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/sci/ - Science & Math

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11991165 No.11991165 [Reply] [Original] [archived.moe]

Formerly >>11963300

New chart (subject to further revision) edition.

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
libgen.is (warn me if the link breaks)
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
>how do I post math symbols?
>how do I succesfully post math symbols?
>a google search didn't return anything, is there anything else I should try before asking the question here?
>where do I look up if the question has already been asked on /sci/?
>how do I optimize an image losslessly?

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Meme charts: https://imgur.com/a/kAiPAJx
Serious charts: https://imgur.com/a/Bumj2FW (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:

>> No.11991214
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lmao look at this dude he made so much effort and nobody is posting in his thread

>> No.11991223

go away newfag, you don't understand what a general is

>> No.11991233

Correct me if I'm wrong. The dot product of two vector yields a new vector, and the cross product of the same two vectors yields a different vector. The vector produced by the dot product multiplication can be interpreted, somehow, as representing the "similarity" between the two vectors yielding it, whereas the vector produced by cross product multiplication can be interpreted as representing the "difference" between them? How and why?

>> No.11991255
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Unanswered questions:

Math questions:

Physics questions:

Chemistry questions:

Biology questions:

Engineering questions:

/g/ questions:

Stupid questions:
>>11972453 [Yes, my question is stupid.]
>>11974311 [No. 1^2 > 0^2, doesn't imply that f(x) = x^2 is increasing.]

No, not like this, /sqt/ bros...
>The dot product of two vector yields a new vector,
Dot product yields a scalar.

>> No.11991340

Gelfand is missing from the chart

>> No.11991352

Gelfand isn't a single book.

>> No.11991522

is calculus always an approximation?

>> No.11991714


How many cases are there of animals evolving to have traits which specifically help inhibit reproduction? Humans do this artificially via condoms to obvious benefit, so there's already a proof of concept. Females of various other species have folds which make insemination more difficult, which by the prior line, I assume is a matter of selection rather than mere coincidence. I haven't found a clear male case of this though. Does the fuck-and-run option they generally have prevent this? Has the impregnating-gender of any species besides humans ever been shown to deliberately avoid insemination? I figured territorial species might do this to save resource, but it seems like they tend to just slaughter the kids or something instead.

>> No.11991848

>female snakes have multiple pockets in which sperm can be stored for up to five year and then, by preference, selected
>humans invent a little finger-glove instead

>> No.11991896
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>tfw previously stupid question
So I have two perfectly synced clocks with binary code assigned as specific intervals (this could be increased given clock precision) and I send a single photon between them assigned 1 in binary (assume instantaneous for simplicity) when the photon is received it is assigned a new binary (1010) in this case, in doing so I have effectively increased the amount of data per bit sent or compressed the data to a single bit, In doing so is the timing of the event not used as additional information? or am I wrong in this case?

>> No.11991902

I think this is the most appropriate place to post my question. Just curious and seeking to understand people's opinions. What does /sci/ think of statistics? Do you consider it Mathematics or is it something less?

I've always loved math and wanted to study a master's in math at a good uni. In all the higher ranked Universities I applied to I was only accepted into their statistics program. I don't know if I'll enjoy it as much as other applied math fields.

>> No.11991911

I need to learn everything there is to know about MOSFETs and IGFETs on a device level, Suggest books plz, already read Streetman's solid state electronics

>> No.11991918

I think it's frequently mischaracterized

>> No.11992033

My opinion is that statistics is one of the most boring parts of maths, but it's still maths.
>I don't know if I'll enjoy it as much as other applied math fields.
Relax, most applied maths is boring. Not inverse problem kino and integral equations, tho, those are great.

>> No.11992161

What do you mean?

Go through Khan Academy or the MIT OCW course - they'll have a linear progression that you can work towards for the next few months. Just keep regularly doing problems, and you'll be good. Google is your friend. I also recommend Paul's Online Math Notes, which explain things really well.

I'm not an expert, but this PDF seems to answer your second question: https://sites.math.washington.edu/~mitchell/Algf/whyrep.pdf

>> No.11992328

since it uses derivatives is it an approximate?

>> No.11992338


>> No.11992339

Not really. Derivatives use the notion of a "limit," which means we can see the number a function or something approaches at a certain point. Something like the slope of the tangent line of [math]x^2[/math] at [math]x=3[/math] is *exactly* [math]6[/math], not approximately.

>> No.11992352

So you mean close to but not exactly. An approximate.

>> No.11992357

I think you're confusing the limit with the difference quotient [math]\frac{f(x+h)-f(x)}{h}[/math]. The limit itself is exact, but the values of the quotient as it approaches the limit are not.

>> No.11992409

Why is college algebra such a pain in the dick? I'm up to Calc 2 and never had as much trouble as i did in algebra.

>> No.11992616

>So you mean close to but not exactly. An approximate.
a limit gets past all of the approximations
a limit is exact

>> No.11992819

Go to /diy/ and find /ohm/

>> No.11992824

Are 2+2 and 3+1 the same thing?

>> No.11992856 [DELETED] 

'aight, I'm gonna repost my unanswered question from last time.

What's representation theory in a nutshell? What makes the subject interesting?

Assume undergrad-tier knowledge in group theory. (Also, I've studied some Fourier analysis on LCA groups, and I've been told that it's closely related to representation theory. I'd love to see how)

>> No.11992931
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This is called PWM. It's a modulation that can be used to digitalize information, but in this context is used to easily control how much power do you want to feed into the stove.
The power is controlled by the duty cycle. If the stove has a 30% duty cycle, it means that it spends 30% of the time turned on and only spends 30% of the maximum power. The duty cycle can easily and digitally be changed. Futhermore, you can build a control system with a feedback loop to monitor the temperature and manipulate the duty cycle instantly on real time to maintain the temperature constant, and all this logic can fit inside a chip.
To do this with AC and transformers is just a pain in the ass and it's too big and expensive. A fucking automatic variable responsive transformer? For a stovetop? Nope.

>> No.11993100

No. They both equal the same number but they are different expressions.

>> No.11993146

I was wondering. If I want to just roughtly know the pH of a solution to the 0.00 magnitude, should I buy some cheap pH meter or a bench pHmeter.

I mean, the cheap pH meter should simply give the lecture as soon as I insert it into the solution. But the bench pH meter, while surely will offer more resolution it means that I have to use a buffer calibration solution, then adjust the pH to calibrate the sensor, then insert the desired solution(with a buffer) in the sensor and add a solution of a strong base or acid until I reach the desired pH.

The thing is that they explained me the process but not the point to it or the difference between a cheap sensor and a bench one, and taking into account that is ten time more expensive I just want to know whats the point for homelab applications.

>> No.11993268

In Freyd's theorem that a category C with products of size up to Mor(C) is a preorder, how do we conclude from [math]f,g:A\to B[/math], [math]f\neq g[/math] that the homset [math]A\to \prod_{m: \mathrm{Mor}(C) }B[/math] contains at least [math]2^{ | \mathrm{Mor}(C) |}[/math] distinct arrows?

>> No.11993299

Thinking it over a bit, I think the argument goes as follows: for each [math]m:Mor(C)[/math] we can choose one of f,g to precompose with the projection [math]\pi_m[/math], and the [math]2^{ \mathrm{Mor}(C) }[/math] cones thus formed are pairwise distinct, otherwise f,g would lift it non-uniquely to the product cone [math]\{\pi_m\}[/math]. The theorem follows from the universal property of [math]\{\pi_m\}[/math], which ensures that a (distinct) lift in [math]A\to \prod_{m: \mathrm{Mor}(C) }B[/math] exists for every (distinct) cone.
Is this right?

>> No.11993348

Sounds correct.

>> No.11993400

how do we know that the properties of numbers are intrinsic and don't just manifest from the way we've chosen to represent them?
as in, why is a number always prime, or irrational, or transcendental, regardless of how we choose to represent it in decimal, binary, octal, sexagesimal, etc?

>> No.11993560

You can do all of the construction of the numbers and a lot of the investigation of their properties in a representation-agnostic way. When you get to the reals though you might have to choose a family of representations (ie base n but you don't need to specify what n is).

>> No.11993567

Got some problems with rotations and quaternions
Let say the rotation of a cube in 3D space is defined by a quaternion Q1(x,y,z,w), it is not oriented the way I want, I want to rotate it permanently on the Z axis by 90° during my whole process
Do I only have to set its rotation by a multiplication with another quaternion Q2 (normalized) which will be oriented by 90° on the Z axis ?
newQ1 = Q2.Q1.Q2*

>> No.11993739

Why can't you divide vectors?

>> No.11993752

I want to symbolically solve
[math] x = \sqrt[2]{2\sqrt[3]{3\sqrt[4]{4\sqrt[5]{5\dots}}}}[/math]
Which is easily seen to be the infinite product
[math]x = \prod_{n=1}^\infty n^{1/n!}[/math]
Taking the log on both sides yields
[math]\ln(x) = \sum_{n=1}^\infty \frac{\ln(n)}{n!}[/math]
But I can't get much further than that.
Anyone have a clue/hint how to evaluate this sum or product?

