyway, I'm trying to break the Smith-Volterra-Cantor set into a geometric sum, with the a's and r's and all, but I'm having trouble factoring this out, any tips?

[eqn]
\sum_{n=0}^{\infty} \frac{2^n}{2^{2n+2}}
[/eqn]

>>11562913
>I'm having trouble factoring this out
Factoring what out? 2^n / 2^(2n+2) is just 1/4 * 1/2^n. Remember your exponent rules.

I'm starting to think there might be some kind of typo in b.

At x = 5cm:
Potential Energy = 2J (shown explicitly on the graph)
Kinetic Energy = .12J (1/2m*v^2 -> 1/2(.015)(4)^2 =.12)
Total Energy is 2.12J

At x = 0cm:
PE = 4J (shown explicitly on the graph)
KE is not known
Total Energy is already at 4J, which is greater than the total energy of the system at x=5cm.

How am I supposed to find the velocity at x=0 when its PE alone is already exceeding the total energy in the system? The velocity / KE of the particle at x=5 would need to have been significantly greater in order for me to find this.
I have to increase the PE at x=5 by 2J in order to have it match x=0, but I've only got .12J of KE.

>>11562985
you mean 2^n/2^(2n+2) is 1/4 * 1/2^(n+2), right?

anyway, i think i've realized my problem, i was overlooking that since there's a 1 in the numerator, it doesn't have to be raised to the same power, so r can equal 1/2^(n+2)

so this ends up being r^2/(1-r), where r = 1/2, right? that math ends up allowing the sum to equal 1/2

>>11563004
errrmeerrrgerrrddd i was forgetting to multiply my resultant sum by 1/4 the whole time

>>11562993
Clearly you have imaginary velocity at x=0. Probably a typo.

>>11563159

Redpill me on concentration inequalities. Do they actually give useful performance bounds or are they just there for rigorous asymptotics?

i don't really get it
in probability, there are these distributions of random variables e.g. normal, hypergeometric etc. from which we can calculate the probability for some x, right?
but how do we know that some random variable X has e.g. a normal distribution?
most examples i find are just assuming that a variable has some distribution from the get-go and just substitute the formula for that distribution to calculate probability for some section
is it something that we just have to know from examining the examples or what?

>>11563159
>>11563199
You can pretty easily find the big circle to have radius [math] R_0=1-\sqrt2/2 [/math]. Then, the line joining the center of the big circle to an acute corner is [math] m=\sqrt{R_0^2+(\sqrt{2}/2)^2}=\sqrt{2-\sqrt{2}} [/math] (which is different from what you had, however I verified all this in solidworks). Noticing this line runs along all the circles' centers, you know that [math] R_0+2R_0a+2R_0a^2+...=m [/math]. So [eqn] 2R_0\sum_{n=1}^{\infty}a^n=m-R_0\implies\sum_{n=1}^\infty a^n=\frac{a}{1-a}=\frac{m-R_0}{2R_0}\implies a=\frac{\frac{\sqrt{2-\sqrt{2}}}{2-\sqrt{2}}-\frac{1}{2}}{\frac{\sqrt{2-\sqrt{2}}}{2-\sqrt{2}}+\frac{1}{2}} [/eqn]
which I really really cannot be arsed to simplify but again was verified in solidworks. Since [math] a [/math] is the ratio of consecutive radii, it now shouldn't be too hard to find the area you are after. [eqn] A=\pi R_0^2 +2\sum_{n=1}^\infty\pi(a^nR_0)^2=\pi R_0^2+2\pi R_0^2\bigg[\frac{a^2}{1-a^2}\bigg]\approx 0.404 [/eqn] i think. this most likely could have been done a LOT cleaner.

>>11564269
Say you are determining hardness of a material, and you have a very large sample size. The way I understand it, is if there are multiple factors all contributing to hardness, and if they are all randomly determined, and if they are all equally likely to influence hardness, then you get a normal distribution of hardness for the population. And of course, if you took multiple readings of each sample, the distribution of the mean hardness of each specimen tends to a normal distribution over the population per the central limit theorem. Other distributions come in different contexts, like the Boltzmann distribution just naturally pops up when you taylor expand the number of microstates and divide by the canonical partition function.

>>11553666
Hello Satan.
I'm writing in to ask a stupid question that came to me this morning. One thing that really annoys me when coding is having to do
>for(condition) {...}
>important_update()
>for(condition) {...}
with the same condition in both cases. I hate having to copypaste the for condition, because, of course, there is always a risk of going back to make changes and forgetting to clone the condition. So anons: Is there a programming language that has something like a "regardless" statement that goes within a loop and allows a block to slice a loop in two (pic related)?

