/sci/ - Science & Math

>>8259781
For random variables I am trying to understand what the below equation means:

Pr[X=v] := Pr[X^-1(v)]

Is it basically saying the probability of v in set V is the same as the probability of falling into the pre-image of v in set U?

I can't do this fucking question
I'm not sure how to interpret it in the first place. I'll upload my working in a sec
I must be making a wrong assumption somewhere

>>8259897

>>8259897
turns out I didn't know what the com energy was

What is the path I should follow to be in the top 1% students of my department?

Undergrad physics here.

Are there any mnemonics for the construction of ray diagrams for convex/concave lenses and mirrors? Just purely introductory stuff.

Why does Faraday's and Amperer's equations have symetry in maxwell's equations, but not Gauss's laws for electricity and magnatism?

>>8260260
What do you mean symmetry?

>>8260270

>>8260252
If there were a cut and dry path, don't you think everyone would be doing it?

>>8260309
>>8260260

In the second equation, you could set up a symmetric variant, by setting it not equal to 0, but to some term corresponding to a "magnetic charge", just like you have the electric charge in the first term. This would, as far as I know, form a consistent mathematical and physical model.
However, we don't allow magnetic charges, as this would correspond to magnetic monopoles, which we do not usually observe.
Hope that's not too wrong!

>>8260316
Thats what i mean. Polarity of electricity and magnetism is not symmetrical. Why?

>>8260321
Because they are not symmetric phenomena. You'll find that special relativity handles electricity and magnetism in a very neat unified way, which I feel makes it very obvious why this asymmetry is justified. Basically, magnetism is more or less dependent on electricity, it results from movement of electric charges and nothing else, which is exactly what Maxwell's equations say if you analyze them in detail.
Probably not the most satisfactory answer? I'll let someone smarter than me handle that, but ever since I heard a good lecture about special relativity I always felt very at peace with the asymmetric properties of electricity and magnetism.

>>8260309
>>8260321

Because you shouldn't treat electric and magnetic fields as separate objects. Maxwell's equations look much nicer when you unify them.

>>8260313
Not necessarily. There are cut and dry paths to getting fit and not everyone is doing it.

If gases like to have uniform density in a container, how come the universe doesn't act like a container?

>>8260336
Thank you. So magnetism is a consequence of electrical "activity," so its not going to necessarily be symmetric.

>>8260338
I dont know how to do this yet. Im finishing up Physics 2. I dont think Ill ever get that far into physics because I was just accepted into the MechE program. The only classes ill go this far into electromagnetism is circuits and maybe materials and thermo, but i doubt materials and thermo will cover much of electromagnetism.

What I should know before taking mechanics of materials? I fucked things and I ending taking it before multivariable calculus and differential equations. Are those classes really important? or I need take them before?.

>>8260722
x=10; you have to repeatedly complete the triangle angle, interior angles always add up to 180, then you get to the last 4 unknown angles and you have to set up a system to get them all in terms of x and then bisect one of the triangles to create a right triangle and solve. At least that was how I went about it w/o trig. Hope that helps

>>8260809
What are you smoking?

>>8260252

I think you ahould learn how to /math/

Afaic lots of undergrad physicis math can br derived from simpler stuff with calculus so you dont havr to remember the whole book going into tests. Also shows that you are not just a nigger memorizing texts so whoever is checking youe test will be impressed at least

>>8260309
Nice. Looks like we're taking the same class senpai

>>8259781
Can I ask a question?

>>8260890
Engineers built the PC you are shitposting on right now, so...

>>8262128
Mathematicians and scientists made computers possible.

my question >>8262185

>>8262192
Why the fuck would you need to "reinvent" the entire math and make it math 2.0? That makes no fucking sense. It would be just exactly like it was with calculus when it was first invented, it was just a new way of doing math, it was still math, it wasn't math v1.1 or some bullshit.

Basically what I'm trying to say is, we wouldn't need to "reinvent" math, but rather invent new math and add it to already existing knowledge of math.

Is speed how quick/fast/rapid something is moving, or is it how much distance something covers in some time? (fuck off with "it's a magnitude of velocity", I already know that and it's merely one of the book definitions)

>>8262562
the former, though with constant speed the two are indistinguishable

>>8262586
Thanks!

>>8262562
>or is it how much distance something covers in some time?

what units do we measure speed in anon?

>>8262651
mg or %, depending on if you mean dosage or purity

For ease of typing just read = as a triple bar.

It seems that na^d = 0 mod a^d and of course a^(dn) = 0 mod a^d, but only if n is a natural number. Do modules only work with natural numbers, or am I just being stupid?

>>8262712
Just use ≡

>>8262712
>>8262731
[math]na^d \equiv d \mod a^d[/math]
[math]a^{dn} \equiv 0 \mod a^d[/math]
[math]a \in \mathbb{N}[/math]

How do you compute [math]\int \hat{r}dt[/math]?

[math]\hat{r}[/math] is the unit vector in polar coordinates.

I managed to find the answer, but only is [math]\dot{\theta}[/math] is constant

>>8262861
How is the unit vector changing with t?

>>8262872
[math]\dot{\hat{r}}=\dot{\theta}\hat{\theta}[/math].

Is that what you're asking?

Just started a Calculus 2 course and the professor (infamous for being shit) started the first day with a bunch of random shit that looks nothing like calc 1...(some sort of rotating 'slices' of a cylinder in a graph and then finding its volume by integrating bullshit)

What do

>>8262893
Give us a less ambiguous question. Spoiler alert: Calc II is the hardest calc course you'll take and III will be a breeze compared to it.

>>8262929
Sorry, yeah I've been hearing that from everyone around, but I'm scared because im juggling physics and a few other classes along with calc II

I just want to know what topics I should start trying to learn from now so I don't die

>>8262893
Volumes using cross sections? I'm pretty sure that's what's you're doing

>>8262954
Volumes using cross sections is from Calc 1

I want to get a headstart on my C++ class next semester.
Where should I start? Can you recommend me a text book?
This will be my first computer language

>>8262960
Well I just finished calc II and he literally just described what I did in the first lesson

>>8262954
Thanks for the lead, better than the "just slice shit up and integrate" explanation the professor gave.