>> No.11993770


Are you sure that the infinite product is correct? The roots are nested, not just multiplied together

>> No.11993783

looks correct imo, nested implies that the exponents are multiplied together, hence the factorial

>> No.11993805

Hi, can I become retarded from listening to youtube while playing games? I heard that multitasking is bad for my brain but is it that bad and is that a serious form of multitasking?

>> No.11993807

Well [math](2\cdot 3^{1/3})^{1/2} = 2^{1/2}\cdot(3^{1/3})^{1/2} = 2^{1/2}3^{1/6}[/math] right?
And this pattern continues, which gives the product, right?

>> No.11993815


Yeah sorry I missed the factorial, my bad

>> No.11993837

Another anon already suggested it, but you really should post this on stack exchange.

>> No.11993848

Yeah, seems like i might have to.

>> No.11993860

>Anyone have a clue/hint how to evaluate this sum or product?

Is it even possible? Wolfram Alpha doesn't give an answer: https://www.wolframalpha.com/input/?i=Sum+from+1+to+infinity+ln%28x%29%2F%28x%21%29

>> No.11993875

I would think so, yes. Wolfram alpha isn't perfect, I've solved series that has closed form solutions where wolfram would just estimate the solution.

But it is entirely possible that it has no closed form solution.

>> No.11993882

well, it gave to me...

[eqn] \ln(x) = \sum_{k=1}^{\infty} \frac{\ln(k)}{k!} = 0.603783 [/eqn]

so, [math] x \simeq 1.82902 [/math]

>> No.11993906

That's super weird. I just rechecked my link >>11993860 and it worked this time. Might be because I'm using my phone and had a poor internet connection

>> No.11994065


that was me! but yeah i think stackexchange would be the most helpful

>> No.11994161

Are these books just really meme books though?

Also, scientifically speaking, how much dick can your anus handle OP?

>> No.11994177

I hit a minor roadblock in calc 2 but algebra word problems fucked me harder than anything, such as: If it takes 10 people 3 hours to paint a wall how long does it take 5 people to paint 4 walls? Or - If a ball is dropped and travel 5 m/s and goes through water at 3 m/s from a height of 20m, how long was it in water (something like that). I'll know how to get the answer "intuitively," but I always fuck up writing it out into an equation and solving it how they want. It's a blog post, but I thought I could relate.

>> No.11994270
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Why isn't the last answer correct? The eigenvalues are 1,3, so the basis for the eigenspace of the smallest eigenvalue should be the column that corresponds to the smallest eigenvalue, which I've entered (and yes, I tried the second column as well).

>> No.11994287

The eigenspace corresponding to the eigenvalue 1 is 2-dimensional.

>> No.11994288

why do heating mantles have a fiberglass lining? why not have like, a steel mesh?

fiberglass is going to abrade and shed glass filiments, so it'll degrade with time. plus a metal mesh would better conduct heat around the flask so hot spots would be eliminated. and there's not a risk of electrical shock because you could just ground the mantle.

>> No.11994291

So you would need both vectors.

>> No.11994316

If we have an implication, and the consequent has some property, then does the antecedent also have that property?
Something like "increasing the amount of cakes in my house has the property of being good. If I buy cakes, then I increase the amount of cakes in my house. Therefore, buying cakes has the property of being good".
Is this logic valid (I don't care about soundness). Or does the fact that the consequent have some property not imply that the antecedent has that property?

>> No.11994334

What's the deal with NRC Research Press? Trying to view an article on my phone and they've just given me a loading wheel for 10+ minutes. No login/credentials prompt, no nothing.

Anyone else familiar with this site? address is just the name with no spaces and a .com

>> No.11994357

no idea about them in particular but i almost always just use scihub to get the real papers.

>> No.11994466

That pdf is from my topology professor at UW. He is dead now. ;_;7

>> No.11994840
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>Are these books just really meme books though?
I'm sorry, I think I might be going blind. Does the chart say meme book somewhere? "The books inside are memes", "the chart contains popular /sci/ meme books" or something similar enough?

>> No.11994946

You're right. Just because it doesn't say meme and because they're shilled definitely doesn't mean they are memes.

You didn't answer my second question about your gay faggot butt either

>> No.11994955

you can come up with mathematically consistent ways to "divide vectors". it just doesn't have any useful meaning, so there's no point.

>> No.11994973

Jesus christ I just learned our galaxy is on course to crash with Andromeda, how do we prepare? Why isn't this on the news?

>> No.11994983

>predicted to occur in about 4.5 billion years
>why isn't this on the news???

>> No.11995228

galaxies don't really "crash," they just sort of get mixed up
and by the time that happens, earth'll probably have produced multiple space-faring intelligent species, so it won't really be an issue.

>> No.11995528

Please help a brainlet with integration. I know [math]\int \dfrac{1}{x} dx = ln|x|[/math] and that [math]\int x dx = \dfrac{x^2}{2}[/math]. But how do they 'interact'? For example [math]\int \dfrac{x}{x}dx[/math].
It would seem logical if it was [math]\dfrac{x^2 ln|x|}{2}[/math]. But that obviously isn't the case and I can't see the pattern.

>> No.11995614

the integral of a product of functions is *not* equal to the product of the integrals of such functions

in order to evaluate the one you suggested correctly, the best shot is to apply integration by parts. taking [math] \color{red}{u \equiv x} [/math] and [math] \color{blue}{\mathrm{d}v \equiv 1/x \, \mathrm{d}x} [/math], we have
[eqn] \int \color{red}{x} \cdot \color{blue}{\frac{1}{x} \, \mathrm{d}x} = \color{red}{x} \cdot \color{blue}{\ln (x)} - \int \color{blue}{\ln (x)} \hspace{4pt} \color{red}{\mathrm{d}x} [/eqn]
one can show that [math] \int \ln(x) \hspace{3pt} \mathrm{d}x = x \big[ \ln(x) - 1 \big] [/math].
[eqn] \int \frac{x}{x} \, \mathrm{d}x = x \, \ln(x) - x \, \ln(x) + x = x \, , [/eqn]
which reproduces the expected result.

>> No.11995662

Would you do linear algebra or calc 2 after completing calc 1? I'm in community college and their suggested math pathway is calc 1, then doing whatever you please until you complete both, of which I can then do calc 3. Which should I do first?

>> No.11995698
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My question is only about C. Since initial height is not given, could I place the x-axis on the final position of the ball? That would make the initial height 3cm and final height 0cm.

>> No.11995704

Are there significant differences between isopropanol and propanol besides the isomeric difference in their structure? Like I see isopropyl alcohol used all the time in sanitation agents, but not 1 propanol. Why is that?

>> No.11995729

Is it possible to create a drug that makes girls insatiable nymphomaniacs who become dumber each time they have sex? Because I think such a drug would be beneficial to society.

>> No.11995749

propene is easier to hydroxylate at secondary carbons than primary (markovnikov vs anti-markovnikov), thus iPrOH is cheaper than nPrOH

also check the msds, idk if nPrOH is safe or not

>> No.11995771

Sick. Thanks bruv. I'm doing a project on IPA for my gen chem 3 class. I don't know what markovnikov is, and I wouldn't have understood your explanation if not for the articles I've been reading specifically about how IPA is manufactured industrially. Either through the direct or indirect hydration of propene, or through the hydrogenation of acetone. I assume hydroxylate and hydrate are synonymous here, I can't imagine either means anything different than "to affix an OH group."

>> No.11995786

Probably calc 2. linalg is more important in calc 3 imo, so it'd be good to take it sooner to your calc 3 so it's fresher in your mind.

Yes. We're just looking for the difference in their heights, which would be 3cm. This would be plugged into [math]mg\Delta h[/math].

>> No.11995816

>This would be plugged into mgΔhmgΔh.
Cool, thanks.

>> No.11995938

Looking up differential amplifiers. What does "suppresses any voltage common to the two inputs" mean? Does it suppress the AC part of the inputs or what?
Why the fuck am I going through a mostly practical circuit class when I'm not an engineer, why are we being assigned the theory instead of it being explained more in depth?

>> No.11995960
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Hello,i want to learn calculus with the infinitesimal approach, but before i need to refresh some precalculus. I have 3 different options and i was wondering if you could help me pick the best one or the most efficent at least.
1)Khan academy precalculus (https://www.khanacademy.org/math/precalculus)
2)Stewart precalculus: mathematics for calculus
3)Simmons Precalculus mathematics in a nutshell.
I don't know if it helps; but, i did precalc, calc I and II in uni. Sadly, i don't remember very much.

>> No.11996023

Between chemical engineering and EE, which would involve less hands on work (with this I mean building things, simulating things, lab work, etc.) Which of the two would be more pen and paper focused, that is, which would have the more courses where I can just read the theory, understand it and apply it to problems without having to build, simulate, or experiment with anything.

>> No.11996176

I would personally recommend Khan Academy, since it's very interactive, and leaving the textbooks as extra references if you need to double check something.

>> No.11996293

different DC biases may cause different linearity responses, in a shitty amplifier.
w2aew has a video on it

idk what your second question is, do you care or not care about practical circuit design?