>>11564329
brilliant, thanks! I did the same problem with an equilateral that had 3 circles spawned every iteration, it was a lot easier due to the symmetry of the equilateral (it worked out to where each circle's center was 1/3 the height of the equilateral it was contained in or something).

I'm not really familiar with solidworks, but essentially it numerically validated the answer, right? confirming the math was correct? and what do you personally use that for anyway, are you an engineer?

>>11564455
>solidworks
is a whole lot of fun and I recommend playing with it at some point in your life. Yes, I just drew the situation we have with a lot of circles, measured radii and ratios and compared with the measuring tool and all that.
>engineer
I study ME

>>11555453
Maybe look into image sensors
Probably would need a master's though

>>11564385
I'd love to help you anon, but I simply do not understand what you're asking.

how the fuck do i interpret sum like that?

This might be better suited for /g/ but I'll repost it here too:

I feel like a retard but don't know where to look
I'm trying to make my own CNN-based OCR program as a personal project (2.2k classes)
I've made my own dataset, and I think it's half decent with random noise/color (before grayscale) for each image; every filename is the class + a number, so it's already labelled
I just have no idea how to train with Python (or MATLAB I guess)
I want to imagine it's as simple as using some API (rather than making the model myself) and just saying:
train_files = everything in directory_train
class = filename[0]
Configure how many layers/nodes/learning rate/etc. I want
Then hit run

But I can't find examples that don't use prebaked loadable datasets

>>11564518
https://www.tensorflow.org/tutorials/images/cnn
Maybe this post is helpful anon?
What you're looking for is probably "Keras API"

>energy is not created or destroyed, it is only transformed
then where did all the energy that exists in the universe right now come from?

what's a good problem book with elementary stuff like this?: >>11563159

Just geometry, trigonometry, sequences/series, basic number theory, combinatorics, algebra and multivariate/vector calculus? It'd be great if I had like a big fat handbook I could flip through.

>>11564669
I don’t think you’ll get a satisfying answer unless you assume a zero-energy universe.

>>11564669
It always existed :^)

don't know if it was already answered, but my semester is about to begin and the uni library is closed due to covid 19. They have some books online but the one I need is not provided as ebook. Any idea where to find it for free? I tried searching, as well as the pirate bay, but is there some specific site where people upload textbooks?

>>11565113
update: i've found what i was looking for, but i'm still interested to know if I could find such a site

Anyone familliar with controls?
For #3, I get 1+9s^-1+14s^-2+s^-1.
However, someone else is saying it's 1+6s^-1+14s^-2+s^-1.
And then online, someone else is getting 1+6s^-1+8s^-2+s^-1.

My professor gave us a worksheet for laplace transforms and convolutions.
One of the problems is:
Find
[math]L\left\{\int _0^te^{2\tau }sin\left(\tau \right)d\tau \:\right\}[\math]

the sin term is missing t. Is that valid, or is there a typo in the worksheet?

My professor gave us a worksheet for laplace transforms and convolutions.
One of the problems is:
Find
[math]\mathcal{L}\left\{\int _0^te^{2\tau }sin\left(\tau \right)d\tau \:\right\}[/math]

which is the convolution of e^2t and sin of something.
the sin term is missing t. Is that valid, or is there a typo in the worksheet?

>>11565189
it's apparently supposed to solve to pic related. Can't tell if the outside term is an s or a 5. The box is because I guess she wants us to simplify by completing the square, but the closest I can get to what she has written is
[math]\frac{1}{s\left(s-1\right)^2-2}[/math]

>>11565189
it's apparently supposed to solve to pic related, but I can't tell if the outside term is an s or a 5. The box is because I guess she wants us to simplify by completing the square, but the closest I can get to what she has written is
[math]\frac{1}{s\left(s-1\right)^2-2}[/math]

>>11565140
>1
Two forward loops: [math] P_1=s^{-1}s^{-1}s^{-1}\cdot 2=2s^{-3} [/math] and the other one [math] P_2=s^{-2} [/math].
>2
Four loops: [math] L_1=-4s^{-1};\ L_2=-3s^{-1};\ L_3=-2s^{-1};\ L_4=-s^{-3} [/math]
>3
[math] \Delta=1+(L_1+L_2+L_3+L_4)-(L_1L_3+L_2L_3)=...=1+9s^{-1}+14s^{-2}+s^{-3} [/math]

You've got [math] \Delta_1=1 [/math] and [math] \Delta_2=1+L_3 [/math] i think

>>11565189
>>11565241
What you've typed doesn't look like a convolution. Anyway, the tau is just a dummy variable. The Laplace transform of the convolution of two functions is equal to the product of the Laplace transforms of the original functions. I think that is a 5, comes from the integration by parts.