>>8262967
You should try something like hackerrank.com where you can do a bunch of problems for c++ (and other languages) from the very basics.

Also YouTube tutorials I guess

Does it matter which school you go to?
I have 2 choices right now: One is a science and engineering school, the other is just a regular 4 year university, however in terms of engineering schools in my state, this school places a little lower than the Science/Engineering school.
I really want to go to the Science/Engineering school, but this one is a bit harder to get into. I also like the campus a lot better than the other. Is it really just school?

>>8263004
Just take the former m8. It's a fucking no brainer.

Do you think its possible to finish a Calculus course and a Physics course over the summer?

I decided to change my transfer school to a much better school and that I like more. If I can manage 5 classes each semester, then I can transfer there in 3 more semesters. This is only possible if I am able to complete these 2 courses in 5 or 6 weeks.

If possible, I would like to get a head start. What are some good calculus textbooks? I heard Spivaks Hitchhikers guide was good but I can't find a pdf for it.

Would you die if I pulled off the Riemann hypothesis?

>>8263004
Picking one with a nicer campus or where you think you'll fit in better is always a good idea. It won't make a huge difference which school you got to.

>>8262785
So is can you only use modulo arithmetic with natural numbers, or is it only in this particular case?

According to some logic manual exercises,
{Mercury, Earth} and {Mercury, Earth, {}} aren't identical
but I thought all sets contain the empty set

>>8263569
They aren't identical.
It's true that {} ⊂ {Mercury, Earth} (empty set is a subset of it)
but not that {} ∈ {Mercury, Earth}
This is because {} is a set of nothing, it is not nothing itself. It's kinda like how {{}} =/= {}
{Mercury, Earth} contains nothing as well as Mercury and Earth but it doesn't contain a set of nothing
Elements in the set {} are contained in {Mercury, Earth} but the set {} itself isn't contained, unlike {Mercury, Earth, {}}

>>8263569
>but I thought all sets contain the empty set
as a subset, but not as an element

sum [n=1..infinity] (sin(pi/nthprime(n)))

Does it converge? n=1..10^6 gives a small value of 8.822...

>want to transfer to 2 different schools
>same majors but each school requires a different science: chem or bio
wtf do i do? I'm planning on taking computer engineering and the school I REALLY want get admitted in requires chem. Also I read a reddit post from the universities board and someone said they're packed with computer engineers. Should I still try applying? Of course, I still have 1.5-2 more years to finish my prereq courses.

>>8259783
Yes, exactly.

>>8263892
>n=1..10^6 gives a small value of 8.822...
so does [math]\log(10^6)\approx 14[/math], and yet [math]\log n[/math] diverges.

I don't know if this is a satisfying answer, but according to Wikipedia, the nth prime number is bounded above by [math]n\log n + n \log \log n[/math] for n>5. Substituting for the prime, the series diverges according to wolfram alpha, which would suggest your series diverges as well since after a few terms its terms converge more slowly.

http://www.wolframalpha.com/input/?i=sum+sin(pi%2F(n+log+n+%2B+n+log+log+n+))+from+1+to+infinity
https://en.wikipedia.org/wiki/Prime_number_theorem#Approximations_for_the_nth_prime_number

What are the potential dangers of AI? you hear musk and hawking say it's scary, but why tho?

>>8264404
There's nothing to worry about, the AI takeover will be glorious. The limits of human stupidity will finally be surpassed.

What's cal grant b - subsistence and fees? I accepted both on top of my pell grant. Tuition is 7k, but all three of those financial aid goes to 12k. Do I still get all the money?

>>8263892
By the comparison test sin(pi/p_n) diverges if 1/(p_n log(p_n)) diverges.
Now use the asymptotic expression for the nth prime p_n ~ n log(n).
You get 1/(n log(n) log(log(n)) + n log(n)^2)
Again by comparison this diverges if 1/(n log(n) log(log(n))) diverges.
Now by the integral test that diverges if log(log(log(n))) diverges, which it does so the original series diverges!

>>8260252
there is no royal road to geometry

>>8264404
The potential danger is that it will kill everyone on earth, or take over human society, or something similar etc etc.

Its mostly bullshit popsci fearmongering. Very very very low chance of any of that ever coming close to happening.

>>8263892
By the comparison test sin(pi/p_n) diverges if 1/(p_n log(p_n)) diverges.
Now use the asymptotic expression for the nth prime p_n ~ n log(n).
You get 1/(n log(n) log(log(n)) + n log(n)^2)
Again by comparison this diverges if 1/(n log(n) log(log(n))) diverges.
Now by the integral test that diverges if the limit of log(log(log(n))) goes to infinity as n goes to infinity, which it does so the original series diverges!

>>8264443
Give me one good reason why this won't happen once we manage to create an AI more intelligent than a human

>>8259781
Help me understand gauss-bonnet formula. I don't get why it works and I don't get geodesic curvature.

Also whatever geodesic curvature is I don't understand why boundaries of caps on picrelated have different geodesic curvatures (they should since areas are different).

Currently doing my under grad in computer science and mathematics in my second year, but my question is what field of mathematics best compliments my studies in computer science. I've decided to focus on database management to hopefully become a DBA so which field of math goes best with it?

>>8262953
Yeah, it's a weed out course.
>Did you take Calc AB
>Did you take Calc BC
>If Calc AB=0, Then proceed to bang head against wall
AB tought you Cross Sectional Volume

>>8264450
IF we can create an AI smarter than humans. Theoretically if that was possible then what would even motivate an AI to start exterminating humans.

>>8263557
Yeah modulos only work with whole numbers, so natural numbers and integers.

>>8264450
I would use AI to establish the global communism :3

>>8262128
>engineers built the PC you're using
That would be physicists and mathematicians who made it possible. Engineers just took glue the parts together.

Will applied mathematics with some coding projects allow me to get a job as a programmer?

>>8264450
Well, why would the AI want to kill us? Why woudl the AI want to take over? How would it get the capability to do either of those things? Why would we make it with the capability? Why would we even bother to make an AI capable of wanting to or becoming capable of any of those things?