>> No.11996298

just drop out and be an actuary already

>> No.11996374

yeah it is the simp wet dream, but girls dont get dumber, since they are the ones organizing the competition among men to pick up the men who will please them sexually the most.

it's like wanting a drug allowed by referees to make the referees dumber

>> No.11996389

>If we have an implication, and the consequent has some property, then does the antecedent also have that property?
yes in logic the usual property is ''being sent to true in the model''

there are logics where some other property is required to be passed over to the consequent.

learn more about weird inference rules

>> No.11996529

The definition of the imaginary unit is i^2 = -1, in other words: any number whose square equals -1 is the imaginary unit. Clearly -i also satisfies this equation, which means that, by definition, -i = i, and therefore i = 0. Where is the error, from a rigorous perspective? Do I misunderstand how implicit definitions work?

>> No.11996582
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is the fourth dimension basically just drawing a line and pretending it's 90 degrees from other axis when it's 45? no spacetime pls

>> No.11996634

{0} ≠{ }

Also, suggest books/websites for high school physics, chemistry, math and electronics other than khan academy.
Thank you.

>> No.11996641

>{0} ≠{ }
check the elements of each set

>> No.11996686

No, it's actually 90° with respect to every other axis. This cannot be done in 3D just like a cube cannot have three angles mutually 90° drawn on paper. What you're looking at a is a projection onto a lower-dimensional space.

>> No.11996733

Look at that fucking faggot, so sure of that claim. Any half decent beginner book in this beginner course would give you that understanding, in its beginning chapters. Right thread for you indeed.

>> No.11996822

> in other words: any number whose square equals -1 is the imaginary unit
No. One of them is the imaginary unit, the other is its negation. Similar to how i^2=1 has 1 and -1 as its solutions. Except that 1 and -1 are distinguished by the fact that 1 is the multiplicative unit, i.e. 1*x=x, whereas -1 isn't. There is no such distinction for i vs -i, nor does it matter.

>> No.11996862

1. How do chemicists remove dirty protective gloves?
2. Anyone manufactures protective gloves from PTFE?

>> No.11996957

Organic chemistry questions
1. Does anyone know where I can find a chart or table ranking common functional groups by frontier orbital (HOMO/LUMO) energy levels? I remember seeing a chart out there once
2. Does anyone know where I can find a chart/table showing reaction rates for common rxns? I vaguely remember seeing one that grouped the fastest ones as "diffusion controlled"

>> No.11996989

how are you doing OP? What are you studying atm?

>> No.11996993

>1. How do chemists remove dirty protective gloves?
take one off by grabbing it by the cuff, up until the finger tips, then with the partially gloved hand do the same for the other glove, they should now be both basically off, then you can bin them/scruntch them into a ball and bin them.

>> No.11997267
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The usual. Got some stuff to solve. The kind of stuff which you can't go and just mechanically solve yourself, it actually requires some form or another of human interaction.
Currently studying C++ programming.
How about you? Doing anything in particular?

>> No.11997384

What's the point of factoring polynomials and functions in general?

my professors don't like when i don't factor a function, even if it's correct, they say it's incomplete if i don't factor them, why is this?

>> No.11997427

not a great deal just some problem sets I meant to get done ages ago, boring ass aPplIeD CS bullshit

>> No.11997601

how should I cite books which aren't finished/published yet? for example "Vector Bundles and K-theory" by A.Hatcher

>> No.11997607

first time going on /sci/ in a few months, glad to see youre still around, 2hu bro

>> No.11997613

grab the cuff of the right glove with your left hand, and pull the glove completely off. you are now holding an inside out glove by the cuff in your left hand. now, grab the left cuff *through the inside out glove*, like a doggy-bag, and take the left glove off

>> No.11997677

It is much easier to reason about, and the professors probably want all the anwers of a similar form for easier grading.

>> No.11997809
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I keep getting this problem wrong. Can someone help me find find P? It does not accept answers from any calculator I've tried.

The eigenvalues are correct, and are 0,0 and -3. So the row reduced forms of that matrices after substracting the eigenvalues along the diagnol are the identity matrix for -3, and for 0 it is:
[math]\begin{bmatrix} -1 & -3 & 11 \\ 0 & 0 & 0\\0 & 0 & 0\end{bmatrix}[/math]

I'm not really clear on how to solve for P from here. I know it has to do with setting the rref matrices above to Ax = 0, and solving for x, but I tried that and my answer was still wrong.

>> No.11997830

Any recommendations for the linguistic and semiotic (syntax, semantics) aspects behind maths?

>> No.11997837

nevermind, got it.

>> No.11997876

the same way you would cite published books

>> No.11997884

I'm taking chemistry 101 this fall semester. But one of the required texts for the lab part is something called "LABORATORY NOTEBOOK 100 CARBONLESS SET"
What exactly is that? It doesn't seem like a textbook. Is it just a special kind of notebook for chemistry? If so, are there other, cheaper (it's like $26 for that specific one listed) ones I could get instead?
The exact ISBN is 9781506647401

I would just email the lab professor, but I've already emailed him like 3 times over the past few months and he hasn't responded yet.

>> No.11997903

For anyone that didnt know yet,
most books are available at the website

>> No.11998009

The other answers are correct, but I can't figure out what's supposed to go in place of the function. It complains when it's not a number.

>> No.11998016
File: 50 KB, 866x344, Screen Shot 2020-08-11 at 12.26.32 PM.png [View same] [iqdb] [saucenao] [google] [report]


>> No.11998028

Did you try swapping x^2 and 2x?

>> No.11998034

all the answers for A-F are correct, it's just the function I'm having trouble with.

>> No.11998037

What's the exact order in which is preferable to read the books in the picture?

>> No.11998041

Oh, right.
Put 1 in.

>> No.11998044

I have a solution but need time to TEX it out

>> No.11998051

1. Copi's Introduction to Logic/How to solve it
2. Pinter's a book of set theory/Halmos naive Set theory
3. Wooton's Analytic Geometry/Mishra's Functions and graphs
4. Uspensky's Theory of equations/Lang's introduction to linear algebra
5. Spivak's Calculus/Courant's Analysis
6. Kurosh's Algebra
7. Kwak's Lineal Algebra
8. Apostol's Analysis/
9. Ross's Courses in probability
2.5. Evan Chen's Euclidean geometry/Brualdi's combinatorics
3.5 Andreescus' Complex Numbers/Kisilev's geometry
4.5 Andreescu's number theory
5.5 Costas Efthimou's Functional equations/ Niven's Maxima and minima
6.5 Demidovich's Analysis problems
7.5 Wallace's Groups, rings and fields/Scott's Group theory
8.5 krasnov's integral equations
9.5 Hay's Vector and Tensor analysis/ Munkres' Topology

>> No.11998054

I don't understand why it was a constant?

>> No.11998066

The integral of the constant 1 function along a "space" returns the "space"'s "volume".
For example:
[math]\int _{a}^b 1 ~ dx = b - a[/math]
For another example, this time the area between [math]x = a[/math], [math]x = b[/math], [math]0 < y < f(x)[/math] is [math]\int_a ^b \int _0 ^{f(x)} 1 ~ dy ~ dx = \int _a ^b f(x) ~ dx[/math]

>> No.11998075

ohhhh I see, thanks!

>> No.11998165


>> No.11998263
File: 163 KB, 850x1202, __yakumo_ran_touhou_drawn_by_chanta_ayatakaoisii__sample-506ff3a5c6693b46c1b0fba342a0479d.jpg [View same] [iqdb] [saucenao] [google] [report]

Best of luck.
Left to right, top to bottom, but if you chose Pinter you'll want to go back and read one of the other algebra books later.
And if you choose Spivak, you still need to read some book about vector calc.
Also, you might want to take two minutes to read the Picard-Lindelof theorem proof somewhere at some point. Preferably before Lee's Smooth Manifolds, since iirc he used it to prove the existence of Flows for vector fields.
The chart wasn't made to be actually followed and is provided as is with no guarantees express or implied.
>has book about functional equations
Literally impossible to take seriously.
>has a book about integral equations
List redeemed.

>> No.11998358
File: 54 KB, 870x350, Screen Shot 2020-08-11 at 2.09.20 PM.png [View same] [iqdb] [saucenao] [google] [report]

Can't figure this one out either. It's a paraboloid along y where only the first octant is being considered. It complains my domain for [math]uz[/math] is wrong, which makes sense because the domain goes from -x to x, which is out of the first octant. But I'm not sure what else to write, or if that's even the problem.

>> No.11998361


Oops, that was me just entering shit to check error messages. I had [math]\sqrt(y-x^2)[/math] orignally.

>> No.11998388

What's the (topology) interior of [math]S^1[/math]? Is it [math]S^1[/math] minus a point? Which point would it be?

>> No.11998407

Yes you can, but the whole point of using different coordinate systems to take advantage of the symmetry of the given problem.
Not saying that it can't be done but it's probably not the most practical way to go.

>> No.11998414

Okay, but what iq do you need to be to successfully get through all these books?

>> No.11998417

Thanks fag for your service you're very usefull. Keep it up!

>> No.11998420


>> No.11998441

Ok I just cleared that up, I was confusing the subspace topology on [math]S^1[/math] instead of [math]S^1[/math] as a subset of [math]\mathbb{R}^2[/math].
I am truly the lowest of brainlets.