>>11565323
forward paths, obv

>>11565323
Honestly I'm lost as to what she wants us to do. It's question 5, and "Theorem 7.4.2" is the convolution theorem in our textbook.
Knowing my professor, she doesn't actually want us to do the integral, but rely on the theorem definition.

Pic related is what I have so far, just the set-up.

I know I need to find an open set in the quotient [math]X/A[/math] that contains the point [math]\{A\}[/math] but does not contain any of the [math]U_n[/math].

I know it has something to do with the [math]V_n[/math] in the original space but I don't know how to obtain the needed set.

>>11565345
All I can tell you is that the integral as is is not a convolution. Maybe you can change a variable or make a substitution?

>>11565323
>Δ=1+9s^−1+14s^−2+s^−3
Guess I got it right. My initial answer had a typo, should've been s^-3 for the last term.

>>11561086
>Impulse is just change in momentum. Does B face a greater change in momentum than A
It does

>>11565637
why?

>>11565676
cause it spends less time on the ramp, change in momentum is F x (change in)time.

>>11565686
>cause it spends less time on the ramp
How do you know that? And if you know that dt is less, how do you know that F is not greater?

>>11565688
cause the direction of the velocity is perpendicular to the ram whereas ball B's is at an angle.
>how do you know that F is not greater
can't see any reason why it wouldn't be greater

>>11565696
Pretty sure the velocity is perpendicular to the normal of the ramp no matter which direction it moves along the ramp. Also, you're literally just assuming that dt is lesser. You should show it explicitly.

Does it worth studying calculus iii+ for computer science?

>>11565708
>pretty sure the velocity is perpendicular to the normal of the ramp no mater which direction it moves along the ramp
I don't understand what you mean
>you're just assuming that dt is smaller
it's pretty obvious, though I wouldn't know how to prove it

>>11565738
If you didn't understand, then I probably didn't understand you.
>it's pretty obvious
It's really not obvious at all.

With regards to a Jablonski diagram, what is the difference between an energy state and electronic state? To my understanding, an electronic state is like S0, S1, T1, fine but so then what is an energy state? And then in all of this where do rotational states come in to play?

>>11565740
>muh proofs
Ok, explain to me how an object going slower is going to take less time than an object going faster down the ramp when the force is constant?

>>11565753
Or I should explain how there is any ambiguity there.

>>11565724
I don't see where it would be of much use

>>11565753
Nigga, I dont know what happens. You're missing the point.
>there is less impulse because dt is smaller
>dt is smaller because its slower
>its slower because there is less momentum
>there is less momentum because...
You see the problem?

>>11565764
I literally don't, there is less momentum because it is released at an angle to the ramp. Did you even read the question?

>>11565764
how can one infinitesimal be smaller than another infinitesimal

>>11565773
clearly there is integration implied anon

>>11553666
What frequency of a single photon would be equivalent to a black hole? Assuming gamma ray lasers an create black holes, which frequency is optimal?

I'm confused about something, what is wrong with the following reasoning: a rocket engine produces constant thrust so a constant force, and they also produce energy at a constant rate. When the rocket is moving slower the energy use would be smaller than the energy use when it is moving faster, since when it is moving slower it moves smaller distances therefore smaller d in Fxd=work done.
This doesn't really make sense, what am I getting wrong?

I'm confused about something, if a rocket is using a constant amount of fuel per second and therefore generating a constant amount of energy how is it that the acceleration (force) is constant given that you need more energy to to change an object's momentum at higher speeds? Is it the weight loss that makes up for it?

>>11565814
>>11565914
nigga what

>>11565940
So you use fuel at a constant rate, that should produce constant energy right? Ok, now the rocket is experiencing constant force on it. But how does that work?
When it's accelerating with acceleration A at 100km/h it will be using the same amount of fuel as it would when it's accelerating with acceleration A at 500km/h. But to accelerate something at 500km/h the takes more energy than the same mass at 100km/h because KE = 1/2mv^2.

>>11565961
I think you're getting velocity and acceleration mixed up
at any rate, the real energy usage would come from accelerating the mass at 100 km/h to 500 km/h. Once it reaches 500 km/h and stops accelerating, barring all outside/nonconservative/noninternal forces, it wouldn't be consuming any energy. Just coasting with the momentum it already has.

>>11565980
>getting velocity and acceleration mixed up
I don't think I am:
>changing a 100m/s object's speed to 200m/s would need adding 30kJ (for a 1kg object)
>changing a 1000m/s object's speed to 1100m/s would need 210kJ
since the acceleration is constant then the it means that at 1000m/s you're consuming more energy to accelerate the object at the same acceleration as an object at 100m/s. But the fuel consumption is still constant, isn't it? So what am I missing?

>>11566013
momentum my guy