I mean, if we want a terminator scenario, there first has to be a prototype robot(s) made before the AI is even up and running that would be able to operate an entire robotics factory to multiply.

There are a fuckton of limitations on what a strictly non-corporeal being created and restricted by human behavior. Lets assume that Ultron gets onto the Internet. What's it gonna do? Shut it down? Remote access something that it realistically has no power to remote access? Even if it gets shut down, its a minor setback. We can just make a separate network and quarantine the AI.

There are just way too many hoops to jump through before an AI could ever become sentient, self-developing, self-sufficient, motivate itself to hate humans, and then find the capability to do something about it.

tl;dr its popsci. Movies taught you that AI is a danger. Its not.

>>8264483
No, modular arithmetic works much more generally than this. It's not interesting, say, in the rational numbers because every nonzero number has an inverse.

>>8264474
>implying they would exterminate us out of hatred or fear
There's simply more efficient uses for hydrogen, oxygen and carbon

An Ivy League uni professor just committed my private code which I shared with him via e-mail to his group's GitHub repo as his own.

I'm a PhD student at a different university.

What should I do?

>>8264608
pizza deliveries

>>8264608
Nothing at all. Keep writing code, I guess.

Where's the nearest black hole

>>8264643
yo momma's ass

Any of you people can provide some insight about Engineering Physics as a degree?

> inb4 it's a meme

I know that I just want to know if I'm going into the right meme

>>8264608
You have the electronic record of this event occurring take it to the authorities

How can I make the most out of my time in University studying Physics? How can I make the most out of it in the private sector?

Who is the first representant of a species and who does it reproduce with?
>there's none, it's a genetical continuum
Okay but what about species that don't even have the same number of chromosomes? How does an individual of the species that has more or less chromosomes than normal manage to reproduce, eventually forming a new species several generations later?

>>8264730
Two organisms don't have to have the same number of chromosomes to reproduce with each other

you guys know any free software that can simulate electrohydrodynamics.

also any good electrical engineering and physics texts with a focus on magnetic circuits, ionization and electric fields.

>>8264738
Aw, for some reasons I thought they did. Thanks anon

Is this correct? The guy I'm watching solve these went by some different approach, but we both got the same result.

>>8264770
I'd go with the other guy's approach if it's not upside-down

>>8264770
>[math]\infty - \infty[/math]
>infinity times 0
>[math](x+1) - (x-1) = 0[/math]
Yeah, you should probably listen to that other guy

>>8264720
>How can I make the most out of my time in University studying Physics?

By thinking outside the box and looking for industry internships for the summer so that you can secure yourself an actual physics position when you graduate and not end up as a teacher.

>How can I make the most out of it in the private sector?

Now do the opposite. While working stay in touch with academia. Maybe find a way to get a masters degree with your company paying for it and/or promising you a better position after acquiring it. If not then study part time anyways to get a masters degree to climb up the industrial ladder with your education. Getting an MBA is also fine.

>>8264805
I just realized what I did... it's too late to do math anyway.
>hey, I hab an idea, we god a walue of 1, why don't we just go ahead and muldibly id by 100000 and ged a million! :DDDD

>>8264488
>That would be physicists and mathematicians who made it possible.

lol, not even close m8. innovation happens in industry out of necessity, and its done by engineers. heres how the discovery pipeline really works.

>industry engineers discover something through educated guesswork/trial and error
>give a bunch of funding to a university and they have some physicist/math guy construct a rigorous framework that defines the phenomena.
>send it back to industry where engineers refine and reiterate

friendly reminder engineers were building functional steam engines long before the laws of thermodynamics were even conceived.

>>8264807

>industry internships.

I'll make this a top priority, thanks.

>>8264608
>>8264683
This, but consider asking him to give you credit first. If you don't mind him using the code it could be better for you.

More of a broad question, but how much material is in a calc1 course compared to say trig or precalc. I haven't taken math since highschool and I need to catch the fuck up on math if I want to graduate any time soon. I've spent the past month and a half grinding through through reviewing Alg I, learning II, Trig, Stats and just finished Precalc. I've been studying around 2-8 hours a day and I'm wondering if it would be reasonable to complete Calc 1 as well before I take a placement test at the end of the month, or should I just cool it and enjoy the rest of the summer? That said I don't hate the studying.

I keep reading that "calc is hard" but I read the same things about precalc and finished that in 4 days. Is it actually hard?

I need to make my mind up ASAP.
What' are the differences and similarities between Computer Engineering and Electrical?
I need to decide which field I want to enter.

>>8265448
Major CE minor in EE
There is a ton of overlap.

>>8265444
I just took a calc class over the summer. I wouldn't say it's hard, but you definitely need to know your material going into it. It was a 6 week class and we breezed through it. What's most important though is to know your trig functions because it's really important when graphing and solving various word problems.

>>8265448
You'll need to check the CE syllabus. Some places CE is basically a CS degree with slightly more focus on hardware, other places it's basically an EE degree with less analog stuff.

>>8264404
You know that trope where someone wishes for something and the genie misinterprets their wish? That's the danger of AGI. A popular example is the stamp collector, where some stamp collector asks an AI to get him as many stamps as possible. The AI could easily interpret this in an unexpected way and turn you, your mom, your dog, Earth, into stamps.

>>8264807
>getting an MBA is also fine

Don't fall for this meme, m8. It's a bad one.

An electric charge q creates an electric field E = qr/r^3 around it. Another charge q' in E will experience a force q'E.

Is it possible for q to experience a force from its own electric field E? If so, how would we describe this, or derive a formula for it? If not, why not? You might say because the field/force is radial, but there has to be a more fundamental explanation, no?

The same question then, but for gravity. Will an infinitesimal mass experience some influence from it's own gravity? I know that gravity is a weak force, but let's not wonder about quantities for now.

What the fuck is natural deduction good for? As far as a deductive system/proof system is concerned, it's so fucking inefficient.

Doing any sort of proofs in it for even rudimentary shit is painful, and in every way inferior to the tableaux method.