>> No.11998776

ChemE>EE, in the sense that people studying ChemE have higher IQs than thos studying EE. The fact that so few ChemE's browse this board proves it.

>> No.11998885

Can we escape this universe into another one? Could the laws of physics be different in another universe? Could fire freeze things?

>> No.11998891

feasibly, no
can the laws be different? sure. but it would have to be a different universe which we aren't sure exists or not. there's nothing stating the laws of physics have to be what they are, they're just observed to be true
could fire freeze things? what the fuck does this mean

>> No.11999111

>easier grading
Used to think this was stupid, until I started working as a grader myself.
When you've gone through 100 exams and more than half of the students don't follow directions for factoring their answer completely, it tends to get on your nerves.

>> No.11999375
File: 210 KB, 1500x688, do you tho.png [View same] [iqdb] [saucenao] [google] [report]


>> No.11999703


>> No.11999737 [DELETED] 

It's [math]\sqrt{10}[/math] or [math]\sqrt{10-y}.[/math]

>> No.11999754 [DELETED] 

It's either [math]\sqrt{10}[/math], or it's [math]\sqrt{y-10}.[/math] I'm leaning towards the latter.

>> No.11999763 [DELETED] 
File: 13 KB, 684x107, mama.png [View same] [iqdb] [saucenao] [google] [report]

I'm apparently setting integral up wrong, pls halp

>> No.11999777

You need to slice the graph on the [math]yz-[/math]plane, and you'll get [math]\sqrt{y}.[/math]

>> No.11999780

ah shit thanks homie, noted

>> No.11999994

Is there any material for learning how to use a proof assistant?

>> No.12000094

where is it?? >>12000000

>> No.12000225

The scalar product of two vectors measures the projection of one vector onto the other one. Since projection depends on the angle in Euclidean space, you can think about measuring the angle between the vectors. If they are 'similar' (= have similar direction), the projection will be large. If they are perpendicular to each other, projection is zero.

The concept is very useful because 1) it allows to talk about angles (or projections, rather) in vector spaces other than Euclidean; 2) any scalar (or, rather, inner) product induces norm which induces metric - and so we can talk about distances between abstract vectors.

One of the most useful examples is a vector space where vectors are functions (like cos(x)). As soon as you introduce an inner product, you can project one function onto another, and compute distances between functions. This allows us to perform analysis - convergence, Fourier series, functional derivatives, etc.

A vector product, by definition, is a vector in a direction that is orthogonal to both of the original vectors, and has length equal to the area of the parallelogram spanned by the two vectors. Vector product is an analog of a much more general concept of an exterior product which is something that allows us to compute volumes. Tthe exterior product on a generic vector space can only be defined for forms and not vectors (form is something that eats vectors and gives you a number, and is linear).

The result of an outer product is also a form and not a vector. In particular, a product of two forms is a 2-form which eats two vectors and gives oriented area of a parallelogram. This explains why vector product gives you area. To transform the product output (the 2-form) into a vector, you have to have some additional structure (like a scalar product). However, this only allows for assigning a vector to a 2-form in either a 3-dimensional or 7-dimensional space. Historically vector product appeared from Hamilton's quaternions.

>> No.12000276
File: 67 KB, 770x444, FBD.png [View same] [iqdb] [saucenao] [google] [report]

Sort of an engineering/kinematics question. What the hell is a kinetic diagram? I'm supposed to make them for my summer class and I keep getting it wrong. Google doesn't really specify and I know it's not a FBD because I got that wrong. Can anyone explain or maybe sketch one out of a simple pendulum?
pic related is a FBD since idk how to make a KD and my professors comment

>> No.12000567

kinetic means when t is fixed, so fix a time and draw the forces+ frame x, y, z

>> No.12000627

Oh wow! Please share

>> No.12000665

why do i feel fucking brain damaged after having been exposed to a 28-30C indoor temperature?
>inb4 git gud pussy
it's clearly warmer than ideal for human productivity, and warmer countries tend to be less developed and be populated by lazy brainlets

>> No.12000685

Go for the calibrated one if you're doing anything quantitative.

>> No.12000689

It won't make you retarded, it'll just make you worse at what you're trying to do. If I try to do my homework while I cook, I'll make mistakes in my homework and/or fuck up my meal, but I won't lose cognitive function.

>> No.12000698

relax nigga
meditate and slow your metabolism

>> No.12000894

Could someone explain to me what support functions are, I've heard they generalize tangents in higher dimensions but that doesn't make sense since they are defined as the distance between a set and it's hyperplane? What's a hyperplane?

>> No.12000983
File: 61 KB, 1920x1080, draft.png [View same] [iqdb] [saucenao] [google] [report]

why is there a gust of wind (the blinds on my open window move a bit, but I can not feel it) when my neighbour opens and closes the door?
my own door is fairly well-isolated

pressure has always fucked with my head

>> No.12001022

you'll get used to it in a week

>> No.12001039
File: 82 KB, 208x208, 208x208.png [View same] [iqdb] [saucenao] [google] [report]

How does one do mathematics?

I read the essay A Mathematician's Lament by Paul Lockhart, and it got me thinking on what it really means to do math. I myself am an data science student, with a math minor. But I've always been interested in mathematics, and decided to use the free time coronavirus gave me to self learn the stuff I won't learn in school, like abstract algebra. However, I came across this essay, and it got me thinking of what it truly means to do math.

I understand what it means to do coding/writing/data analysis: you have to make something. You can't learn coding only by reading books, you can't learn to write stories only by reading fantasy, and you can't analysis data only by seeing what others do: these are all steps of the process, not the process itself.

But from what I understand, (again, from what I, a noob, understand) there's nothing like that for math. There's competitions, doing exercises in the textbook, or research, and competitions in my experience is just really intense exercises. Is self studying from a textbook, like how the wiki says, https://4chan-science.fandom.com/wiki/Mathematics says, enough to say you do mathematics?

>> No.12001044

I came up with an interesting-to-me problem that I'm having trouble conceptualizing an answer for.

I'm trying to come up with something that, when given two other functions f(x) and g(x), outputs the function that always stays directly between the other two functions.
A physical intuition I've come up with is that f(x) and g(x) both have a "pull" between them. The more one of the function pulls, the harder it would deflect the line between the two.
I've noticed two properties for the thing. One, the output function should always pass between the points of intersection of the two functions. Two, if f(x) and g(x) are inverses, the output function would be the identity function y=x

I don't know how to actually solve this though. "Pull" tips me off that it's going to deal with second order derivatives, but since this is supposed to take in any two functions, I don't think a regular second-order differential equation is sufficient.

Would this be solved with the Calculus of Variations?

>> No.12001051

That's just the convex property of functions, check out convex optimization, it actually uses calculus of variations and lagrange multipliers, if you did math up to calculus 4c you'd know this.

>> No.12001053

that explains it, I've only done up to ODEs and calc II

>> No.12001103

Do I need to use Stoke's Theorem to find what points belong to the boundary of the set of an annulus?

>> No.12001105
File: 2 KB, 169x110, 1573658353685.png [View same] [iqdb] [saucenao] [google] [report]

I honestly don't see how you simplify the top to the bottom I'm feeling extra dumb today.

>> No.12001112

Multiply both top and bottom by the denominator but switch from adding to subtracting.

>> No.12001147
File: 95 KB, 283x343, 1596526225700.png [View same] [iqdb] [saucenao] [google] [report]

I got [math] -2\sqrt{3}-10 [/math] now and I keep finding errors so I know I made some big fuck up in my early calculations.

I think I'm just going to take a shower and a nap, I shouldn't have left all the semester homework for the last week honestly, I got the dumb.

>> No.12001157

You should get -2*sqrt(3)-4 as your new numerator and -2 as your new denominator. Then simplify and you get 2+sqrt(3)

>> No.12001180


>> No.12001195
File: 27 KB, 700x467, 1583878742628.png [View same] [iqdb] [saucenao] [google] [report]


Just gotta keep track of the minus signs bud

>> No.12001225

No closed form, though :(

Do share!

>> No.12001241

after taking a shower and getting some hot cocoa I fucking did it, I feel so dumb now for asking simple shit.
Thanks anons, you guys are amazing.

>> No.12001249

>https://4chan-science.fandom.com/wiki/Mathematics says, enough to say you do mathematics?
dieudonné said a mathematician is guy a who published a novel proof of a theorem, that's it.

>> No.12001316

Probability of rolling a 1 at least 600 times out of 1000 rolls on a 4 sided dice?

>> No.12001332

Is degree in materials engineering worth it or will i be unemployed for life?

>> No.12001388

CDF of the binomial distribution

>> No.12001398

Is medical research in America looking to be a good career path or will I just be cucked by pajeets?

>> No.12001425

sounds pretty niche t b h

>> No.12001467
File: 20 KB, 248x248, 1569950729430.jpg [View same] [iqdb] [saucenao] [google] [report]

how do you become smarter?

>> No.12001483

so what's the deal, do good GPAs not carry as much weight anymore due to COVID, since everyone's just cheating?

>> No.12001493

get air cond

>> No.12001505

it will become easier to get a job without a degree with boomers retiring and more people getting redpilled about the college jew


>> No.12001603

Gravitons are hypothesized and generally accepted to exist, although specific details vary since we don't have a verified theory of quantum gravity yet. We have not experimentally observed gravitons and may never do so, because gravity is such an incredibly weak interaction. But an experimentally proven theory of quantum gravity may indirectly verify the existence of gravitons.

What do you mean by "undergrad branches"? This phrase doesn't make any sense to me.

>> No.12001645

For an unbounded self-adjoint operator [math]A[/math], is there any alternative (but equivalent) way to understand [math]f(A)[/math] besides the spectral theorem? Of course in the bounded case you can talk about a series expansion if it converges etc. (e.g. Taylor series of [math]f = \exp[/math]), but this doesn't work for the unbounded case.

I'm most curious about whether such an alternative approach, if it exists, could be used for practical computations. For example, in linear PDEs involving the Laplacian you take formal solution as being something like [math]e^{-\Delta t}[/math] acting on the initial conditions, which you actually compute by diagonalizing [math]\Delta[/math] (by separation of variables, for instance). I wonder if there is approach that will still give me a workable representation of [math]e^{-\Delta t}[/math].

>> No.12001695

Hmm... I'm not sure if it fits your needs, but you should take a look at references on the heat kernel expansion. There are several methods using this expansion in spectral geometry. For a review, there is: https://arxiv.org/abs/hep-th/0306138 (but its more physics-related)
To a more mathematical-inclined ref., there is a book called "Asymptotic Formulae in Spectral Geometry", by P. Gilkey (i think it can be found on libgen)

>> No.12001776

>For an unbounded self-adjoint operator A
>A, is there any alternative (but equivalent) way to understand f(A)
>f(A) besides the spectral theorem?
in predicative maths, there is only the spectral method, check Bas Spitters work
and his phd thesis

. IF there is another method it will be only in classical maths.

>> No.12001791
File: 310 KB, 1920x964, J.png [View same] [iqdb] [saucenao] [google] [report]

>cost function is a sum of dozens of functions
>some are convex and some are concave
Is there an algorithm that is guaranteed to find the global optimum?

>> No.12001792
File: 4 KB, 845x168, volumeTriple.png [View same] [iqdb] [saucenao] [google] [report]

So x goes from [0,2], y [0,2] and z [0,4]. So if my integral is dxdydz, the bounds of each integrand is just 0,2 for dx, 0,2 for dy, and 0,4 for dz right?

>> No.12001798


>> No.12001810

no, because then you're integrating over a cuboid of side lengths 2,2,4, instead of the triangular-shaped region defined by that plane.
Your bounds of integration will not be constant for 2 variables. Say you start with the z integral, you'll be integrating from 0 to something like 4-2y-2x, etc..

>> No.12001817

yeah all the partial derivatives will be 0 at an extrema

>> No.12001835

ahh, duh thanks. So if my order of integration is dzdydx, then I'd have z from [0, 4-2y-2x], x from [0, 4-z] and y from [0, 4-z]?

If so I think I get it

>> No.12001844

not sure which doors correspond to what in this diagram

>> No.12001849

close, but whatever you integrate last can't have earlier variables as your bounds of integration, otherwise you're going to end up with an answer that isn't a number.
so if your first integral is over z, you can't have z in any of your following integrals.

>> No.12001855

so would I be doing dz [0, 4-2x-2y], dy [0, 2], dx [0,2]? or dy need to be something in terms of x?

>> No.12001864

>just solve a huge system of nonliear equations bro

>> No.12001871

in general, it's helpful to think about the problem this way:
if your bounds are [0,2] for x and y, then that means you're integrating up to the point 2,2,z. is this point valid geometrically? well if you impose the condition on z that you did, then yes.
as long as this is true for any points x,y,you can pick, then your bounds of integration for x,y are just [0,2]. if you need to impose another condition for y to restrict your region, you can do that.

>> No.12001873

yes that's literally what you have to do
turn it into a linear algebra problem and solve it on a computer in 5 microseconds

>> No.12001874

>Of course in the bounded case you can talk about a series expansion if it converges etc. (e.g. Taylor series of f=exp), but this doesn't work for the unbounded case.
Couldn't you still talk about pointwise convergence, tho? Not [math]\exp (A) = \sum \frac{A^n}{n!}[/math], but [math]\exp (A) x = \sum \frac{A^n x}{n!}[/math]?
I wouldn't be surprised if the convergence of the usual Borel functional calculus of exponential of A evaluated at x existed if and only if this pointwise power convergence happened.
>Is there an algorithm that is guaranteed to find the global optimum?
See the first response.
tl;dr I don't think your conditions actually help with anything.

>> No.12001883

Could someone explain to me what Stephen Wolfram's computation physics autism breakthrough means? Like, what exactly is he doing? What I gathered was that he's basically throwing shit at the wall until it sticks by taking really abstract yet fundamental math, and seeing which combinations of shit result in laws in math that results in the laws of physics that we empirically observe. Because he can disregard huge swathes of possible-systems that don't have laws we see in our world, he hopes to eventually narrow it down to a selection of systems that can be used to predict new phenomena.

Did I get this right? Where am I wrong?

>> No.12001885

thanks buddy

>> No.12001930

Any quantum physics/quantum computing nerds here? I'm trying to understand pulse level programming and when I would want to use it.

If I'm understanding it correctly then it can help me perform better calibrations on qubits and optimize gate errors. However I've also seen discussion about transmon qubits and coherence times.

I'm honestly just a little lost.

>> No.12002108

>nonlinear system of equations
>just turn it into a linear algebra problem, bro
>inb4 just solve the nonlinear equations
You just went from testing a lot of initial guesses for the optimization solver to testing a lot of initial guesses for the equation solver.
>tl;dr I don't think your conditions actually help with anything
I'm not sure why you concluded this from the link you posted.

>> No.12002278
File: 15 KB, 834x152, tripleMOM.png [View same] [iqdb] [saucenao] [google] [report]

Suprise suprise, it's me again. This time trying to check that I set this up correctly.

\int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} \int_{0}^{3} (9-((\rho)^2sin^2(\phi))(cos^2(\theta)-sin^2(\theta))\rho ^2 sin(\phi) )d\rho d\theta d\phi

>> No.12002384

Looks correct to me.

>> No.12002481

Thanks, obviously I had factored the original expression after converting to spherical. But glad to know it looks good.

>> No.12002498

Cosmology question :
Susskind in his talks say the universe is a closed system (or will be when the Hubble constant reaches equilibrium and stops changing) because, in a universe with constant H, objects can never leave nor enter the cosmological horizon (which horizon is he talking about precisely, I don't know). And that as such the cosmological event horizon is something like a big black hole surface where objects get closer and flattened but never cross it.
How can that be true? I mean I understand why an object can't enter our universe because it would have to move faster than light, but why can't objects just leave? They can just leave it by staying immobile in space and let expansion do the work can't they?
Or is it some GR fuckery I should just study GR to understand?

>> No.12002733
File: 61 KB, 980x1674, lft_reg.png [View same] [iqdb] [saucenao] [google] [report]

Why wouldn't pic related work? Seems like the most obvious way to fit a linear fractional model, but no one does it.

>> No.12003038

should not matter
all doors are closed except for one which is opened and closed
the blinds shudder in a room that has a closed door as a result

>> No.12003546
File: 49 KB, 697x509, linkage.png [View same] [iqdb] [saucenao] [google] [report]

I'm trying to find the work done by the motion constraint of the 4-bar linkage system(pic related).
[math]W_{motion} = \tau_{motion, torque}\Delta\theta_O[/math]
I ran it in a simulation so I know the angles and angular velocities of all the components, but I'm not sure how to set the equation up, or what [math]\tau_{motion, torque}[/math] is really referring to.

>> No.12003581

I've got a little more than 15 days to study for a math class that involves the following

>partial derivatives
>double intergrals
>triple intergrals
>line intergrals

any online resources that I can study that doesn't go on for 10000 pages with a bunch of definitions and just goes straight into the catch with some clear explanations for a beginner in this subject?

>> No.12003639

paul's online math notes

>> No.12003681

not solution, but might give ideas

>> No.12003799
File: 24 KB, 789x667, cap flux.png [View same] [iqdb] [saucenao] [google] [report]

In this charging capacitor with electric field confined to the space between the plates, is there a magnetic field outside the plates due to the displacement current or not?

In the differential formulation, because the electric field at the point outside the plates is absent (and constant), any magnetic field there would be irrotational.

In the integral formulation, it appears there would be a magnetic field out there because the point is on a closed path through which the electric flux is changing-- unless the total path integral is somehow zero.

So is there a non-zero irrotational magnetic field there?

Do you know the masses or rotational inertias of the members?

>> No.12003820

Yes I know the mass but rotational inertias of the members

>> No.12003936
File: 175 KB, 1024x765, 1594487491111.jpg [View same] [iqdb] [saucenao] [google] [report]

Big Brain Question: The Custodian™ in your apartment had 14 packages of light bulbs. After using 22 bulbs, he has 8 packages and 2 bulbs left. How many bulbs are in each package?