Furthermore, it seems like the axioms for the different inferences are way less intuitive despite its "natural" namesake.

>Axiom of Completeness. Every nonempty set of real numbers that is bounded above has a least upper bound.

What does this have anything to do with the set R contains no gaps?

The only way I understood it is that if we apply this axiom to N we will never be able to 'reach' that number given its irrational. But in R whatever finite number that we put as the upper bound, the least upper bound will "immediately" exist.

For instance in N and sqrt(2) as the upper bound, our least upper bound will not exist because we can never "reach" the number. But in R we can just say "Well there you go, sqrt(2)"

Can someone provide a more mathematical explanation?

I don't know shit about pulleys. If I know m1 and m2 and there's no friction, how do I find T and the acceleration. Why am I so goddamn dumb and why is this problem not discussed on the internet as far as I can find.

I'm doing limits and, do I have the concept right?

We have elements of domain, and their corresponding codomain elements. As the domain elements approach a certain value, so do their corresponding codomain elements approach a certain value too.

I worded this the best I could, just try to understand if I see it the way I'm supposed to.

>>8266505
F = ma is all you need.

Draw all the force vectors. Apply Newton's second law.

>>8266505
Isn't T = ma
Do you know the force?
F = ma
So you can just sub in
T = F = ma

F/ m = a

Then T = ma.

I haven't done this shit in forever but it's something like this right? It's still a mystery how I passed physics one in university...

>>8266514
I think you have the basic idea.

[eqn]\lim_{x \rightarrow c} f(x)=L[/eqn]

Means we can make [math]f(x)[/math] arbitrarily close to [math]L[/math] by choosing [math]x[/math] from a suitably small interval around [math]c[/math].

>>8266505
You know that Newton's laws tells you that the sum of external forces acting on an object is equal to ma. Your first step should be to draw a force diagram for the forces acting on m1 and m2. After, break down the net forces for each block making sure to not confuse your vertical and horizontal components. Last thing is to recall that the definition of a massless string (which I'll assume is the case for your pulleys) is that the tension is equal along the entirety of the string.

>>8266531
>>8266537
>>8266552

I got it all sorted out. I had a fundamental misunderstanding of the tension along the floating pulley. Thanks.

How is mathematical research conducted? What is the process from the start?

How do I into DEs? I'm especially interested in solving them numerically. I already know how to program really well and am comfy with numerical methods for other things like optimization. Looking for a good book or maybe even video lectures,

>>8266505
F=ma.

The rightward force on m1 is T:
T=m1*a1

The net downward force on m2 is g*m2-2*T:
g*m2-2*T=m2*a2

If m1 moves to the right by distance d, m2 moves down by distance d/2. So the speed and acceleration of m2 are half that of m1:
a2=a1/2

So:
T=m1*a1
g*m2-2*T=m2*a2=m2*a1/2

=> g*m2-2*m1*a1 = m2*a1/2
=> g*m2 = m2*a1/2+2*m1*a1
=> g*m2 = a1*(m2/2+2*m1)
=> a1 = 2*g*m2/(m2+4*m1)

[Note: a2=a1/2 = g*m2/(m2+4*m1); as m1 approaches 0, this tends to g*m2/m2 = g, i.e. m2 is in freefall.]

=> T = 2*g*m1*m2/(m2+4*m1)

[Note: if m1 is much larger than m2, this tends to T= 2*g*m1*m2/(4*m1) = g*m2/2, i.e. T is half the weight of m2.]

>>8266514
For sake of brevity, if [math]\lim_{x\to c} f(x) = L[/math] exists, we say that [math]f[/math] converges to [math]L[/math] as [math]x \to c[/math].

What's the name of the qualia reconciliation problem?

>>8266606
>>8266551
Yep, I got the idea then. Thanks lads.

>>8266603
One first obtains knowledge and understanding of some mathematical object. This leads one to ask questions. These questions are then attempted to be answered, and these answers to lead to new questions. For sufficiently nice choices of questions and answers, this process converges to a paper, preferably in a finite amount of time.

>>8266603
>1. Find interesting question
>2. Bang your head against your desk/board/wall
>3. Check if someone has done something similar
>4. Find a paper from the 70s that proves a more general result that trivializes your question.
>5. See 2.
>6. Go back to 1.

>>8266474
>For instance in N and sqrt(2) as the upper bound, our least upper bound will not exist because we can never "reach" the number. But in R we can just say "Well there you go, sqrt(2)"

> But in R
Exactly, you had to go to a complete space for your set to have that that point, since it's not in your original set.

Just like you said, you can find rationals as close as you want to sqrt(2), but it isn't an element of the space (considering the rationals as a metric space with the metric being |x-y| ).

Basically you may have cauchy sequences without a limit point depending on which space you work.

Herro, would be great if someone could give me a hint ( or the solution ) for these problems. For (b): How to if we had to check the mapping for surjectivity?

(b) We are given the set S and T. Is the relation R <_ SxT a Function?

(c) Is the mapping f:R3->R2 [...] injective?

>>8266605

I'm sorry you typed all that after I already figured out where I had gone wrong. Maybe you can help here rather? I've got an atwood machine (but with two fixed pulleys) with masses 190kg and 98kg, and the acceleration that I find is 3.13m/s^2. However, the website I do work on is claiming that the correct answer is .319m/s^2. Where am I going wrong? I get the expected equation of a = g(m-M)/(m+M), is that not correct in this case for whatever reason?

>>8266636
Definition of function: A relation where for every element of the domain there exists only one element from the codomain such that those elements form an element of the function.

Look at R you see that 4 is mapped to b and also mapped to c so there this one element from the domain has two images.

Therefore R is not a function.

Regarding c.


Definition of injective: f(x)=f(y) implies x=y

Counterexample:

(0,1,0) and (0,0,1)

f((0,1,0)) = (0,0+1) = (0,1) = (0,1+0) = f((0,0,1))

Therefore it is not injective.

You see how I solved this problem just by referring to definitions? You should think about that more often. If you are studying mathematics then your definitions are your fucking bible.