>> No.12004002


>> No.12004045

That's fucking bullshit, W T F

I was looking through some old papers (throwing crap out) and my younger brother answered the same fucking thing and got marked wrong

It was like 4AM and despite being a 2nd year Comp Sci moron I was like wait wat and then I was like it has to be 4

remedial college math is a fucking scam

>> No.12004071

dumb dumb

>> No.12004287

Any opinions on chemical engineering? I'm from argentina if that changes anything.

>> No.12004312

Good choice if you can find a sector you care about and can handle the university course. Make some good money.

>> No.12004319

it's fun

>> No.12004359
File: 40 KB, 828x618, data.png [View same] [iqdb] [saucenao] [google] [report]

what would this data distribution be called, where can I read up some info on how to analyze pic related? clearly it's got an upper and lower bounding line but is that the extent of what you can get out of it?

if it matters each data point is a 'processor' that has a number of jobs and a time to finish. so the finish time is dependent on the number of jobs and the jobs are high variance.

>> No.12004360

Who has the table of universal (valid for all unit systems) Maxwell's equations? I remember seeing it once where each of the equations had an arbitrary constant multiplier like a kappa or a beta and then the constant multipliers were all constrained in their relationships to each other and to the speed of light or 4pi or something.

>> No.12004383

Literally every source of light is designed to flicker ina high frecuency. Old lightbulbs at 120hz, LED screens and lighbulbs at whatever the pwm thingy is set to (or 120hz if they have shitty circuits), fluorescent are even worse and have complerte shit frecuency, you can see the blinking in most. Wtf?? really. Why the fuck would you use PWM instead of less LEDs? Eficiency is probably not even really improved... same with the fag fluorescent bulbs.

>> No.12004397

Take logs.
Is there any other structure to the data? Are there any levels you can break it into?
It looks like there are at least kind of clusters, are they meaningful groups?

>> No.12004403

sorry, this was an MSpaint representation. there are no clusters, it's pretty much completely even throughout, only difference is the decreasing density

>> No.12004423
File: 28 KB, 970x500, 0857da586028805d8c0ddfbff41afff80.png [View same] [iqdb] [saucenao] [google] [report]

Have you tried looking at the data in polar coordinates? It looks kind of like it could be approximated by uniformly choosing a norm and then uniformly choosing an angle between the two bounds.

>> No.12004540
File: 3.83 MB, 2048x1536, 5F230F1F-A43B-4F17-91CA-8BAB3635FDBB.png [View same] [iqdb] [saucenao] [google] [report]

Hey does anybody know of book of like first year calculus with loads of pictures and explanations? I’m rarted and will die without some good pictures.

>> No.12004597


>> No.12004855

Hello fellow argie
Where are you going to study?

>> No.12004868

you can compute the result explicitly for h =/= 0.
Im not sure what you mean when you say it is not exact?

I doubt the way you intend has a mathematical definition.
The only thing i can think of with respect to exact is exact sequences which dont have so much to do with derivatives.

>> No.12005074
File: 1.60 MB, 1200x628, file.png [View same] [iqdb] [saucenao] [google] [report]

what happens if you cut a vein? like pic related, if you were to take a knife and slice this thing in half, what happens? does the receiving end shrivel up and die? what about all the little branching paths? Do they deflate? and when it heals over, does it reconnect two the two halves, or does it just seal the ends of each? will a new vein grow to replace it if that's the case?

>> No.12005120

> Im not sure what you mean when you say it is not exact?
He means that the quotient for some finite h isn't (exactly) equal to the limit.

>> No.12005252

Is [math]f(x) = 2^{x-3}[/math] the same as [math]f(x-3)[/math] ?

>> No.12005267

no, f(x) and f(x - 3) are different things
if g(x) = 2^x, then f(x) = g(x - 3)

>> No.12005292

Im trying to find a harmonic conjugate of u(x,y)=x^2-y^2-x-1.
My attempt: du/dx=2x-1=dv/dy => v(x,y)=2xy-y+c(x)
==> c(x)=x+c
My teacher told me this was incorrect but i cant seem to find where i went wrong. HELP

>> No.12005296

And why if i have an exponential function like [math]h(x) = 3^{x-3}[/math] then the graph moves 3 units to the right? shouldn't it move 3 units to the left (negative)?

>> No.12005309

Check your work with [math]\frac{\mathrm{d}v}{\mathrm{d}x}[/math].

>> No.12005325

When you have a graze or light cut, where is the blood coming from?

>> No.12005327

there is no "irrotational magnetic field" while the capacitor is charging, unless you consider spurious fields from edge effects.
when it's charging you get a circulating magnetic field that circulates along the axis of the capacitor

>> No.12005329

3^0 = 1
where does 0 go when you change from x to x-3

>> No.12005335

that's a common (but wrong) intuition
take [math] f(x) = 3^{x} [/math] and [math] h(x) = 3^{x - 3} [/math]. as you already understand, that's just a translation along the [math] x [/math]-axis. so, the images of [math] f [/math] and [math] h [/math] are exactly the same, right? for a given value of [math] f(x) [/math], say, [math] f = 3 [/math], we see that such value occurs at [math] x = 1 [/math] ([math] f(1) = 3^{1} = 3 [/math]). now, what about [math] h(x) [/math]? you can easily see that it actually occurs at [math] x = 4 [/math] ([math] g(4) = 3^{4-3} = 3^{1} = 3 [/math]). so, in order to obtain a given height of [math] f [/math] using the other function, we had to evaluate it at [math] 3 [/math] units to the right

>> No.12005354

Think the other way around. You are not moving the function, you are moving the x axis. So, you really changed the axis 3 units to the left, which, from the perspective of the graph of the function, makes it move 3 units to the right

>> No.12005378

any1 have a resource, or image, with the magnetospheres of each planet in our solar system and the sun, so i can see them relative to one another?
Particularly with orientation and strength and direction of rotation of the planet

>> No.12005379

ok, let me say something, I don't know where this came from, but I tried everything and nothing of value came about. This probably cannot be cast in a closed form, using known constants &/or values of elementary functions.

>> No.12005386

Thanks anons

>> No.12005408
File: 3 KB, 281x224, DiffY.gif [View same] [iqdb] [saucenao] [google] [report]

What is a better way to word a "range interval" for a given function that more informatively denotes what it is? All I'm trying to do is describe the (dy) differential for a standard function of one variable, but I can't think of the most efficient way to word it. My first instinct was to call it the "difference in height" between the point on a line tangential to the given curve and another point along that line an arbitrary distance (dx) away" but to describe it as "height" completely misses the point. It's an interval of solutions or a solution set but even describing them as "solutions" implies that there was a problem that needed solving, which again is not relevant. How can I describe this interval of solutions in a way that doesn't miss the point? My mind is blank. Pic somewhat related.

>> No.12005409

thank you very much!

>> No.12005413

Where can I buy a 1Hz power supply? At least 75VA. Money is nothing to me.

>> No.12005435


>> No.12005457

Well, I took my chance in an estimate of a upper bound, using
[eqn] \sum_{k \in \mathbb{Z}^{+}} \frac{\ln(k)}{k!} \leq \int_{1}^{\infty}\mathrm{d}\omega \hspace{2.8pt} \frac{\ln(\omega)}{\Gamma(\omega+1)} \, , [/eqn] but it appears that the integral also suffers from the same problem. Actually, I believe that this problem may be connected with the one related to the Fransén–Robinson constant [math] F [/math]: https://en.wikipedia.org/wiki/Frans%C3%A9n%E2%80%93Robinson_constant
> It is however unknown whether F can be expressed in closed form in terms of other known constants.

Numerically, however, we can see that this upper bound is very close to the value of the series. WolframAlpha gave me something like
[eqn] \left\lvert \sum_{k = 1}^{\infty} \frac{\ln(k)}{k!} - \int_{1}^{\infty}\mathrm{d}\omega \hspace{2.8pt} \frac{\ln(\omega)}{\Gamma(\omega+1)} \right\rvert \approx 0.0809088 [/eqn]

>> No.12005490

ah thx

>> No.12005496

be patient im writing out my sollution
i hope to have it done by tomorrow

>> No.12005512

Knowing that a group of bacteria triples every 20 minutes, and the initial population of bacteria was 20.000 i have to design a function that determines bacterias after a certain amount of hours

i came up with this:

[math]b(t) = 20000*3^{ \frac{t}{20} }[/math]

and i think it works, but what do you guys think, is it a good way to put this?

>> No.12005537

looks good to me

>> No.12005646

That's right, but the time argument of your function is in minutes. So, in order to calculate, for instance, the population after 1 hour, you have [math] b(60) [/math]

>> No.12005788

I just wrote an ML exam, one of the questions asked us to find the covariance matrix of 3 data points: (-1,-1), (0,0), (1,1), find the eigenvalues, and eigenvectors, and the PCs. Isn't the variance 1, the covariance 0, the eigenvalues = 1, and the eigenvector = 0? And aren't the PC's also 0?

>> No.12005992

I have kind of a fun question w/ practical application about control engineering. I never took the class so sorry for being layman-ish.
I have a plant that takes in 2 components and creates a widget outta em. I want to design a controller that will make the plant produce widgets at a certain rate. In summary I have a system that can take 2 inputs: the rates of change of the components, and has 1 output: the rate of change of widgets being produced. Assume I'm kind of more retarded than I actually am and I know nothing about how the plant actually works, I just want widgets flowing out. How do I design a controller to hit a quota of x widgets per second by controlling the inflow of components?

Practical example: I'm playing Factorio producing green circuits and I want to dynamically adjust the inflow of iron and copper plating to my (infinitely many) assemblers such that I can reach a set amount of green circuits per second that I've chosen, without going to the wiki and crunching all the numbers by hand.

>> No.12006219

UBA probably, or UTN. I'm thinking between EE or ChemE. I'm 21 though so I'll be graduating at 26if everything goes smoothly, that worries me a little but from what I've seen is not uncommon. These last two years I have been working as a mechanical technician (I'm from a technic school, electromechanic).

>> No.12006220

it's not 4

>> No.12006251

It is indeed 4.
14P - 22B = 8P + 2B. P = nB. Find n.

>> No.12006422

Capillaries are the smallest blood vessels in the bod, about one red blood cell in diameter, and are the last mile of blood delivery. Capillaries are small and have weak pressure, so light cuts and grazes are easy to repair by the clotting cascade.

>> No.12006534

human body anon, please answer >>12005074 too

>> No.12006558

Good list for once.

I really like munkers for some reason.

>> No.12006627

Do the stars in the milky way cause light pollution the same way it works here on earth. If our galaxy went dark will we be able to see more? Or if we have a satellite outside our galaxy will we be able to see much further away?

>> No.12006645

you bleed everywhere and if you're that old you die
>does it reconnect two the two halves, or does it just seal the ends of each?
not unless you stitch/glue them together.
>will a new vein grow to replace it if that's the case?
hell no.
You are seriously underestimating the gravity of that kind of injury

>> No.12006905

I'm a chemcuck who never really enjoyed calculus, but I've been told analysis makes it all better
Is analysis better for enjoying calculus

>> No.12006987


t. fellow chemcuck

>> No.12006999

why do we use milliseconds but not kiloseconds

>> No.12007005

You mean like the Zone of Avoidance?

>> No.12007034

because napoleon

>> No.12007044

Read Zorich’s Mathematical Analysis. Specifically chapters 5 and 6, you can completely ignore the rest of the book and volume II unless you have the patience for the full development of calculus on manifolds in which case read both books. He presents the best possible modern treatment of differential calculus, leaps and bounds above that of Tao and Rudin. I think the exercises are much less abstract and so probably inferior for the purposes of a mathematics undergrad but much better suited for scientists. There are no solutions provided nor will you find any online but that is part of the fun of these russian math textbooks.

>> No.12007049

meant for >>12006905

>> No.12007072

1 blood cell, seriously? Do they get blocked up all the time then?

>> No.12007089


>> No.12007134
File: 827 KB, 589x600, decimal time clock.png [View same] [iqdb] [saucenao] [google] [report]

During the french revolution a movement was made to change the way we mesure things, you know, the metric system
that extended to time as well, so for a time in france there was indeed "kiloseconds", so for writing time it was
>XI. Le jour, de minuit à minuit, est divisé en dix parties, chaque partie en dix autres, ainsi de suite jusqu’à la plus petite portion commensurable de la durée.
>XI. The day, from midnight to midnight, is divided into ten parts, each part into ten others, and so forth until the smallest measurable portion of duration.

>La centième partie de l'heure est appelée minute décimale; la centième partie de la minute est appelée seconde décimale. (emphasis in original)

>The hundredth part of the hour is called decimal minute; the hundredth part of the minute is called decimal second.

whe Napoleon came to power he removed decimal time because it was too confusing, and also the church kept using the old time we still use

>> No.12007138


nvm there was an error in my work :(

>> No.12007159

wow, interesting. who started the movement and why did they demand it? doesn't seem like it had a lot of connections to the overall goal of the revolution

>> No.12007160

I'm curious to see it anyway

>> No.12007171

long story short
the goal of the french revolution was to, as the name implies, revolutionize everything

>> No.12007215

but why time?

>> No.12007252

A good number of the french revolution lads hated absolutely everything with any relation to christianity and or royalty and tradition.

>> No.12007267

why not? the rest of mesurements (weight, distance etc) were changed too, it would not make sense to not also do so with time

nowadays we have mathematical ways to reach all these values, and that also includes a way to messure time mind you

>> No.12007277

so it's change for the sake of change?
>nowadays we have mathematical ways to reach all these values
that sounds like a backwards way to go about stuff, putting results first before methods

>> No.12007313

>so it's change for the sake of change?

>> No.12007333

very cool

>> No.12007378

is it really that bad? I see these things running all over the top of my hand. people get cuts all the time, are they just never deep enough to completely kill the vein then?

>> No.12007774

Worth it to pursue a chemical engineering degree at 26? I can afford it, however I'm not sure how it will be to be a new graduate at 30. Any opinions or siggestions? Anybody did something similar? I've been working in IT since I finished high school. It's not a bad job I have but I don't really feel too passionate about it. Of course, starting the degree would mean qutting it.

>> No.12007801
File: 18 KB, 550x156, Annotation 2020-08-14 123043.png [View same] [iqdb] [saucenao] [google] [report]

pls help me cheat in mi homework

>> No.12007817
File: 12 KB, 228x221, 1420358221200.jpg [View same] [iqdb] [saucenao] [google] [report]

I'm taking "physics for engineers" in two weeks and I've never directly studied physics in my life (outside of a few random physics applications thrown around in math classes here and there), how fucked am I? I did recently "pass" a Calc III class, though that means very little as my actual mathematical understanding is still pretty much Calc II level and I'm very shaky with vectors. Vectors are pretty important in physics, right?

>> No.12007832

my physics for engineers was split into 2 parts. first class was basically reiterate highschool grade 12 physics class, and then sprinkle some new info on the end, so nothing hard, then the secod class was continuing on from there and basically all new stuff, wasn't that bad, though the calculations sucked ass. the math you do tends to be simpler, like if you're using integrals, they will all be solvable with the same method so you don't have to study anything else, or similar

>> No.12007836


>> No.12007841

>Worth it to pursue a chemical engineering degree at 26? I can afford it, however I'm not sure how it will be to be a new graduate at 30.
A degree is a degree. Simply don't divulge to people how old you were when you got it. Don't expect to get hired at some prestigious high paying job unless your skill and knowledge happen to be DEMONSTRABLY off the charts. Hell, if you were that good, they'd hire you whether you had a degree or not. Basically just keep low realistic expectations and there shouldn't be an issue.

>> No.12007856

if its what you're passionate about then there's no good reason not to do it
as long as you don't have huge expectations of a better life and you realize that a degree is what you make of it, then there's no problem
you will fail only if you get stuck in a world of hypotheticals and baseless judgments from normies and your own mind

>> No.12007896

speed = 1st order derivative
acceleration = 2nd order derivative
force = mass times acceleration
torque = turning force

>> No.12007981

I already knew all of that. Does that mean I'm going to pass?

>> No.12007999


>> No.12008005

and vectors are just the things added up in each x,y,z dimension

>> No.12009305
File: 390 KB, 500x600, eirin_milk.png [View same] [iqdb] [saucenao] [google] [report]

Is properly reading through Bryant's book on exterior differential systems worth it or should I just look up the big results on wikipedia?

>> No.12009326

Maybe define x_n to be the Analogous expression that terminateS after the nth root Find a relation between consecutive terms and take a limit or find a steady state sort of thing. Not sure

>> No.12009378

How significant is weight in the top speed of production coupe type cars? Take, for example, a 4000 lb Veyron. How much rolling resistance would it have at 250 mph? Related question, how much horsepower does a car like that produce at top speed (how much total friction does it experience)?

>> No.12009428

It depends on context. 1,-1,i and -i are all units within the Gaussian integers because they have inverses therein.

>> No.12009432

Algorithms for optimal allocation of bets on many simultaneous events
I don't understand the results.
If I have simultaneous bets:
Should I bet each one the Kelly number?
Should I bet a fraction of the Kelly? (but every bet is different)

>> No.12009441

>this logic
does 1=-1? so then 1=0?

>> No.12009455

Are the legs in a split phase power systems necessarily an inverse of each other? The way I, vaguely, understand it is that they’re just hooked up to opposite sides of the winding so it’s similar to a single water pump where one side experiences a push and the other experiences an equal pull. So you can only get a 180 degree shift with split phase. Is this correct? Also, if not, is the way phase shifting occurs in in a two phase system significantly different than than in a split phase system?

>> No.12009470

Seems reasonable to me. But I think E will be singular. You’ll need a minimum length x or some other regularization. You have a sign error in line 2.