>>8266636
>How to if we had to check the mapping for surjectivity?
>>8266655

Oh.

A function A----f---->B is surjective if and only if DomF = A

You see that the domain of the function is indeed the entirety of S. So it is surjective.

Again, definitions.

>>8266637
> I've got an atwood machine (but with two fixed pulleys)
How does having two pulleys affect it?

> with masses 190kg and 98kg
For a single pulley, a=g*(m1-m2)/(m1+m2) = g*92/288 = 0.319g = 3.13 m/s^2.

> and the acceleration that I find is 3.13m/s^2. However, the website I do work on is claiming that the correct answer is .319m/s^2.
It's 0.319444... g = 3.13375 m/s^2.

Someone has the units confused (either they're asking for the answer in g or they forgot to multiply by g).

>>8266661

I didn't think it mattered, but since it was telling me I was wrong I thought I should mention it just in case there was some simple shit I was overlooking. Thanks for showing me the relation between the expected answer and the actual answer, that was huge and I never would have seen it since I make the mistake of doing my calculations all at once rather than in small steps.

>>8266659
thanks, I appreciate it bby
luckily studying informatics so its not only maths coming at me

>>8266669
>studying informatics

Well, I guess that explains a lot. I've never met a non-math student who actually grasps set theory and algebra.

The cult of definitions is only really taught properly to us math majors. Seriously my notebooks read like a dictionary and that is the advantage we have over everyone else.

so i'm taking algebraic topology in a few days, and i already know quite a bit about it, but i have almost no intuition for the basic topology stuff
i know how topology works, and i can work through some pretty involved proofs, but i don't have a very good grasp on why things were defined the way they were, or why certain things work

is there any resources that give a comprehensive, intuitive description of mathematical stuff?
i'm mainly looking for topology-related stuff, but any intuition-building resources are appreciated (especially analysis and algebra stuff)

i did check the /sci/ wiki, but all that's there is just a bunch of textbooks which don't give any intuition at all

How could human beings reach the point where we convert more of our food to energy and so need to eat less and poop less?

>>8266736
By requiring less energy to begin with, or eating food that is very high in calories?

Does anybody know how to calculate the gauge-invariance of a Feynman amplitude? I understand the polarisation vector substitution by the wavevector but I cannot find the calculation itself.
http://physics.stackexchange.com/questions/112994/polarization-vectors-in-scattering-amplitudes

>>8259781
Well, erm, everything in our daily lives is based off of an algorithm, all planets or bodies in the universe hold some sort of magnetic or electrical field and even our brains give off electrical signals, all gymnosperms and angiosperms follow the "golden Ratio" and everything we know in the universe can be explained using math, even the complex code for life can be written out by a computer. It is very likely that we are a computer simulation due to the unexplainable nature of certain phenomena, one instance being the fact that there is a "maximum" velocity that can be reached, represented by "C" , or the speed of light, yet this seemingly unbeatable speed is completely left in the dust by the opposing power of the super-vacuums known as blackholes. Which very well should not exist and trap everything inside of its super massive center. We also cannot see the edge of the universe, most say it is becasue the universe is expanding and therre is "nothing" outside of the edge of our expansion, but I prescribe to the belief that it is the edge of our simulated "reality". Hurr durr, look at me, I know nothing about science, roast me like I'm in /b/ *mmmrrrrpppp* wubbalubba-dub-dub /sci/-cunts.

What does division represent in physics? If we take for ex. [math]\vec{a}=\frac{\Delta \vec{v}}{\Delta t}[/math],which stands for acceleration is change in velocity over time, why is this represented with a fraction? What I'm trying to say is, what happens when we can't divide any smaller? What does it represent in infinitesimally small values, the smallest of smallest possible? How do you define acceleration then? We can keep going smaller and smaller, seconds, hundredths, thousandths? I'm sorry if this makes no sense.

>>8266896
It makes sense.
This is actually where the idea of infintessimals comes from.
As you get smaller time steps which implies smaller velocity steps, you approach the instantaneous acceleration.

PS formally when you get to infintessimals, division isn't really division, but part of the differential operator

>>8266896
>, why is this represented with a fraction?

Because fractions have properties we desire.

For example. What happens when the change of velocity is huge but the change of time is really small?

That shit is going really fucking fast. If in a second you can move 500 meters then fucking shit you are fast.

So we want a relation between a and b that increases its value when b gets small and also increases its value when a gets bigger.

What better than a/b

a bigger implies a/b bigger and
b smaller implies a/b bigger

It is pretty good.

>>8266911
>>8266960
Ok I get what you're saying, I think I'm onto something then, because I always used to look at a combined value of a fraction (in physics), 12/4=3, but it's not actually a combined value (in physics)? Is it just a convenient way of saying "you're going 500 meters in a second"? As you could also be saying "you're going a 1000 meters in 2 seconds? So basically the idea of acceleration isn't that acceleration is a single element as in "holy fuck you're going 3000 accelerations slow down!" but rather for acceleration (or some other ideas in physics) to be represented, it always requires two elements, non-combined?

I'm sorry if I make it look like I'm on LSD and crack at the same time, but please bare with me.

How does the transistor multiply the current? Why not just use resistors or a more simple circuit?

Any way to determine distances between two given planets in the solar system on a given date?

This is the best I've been able to find but it only gives that planets distance from earth.

I'd like to know the distance between venus and mercury on this day in the year 2100, for example. Absolutely everything I've found only either gives you the average distance from the sun, or the distance from earth. Or celestia which gives you the distance from a random fucking point in space.

I'm assuming some kind of orrery/planetarium simulation is what I need, but so far nothing fits the bill.

Ideally a website like
http://www.fourmilab.ch/cgi-bin/Solar
The most annoying thing about that website is that it has the information but doesn't display it.

>>8267044

http://www.gunn.co.nz/AstroTour

There's a distance checkmark which opens another box. You select your pair and it'll draw a line between the two and give you a distance.

I dont get what the second question is trying to ask. the answers are a = -1, b = 3

>>8267065
you got it wrong from the start

>>8267071
but i havent done anything yet

>>8267079
>answers are a = -1, b = 3

WRONG

>>8267099
thats the answer from the worksheet

>>8267065
They want you to realize that they are the same thing

I'm currently studying Software Engineering, and so far I've loved calculus classes, and I want to learn more about why it works and how it works, so I've been thinking about pursuing a degree in pure math or applied math, but I don't know if it's a good idea, learning all that would help me as a software engineer? or it'd not be worth the effort?

>>8267099
a=-1 and b=3 are fine.

>>8267105
pick values of a and b to get the third equation. There is a value of 1x in the third equation, so you have
[math]
2a+b = 1
[/math]
by looking at the factors on x. Now look at the factors on y, you have
[math]
-3a +b = 6 \,\,\,.
[/math]
Lastly, look at the constant factor in the third equation, you then have
[math]
-a -3b = -8 \,\,\,.
[/math]

Solve that system however you want, it turns out to be consistent with solutions a=-1 and b=3.

>>8267399
thanks anon i understand now

>>8266701
>but i don't have a very good grasp on why things were defined the way they were, or why certain things work

Like what?

How the fuck do I do this

I hate sequences

>>8267441
It's possible to do a ratio test on part a of question 3. There's a little hint for you.

I get Calc3, Linear+Abstract, Algo., Leaning to touch type and use Latex. What ideas do you think I'm onto?

is 5 like an even odd number

>>8267441
It's quite easy to show that n!/sqrt(n) when n >= 1 is always greater than or equal to 1 desu senpai.

For b you just have to realize that n^3 will grow quick than the other, i.e. take the limit as n approaches inf and you will see it is convergent.

>>8267441
[math] \lim_{ n \to \infty} \dfrac{ n! }{ n^{1/2} } = \infty [/math]

and in fact it grows strong than an exponential as:

[math] \lim_{ n \to \infty} \dfrac { 1 } { (n-1-c)! } \dfrac{ n! }{ n^c } = \infty [/math]

[math] \lim_{ n \to \infty} \dfrac { 1 } { (n-c)! } \dfrac{ n! }{ n^c } = 1 [/math]

[math] \lim_{ n \to \infty} \dfrac { 1 } { (n+1-c)! } \dfrac{ n! }{ n^c } = 0 [/math]

Why in the world is max O = -infinity and min O = infinity
I know this is very stupid early calculus but for the life of me I can't understand why

>>8267940
Ok I don't know if those properly format as the empty set symbol but that's what I meant

>>8260859
how did you get angle BDE and DEC?

>>8266701
I'm thinking of taking it this semester. I'm strong in Topology but not so much in Algebra, what are the algebraic prerequisites? At the moment I'm good with finite group theory but not so much field theory

>>8259781
the metre is defined as the distance light travels in a vacuum in 1/299,792,458 of a second.

A second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

9,192,631,770 ÷ 299,792,458 is 30.6633189885

So my question is this:

Is it actually possible to measure 0.6633189885 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom or is the metre measured as the distance light travels in a vacuum in 31 periods multiplied by 0.98925806452?

>>8267997
hatcher's algebraic topology is a good way to get the full experience
IMO if you can understand chapter 1 and work the exercises then you're pretty much prepared for the whole thing

https://www.math.cornell.edu/~hatcher/AT/AT.pdf

>>8259781

is their such thing as a "distance derivative"

like [math]d(x) = \sqrt{x^2 + f(x)^2}[/math]

>>8268059
>derivative of distance
You mean velocity?

>>8268071

nah I mean like how a derivative is slope, this one is distance from 0,0

>>8268059
arc length?

>>8268071

Got it backwards, boyo.

What happens here that it goes from 101 to 85 in the last step?

>>8268550
101-2*8
Write his substitution down and see for yourself

>>8268461
No, he didn't, you did.

>>8268559
Ok but where does he get the "2*8" part from? This is really confusing for me & none of my school's tutors understood it.

lim(x→0)(1-cos(x))^(sinx)
can someone help me prove this limit is 1

>>8268590
Define it as taylor series and plug in small values like [math]10^{-4}[/math]

>>8268597
I have to do it without taylor in this chapter; there is another way

>>8268603
Draw a right angled triangle inscribed in a circle and try to visualise whats going on as [math]x\to 0[/math].

>>8266325
Anyone?

>>8268590
[eqn]
\sin(x) \sim_0 x \\
1-\cos(x) \sim_0 x \\
\lim_{x \to 0} (1-\cos(x))^{\sin(x)} = \lim_{x \to 0} x^x = 1
[/eqn]

Bump

>>8268590
I tried again and found it by rewriting the function as a power of e
so
[math]e^{ln(1-cos(x))*sin(x)}[/math]
this e^0 which is one

>>8268617
this is fishy, x^x doesn't behave the same way as the other function

>>8260252
Suck a lot of dick,get close to your professors you will be no1 in to time.

>>8268677
also using hopital to get rid of ln1-x

>>8268550
>>8268581
there's cross products
x^2+ (1/x)^2 =! (x+1/x)^2
x^2+ (1/x)^2 +2 = (x+1/x)^2
for some reason it is just very badly written out

How do elements keep their electrons and protons intact during an electromagnetic induction? If protons and electrons are separating, wouldn't the atoms turn into entirely different elements?

>>8267940
>>8267940
> Why in the world is max O = -infinity and min O = infinity
It ensures that the equivalences:
max(A `union` B) = max({max(A),max(B)})
min(A `union` B) = min({min(A),min(B)})
hold when A or B is the empty set.

>>8268677
>this is fishy, x^x doesn't behave the same way as the other function
https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule#Other_indeterminate_forms

if you want the normal vector of a point on a unit sphere, it's easy right:
Nxyz = Pxyz

but let's say the sphere is "squeezed" in the z direction, so x is in the -1 to +1 range, y is in the -1 to +1 range, but z is in the -0.5 to +0.5 range. how do you find the normal at e.g. Pxyz = { 0, cos(60 deg), sin(60 deg) / 2 }?