>> No.12009504
File: 382 KB, 1492x765, sets.jpg [View same] [iqdb] [saucenao] [google] [report]

I found an old set theory question on stackexchange, and one of the answers seems really wrong, but I don't know enough about set theory to be sure. See pic related.
As far as I can tell, 5 should be false regardless of whether it is referring to a subset or a proper subset.
One of the guys answering says that it actually becomes true if the notation means "proper subset of," but isn't that just making the relationship *more* restrictive?
To my understanding, Y is not a subset, proper or otherwise, of Z, because the null set is not in Z (although the null set is a subset of Z.)
And when he says "the null set is contained in every set," isn't that wrong? I thought the null set is a *subset* of every set, but it's not *in* every set. Or in other words, the contents of the null set are in every set, but the null set itself is not.

>> No.12009521
File: 1.88 MB, 500x281, giphy.gif [View same] [iqdb] [saucenao] [google] [report]

Are dark matter/energy real, or were they just invented by physicists to make the numbers add up? I know that our current theories of the universe don't hold up without them, but is there any evidence that they actually exist? If not, then it just seems like a desperate attempt to patch up incorrect theories.

>> No.12009537

Dark matter is a placeholder for "something that we can't observe via light that acts as an apparent mass" or something like that. it basically means our theories are incomplete because we can't explain galactic behavior without introducing something new that we haven't observed directly
there are many candidates for what dark matter might be. the current favorite theory is axions, because they answer the Strong CP problem as well.

>> No.12009579


For some reason they correctly define [math]\subseteq[/math] in the response to Q4, but then make a mess of it in Q5. I think you're correct though; [math]Y[/math] is an element of [math]Z[/math], not a subset.

>> No.12009586

is psychology a science?

>> No.12009593

why wouldn't it be?

>> No.12009600

idk some people say that it’s not a “real” science

>> No.12009609

those are also the people posting iq threads
it's not a hard science (hard meaning "pure," not "difficult") but it's absolutely a science. just complicated by the fact that we barely understand the brain and people are unreliable test subjects

>> No.12009626

oh okay, thanks! i was always confused if it actually was or wasn’t.

>> No.12009654

someone posted a pic for the trivium, and like a dummy i didn't save it. anybody have that?

>> No.12009730
File: 477 KB, 1351x1054, file.png [View same] [iqdb] [saucenao] [google] [report]

I found it. Here it is:

>> No.12009782
File: 1.86 MB, 2801x3913, 20200814_202029.jpg [View same] [iqdb] [saucenao] [google] [report]

When working with a transistor, what is the circuit that feeds the base and how do I find its Thevenin equivalent? Circuit is pic related.
I don't give a shit about circuit design, it's just an obligatory class for my Physics degree for some reason. I want to have an idea why.

>> No.12009972
File: 1.65 MB, 5500x6699, top.jpg [View same] [iqdb] [saucenao] [google] [report]

I'm running a 10s simulation of a spinning top and trying to find the time period of the oscillation by plotting the center of mass x and z-position.
Its almost entirely consistent from t=1.5s, but before that, the max and min amplitudes have a kind of zig zag spike before continuing with the consistent slope. pic related, top graph shows the first 2 seconds with the spikes, bottom shows first 4 seconds with consistent period.
I think this is how the program approximates the results, but I'm not sure. Did I fuck up somewhere along the way?

>> No.12009978
File: 64 KB, 564x795, keikakudoorknob.jpg [View same] [iqdb] [saucenao] [google] [report]

I do not really understand the person who asked it either
>1: \0 \in X
>I know this is false because the null set is not an element in any set
>2: \0 in Y
>I don't understand why this is true
>6: X=\0 and X \in Y
>Same reason 2 is true. I understand this one.

it is like the asker did not really think it through
stackexchange is such a shitshow

>> No.12009983

is it still wobbling from just having spun it?
it's hard to know without knowing what this program does. is it simply measuring x and z position? or doing some operation on it

>> No.12009986

it's even color-coded, bless you anon!

>> No.12010074
File: 1.31 MB, 960x540, topsim.webm [View same] [iqdb] [saucenao] [google] [report]

Yeah, when I simulate it with a step size of 0.01, it noticeably wobbles at the beginning. When I run it with a step size of 0.05 it looks smooth and normal.
The graph is tracing the center of mass of the top.
webm attached shows same simulation, step size 0.01 and 0.05.

>> No.12010081
File: 284 KB, 500x606, 1576729093021.png [View same] [iqdb] [saucenao] [google] [report]

why does nobody reply my stupid question>>12001467

>> No.12010090

it could be stabilizing? unless you're already initializing it in its stable motion
a smaller step size should always be more accurate. the larger step size might look smoother but that's just because it's ignoring the initial wobbling

is this a physics-based modeling? if not then forget everything I said because it shouldn't wobble if you're not including physics.

>> No.12010124
File: 108 KB, 1404x919, Untitled.png [View same] [iqdb] [saucenao] [google] [report]

I'm trying to proof that tower of hanoi can be done in [math]2^n-1[/math] steps. Can someone please check my proof?

>> No.12010178
File: 687 KB, 1537x2134, C1750A9C-58E7-404E-81AD-496F2F3EBE90.jpg [View same] [iqdb] [saucenao] [google] [report]

How to I remove the metal studs from these gluey vitality-sensing increments?
I tried putting it in acetone
I tried boiling it in acetone
I tried burning it in acetone
I’m at a loss

>> No.12010207

I'm not sure if that's the case, the was top started at an angle and was given an initial angular velocity of 40 Hz.
I don't think I did anything wrong, so I assume that the wobble/spikes are result of a numerical approximation
and this is physics based modeling.

>> No.12010229

well, you made a lot of statements but then, on an unrelated note, you said that it was impossible that moving dk requires fewer than 2^(k-1) - 1 moves, without saying why it's impossible.

I'll assume that it could be shown pretty easily with what you have if you just analyzed the recursive algorithm you're describing a little more, or maybe I'm just a brainlet.

>> No.12010280

Thinking of dropping my IT job and going in on Psychology at uni.
Is this really wise? I want to be a clinical Psychology but i heard it takes almost 12 years to get to that point.

>> No.12010453

How old are you? Whats your financial situation, do you have financial support? are you in the US?

>> No.12010467

Mo chemists INT?
Just Christopher Boone?

>> No.12010675
File: 171 KB, 724x1023, suwako_milk.jpg [View same] [iqdb] [saucenao] [google] [report]

I'm not saying you lads have to wait until I come over and make the thread right.
I'm also not saying you need to copy and paste the pasta or put a 2hu image on the OP.
But you need to put /sqt/ in the title, seriously.
Because it's asked every thread.

>> No.12010684

if then why isnt the answer on the OP?

>> No.12010886

Good fucking luck reading those books without the constant guidance of a high-ranked institutions.

>> No.12011099


>> No.12011117

I'm learning damped oscillations.
This "variation of roots with damping ratio" diagram is confusing
Can't figure out why the things circled in green are where they are.
4channel has blocked my country from uploading images, so here it is : https://i.imgur.com/5rGAC3W.png

>> No.12011119

Would appreciate if an anon would directly post the image here

>> No.12011151
File: 113 KB, 1078x891, 5rGAC3W.png [View same] [iqdb] [saucenao] [google] [report]


>> No.12011161

Say i have [math]a \cdot c = b[/math]

I know that [math]a = \frac{b}{c}[/math] is valid but what about [math]c = \frac{b}{a}[/math] ? is this valid? i never got clear when is it valid to pass a product as a division in the other side ot the equation

>> No.12011177

what have you tried?

>> No.12011188

nothing, thats why i asked what you are supposed to do

>> No.12011191

Never seen an answer to it that's actually worth archiving. Just grab some advice from google lmao.
>is this valid?
>i never got clear when is it valid to pass a product as a division in the other side ot the equation
When the term you're passing is non-zero.

>> No.12011197

>Strong CP problem
Pedobear is a physicist now?

>> No.12011208

Alright understood, it's just where one of the roots lie on x axis when zeta equals that value.
imo that's a really confusing way to label

>> No.12011230

replace dot product with cross product, now is it still valid?

>> No.12011231

The roots of s^2+2.ω0.ζ.s+ω0^2=0 are s=-ω0.ζ±ω0√(ζ^2-1). In the time domain, x(t)=a1.e^(s1.t)+a2.e^(s2.t) where s1, s2 are the roots.

If ζ=0 (undamped), then s=±i.ω0; in the time domain, this is a constant-amplitude sinusoidal oscillation.
If |ζ|=1 (critically damped), then s=-ω0.ζ, a duplicate root which is real and negative. In the time domain, this is a.t.e^(-ω0.t).
If |ζ|<1 (underdamped), √(ζ^2-1) is imaginary so the roots form a complex conjugate pair; in the time domain, you have (e^-ηt).cos(ωt+φ), i.e. an exponentially-decaying sinusoid.
If |ζ|>1 (underdamped), √(ζ^2-1) is real and you have two distinct real roots, meaning exponential decay in the time domain.

>> No.12011241

and what if i have [math]a + bc = d[/math] could i do [math]a + b = \frac{d}{c}[/math] if [math]c \neq 0[/math] ?

>> No.12011263

No, but you can do [math]\frac{a}{c} + b = \frac{d}{c}[/math].
You shouldn't think of it as "passing to the other side", you should think of it as "dividing both sides by c".

>> No.12011500

Thank you!
Was confusing at first but now it makes sense

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