>>8268793
oh no i know that x^x is 1 I was saying that
you can't use x^x as an approximation of (1-cos(x))^(sinx)
1-cos(x) does not evolve the same way as x for small angles

Did you misunderstand what I was trying to say am i still being dumb? Your post did make me realise what I had to do so thanks i guess

>>8268590
[eqn](1-\cos x)^{\sin x} = \exp((\sin x)\ln(1-\cos x)) = \exp\left((x+O(x^3))\ln\left(\frac{x^2}{2} + O(x^4)\right)\right) = \exp(2x\ln x + O(x)) \underset{x \to 0}{\to} 1 [/eqn]

>>8268857
yeah that's what i did, did you not read the thread?

Maybe i just misunderstood your first post, i feel like i'm being ignorant

>>8260336
>magnetism,...,results from movement of electric charges and nothing else
>nothing else
explain permanent magnets then, how are they able to create a static magnetic flow with out any "movement of electric charges"

>>8268854
you are correct, that approximation is wrong. He is a moron or really confused.

>>8266325
>Is it possible for q to experience a force from its own electric field
nope, not possible since the charge is the origin of an vectorfield, which vectors all point away from the initial charge who created said field, of course one may say that when getting infinitesimal close to the charge the e-field is still there with mathematical up to infinite strength, which, of course, cant be, so you see that theoretically on the place of the charge the el. field of that charge is present, but has no influence on the charge, even if an actual force might apply the sum of all vectors on that point would be zero (drunk + english not first language)

>>8268913
Yeah I was expecting something like that.

But what if we have a charge density instead of a point. Lets take a cube for example. Assume that the center of the cube has charge q and the corners have a charge of q, 2q, 3q and 4q. Would there be an effect in this case? Or would that simply place the origin of the field somewhere else so that everything nullifies again?

Thanks for replying anyway, I appreciate it.

>>8268960
>Assume that the center of the cube has charge q and the corners have a charge of q, 2q, 3q and 4q
>Would there be an effect in this case?
sure, when there is more than one charge, they influence each other, assuming that the charges cant leave the cube they(assuming same polarity) would try to maximise the distance between then due to their force fields
btw. charges are irl exclusively on the surface of the medium holding the charge so saying
>center of the cube has charge q
is tecnically bs
>Or would that simply place the origin of the field somewhere else so that everything nullifies again?
no the e-field is always the sum of all charges "contibuting" to the field, depending on the distance from the point you want to know about the field to all charges, with thier influence depending on the distance to the point of course, it is possible that on certain points the sum of the field vector might become null due to the arrangement and value of the charges
however, when the distance between you and the "cube" is really big, it is possible to view all charges as a point charge with the value of the sum of all charges withing the "cube"

how do I cite a doc of this nature:

http://www.accessdata.fda.gov/cdrh_docs/pdf3/P030017B.pdf

in an academic paper?

like, i'm not asking for a format, just, what "type" of doc is it (ex.: journal article, press release, &c.).

I need to use IEEE format, if it's of any consequence.

Thanks, /sci/.

[pic unrelated]

>>8260392
He's right, you know.

>>8268985
All right, thanks.

Another maybe stupid question then.
From your first post:
>...the origin of an vectorfield, which vectors all point away from the initial charge who created said field...

What if the vector field was described in an asymmetrical curved metric or w/e, i.e. where the base contains vectors of different length. Could that result in a situation where there is a resulting effect at the origin?

I started doing derivativatives today, and I'm kind of starting to get the point of it. Thing is, couple of things doesn't yet make sense to me. If a derivative is a function that describes how fast another function changes, how does that connect to describing for example speed at that particular point in time? How does it work man, fuck. I lied I suppose, I don't understand shit.

>>8269031
>What if the vector field was described in an asymmetrical curved metric or w/e, i.e. where the base contains vectors of different length
doesnt matter how much "mathmatics" you do, if there is only one (point) charge in an empty room, or with something that might influence the e-field, nothing happens, source cant influence itself, like you cant grab yor feet with your hands and lift yourself in the air, there is no outside effect that might apply to the charge, which leaves only the charge itself as the reference point of the inertial system, the charge is always static, relative to itself, so there is no chance of any "resulting effect" to appear

>>8269053
K thanks. Out of questions for the moment.

Currently working with Taylor and Maclaurin series, I don't understand what the "a" in the formula means, apparently some point, but I don't really get it, does it make a difference which "a" I pick when I want to approximate a function's value?

>>8269058
may i ask what created those questions of yours, have you had lecture in theoretical electrotech, leaving some of the things unclear, or are you reading up some stuff by yourself ?

>>8268845
If you transform a surface by a linear (matrix) transformation, normals are transformed by the inverse-transpose of the matrix.

So for
> Pxyz = { 0, cos(60 deg), sin(60 deg) / 2 }
the normal will be
Nxyz = { 0, cos(60 deg), sin(60 deg) * 2 }

in basic vector math, is |x| == ||x|| or are they different?

thanks

>>8269062
A Taylor series approximates a function in the vicinity of a point a.

For points sufficiently close to a, the series converges; for points farther away, it diverges.

For a series truncated to a finite number of terms, the deviation between the series and the function it's approximating grows as you get farther from a.

if |x-a|<1, then |(x-a)^n| gets smaller as n increases. If |x-a|>1, then |(x-a)^n| gets larger as n increases.

For x sufficiently close to a, |(x-a)^n| will always shrink faster than c[n]/n! can grow. For x sufficiently far from a, |(x-a)^n| will always grow faster than c[n]/n! can shrink.

>>8269063
I wasn't allowed to take courses from my first semester because I had to finish some other courses first. So I missed out on 'general physics: electromagnetism'. I was however free to take almost all courses from the second semester, despite missing the knowledge from previous courses. Now I'm studying for 'introduction to classical field theory', where one chapter is about electromagnetism.I missed a few classes about these chapters so it feels more like self study sometimes. I do get stuck sometimes in derivations etc. but for now I'm able to see the connection between different steps, and sometimes I manage to derive things without clear steps.

Those questions popped up randomly in me while I was reading the part on electric phenomenology, definitions etc. I guess the lack of theoretical background and some random quirk in my mind created those questions.

I like to ask myself "fundamental" questions like that. Stretches the mind a bit and it helps me developing a better understanding of the material.

Is speed how fast something is moving or change in distance over change in time? What is a speed at an infinitesimally small values? If average speed is 50 km/h, what is the speed at 0.000001 seconds? I don't understand how it all relates, the formulas, everything.

>>8269113
Ow that pic was meant for another post.

>>8269113
In calculus that would be considered the intermediate value theorem. (Pic related)

>>8269122
Yeah no, I was planning on explaining derivatives to someone here. More in the context of physics, i.e. distance traveled and velocity. Though, sure one could explain the intermediate value theorem with this as well.

>>8269116
>Is speed how fast something is moving?
"speed" is defined as the change of position relative to time (required to obtain such a change)
>What is a speed at an infinitesimally small values?
> If average speed is 50 km/h, what is the speed at 0.000001 seconds?
should be something around 50 km/h, if the change in time is infinitesimally small, the distance will be infinitesimmally small too, "speed" is just the relation between both of those

is there a term in psychology which refers to identification of an object as some certain thing (like, something you refer to starting with a capital letter)?
like, you are in, say London, see this fancy tower and you realise you are seeing Big Ben.
I need something more basic than face recognition, of which face recognition is just an example, one of many ways to accomplish the same task

>>8259781
There was a thread earlier on /pol/ about the yellowstone caldera and someone wondered how loud it would be. I know that one of the loudest sounds in recorded history was the eruption of Krakatoa at 150 db that could be heard as far away as perth Australia. How would I go about calculating an estimation of how loud the sound would be from an eruption at yellowstone with a given a realistic of energy released.
> bonus points how would I calculate how far the sound would travel

sorry it's been ages since I've taken a physics class :c, feels scientifically illiterate man

>>8269116
Infinitesimal values are just a tool. I assume that you understand how to calculate the average velocity. (x2-x1)/(t2-t1) Which means the distance you traveled over a certain time. Now you go to very small scales, and you work with infinitesimals. You can define x2-x1 = dx and t2-t1 = dt and you get dx/dt.

See >>8269113 pic related. The red line show the average velocity = (B-A)/(b-a) = the slope of the red line. Now let's say you're interested in the velocity at point c. You could move a and b closer to c, and you'd notice how the red line changes. Visualize how the red line would be when a and b are on the same spot as c. Or alternatively take point of interest c and a random point a, and move a towards c. Mathematically this is represented as
[eqn] \lim_{a \rightarrow c} \frac{f(a) - f(c)}{a-c} [/eqn]

And this is the definition of a derivative. The exact definition might differ, I corrected it here to my context. Usually it's x and a.


I'm not the best at explaining, but I hoped this helped a bit.

>>8269033
Picture a graph with d(distance) as ordonée and t(time) as abscisse. You know that s(speed)=d/t.
When you do the derivative of a point in time t2 you do f(t)-f(t2)/t-t2 as t1 approaches t2.
It's the same.

>>8269227
can you recommend a good place to learn basic calculus from, I took precalc ages ago and I plan on going back to college and majoring in cs and I want to be able to take calc without having to waste my time going over precalc and basic algebra.

>>8269239
You should check out khanacademy if you can skip directly to the calculus parts.
Apart from khan I don't know any sources in english but I've heard good things of Rudin's analysis (Principles of Mathematical Analysis) I think it is. You're going to have to re-learn everything with rigor anyway so why not start by learning it the hard but proper way.
It'll probably be more challenging though.
Also, don't do CS, do maths.

>>8269076
woah really? that was my intuitive idea but i didn't know if it was correct. thanks man!

>You can imagine that when the surface of a sphere stretches (so the sphere is scaled along one axis or something similar) the normals of that surface will all 'bend' towards each other. It turns out you need to invert the scale applied to the normals to achieve this. This is the same as transforming with the Inverse Transpose Matrix.
this is so cool, the simplicity and elegance of it, now i know what to google, thanks again

>>8269137
I don't know how to calculate the volume, but I'm fairly sure you'd hear it on the opposite side of the planet.

Krakatoa was just a big volcanic eruption, Yellowstone would bury a quarter of the US in ash.

>>8269257
On second thought, baby rudin might be a bit too difficult for a beginner. So sorry apart from khan I wouldn't know.

>>8269239
>>8269282
Stewart's Calculus might be a good book.

For vector calculus maybe Vector Calculus by Marsden and Tromba.

>>8267451
>>8267937

thanks lads, i managed to find it using the ratio test

>>8267885
I get that bit, but doesnt the limit of sin (n) not exist?

why do fermionic fields make a repulsive contribution to the casimir effect?

Anyone here know much about Inorganic Chem naming schemes?

I got a question wrong on this quiz but there is no feedback. I am pretty sure it is this one since it is the only one that did not have a blatantly right answer but I cannot work out what I did wrong.

>>8269094
bump

I have made myself a cup of turkish caffee and poured a little bit of cold water so I can drink it sooner.
Why does the mixture move in spiral in my mug?

I'm genuinely interested in mathematics as a hobby but I don't want to go to school for it. how do i start self studying? I have no real experience with real math at all outside of shitty algebra for brain dead high school kids. is there a specific place to start or a progression to follow or is it all just pretty pick and choose what you're interested in?

>>8270471
Do what I'm doing. Take free online classes on places like EdX or Khan academy.

I graduated with a bio and env sci degree with a shitty gpa, but I did get it up to diffy q and linear algebra in my senior year (failed them, though).

Now I retook those classes on EdX and I took their 3-class quantum class too. I'm also taking some classes on data analysis and a quantum chemistry class. There was also a 4-class series on first year astrophysics. I'll never get any credit for any of it and I can't advance my future.... but it keeps me sane. Eventually I'd at least like to be on par with some field of physics at the graduate level.

>>8269366
>I get that bit, but doesnt the limit of sin (n) not exist?
just replace the sin^2 part with 0 which makes the sequence bigger. since the bigger sequence converges, also the original one does

Is it possible to simplify this any more to find r?

r^x2/r^x1 = y2/y1

If it helps I started with f(x) = ar^2, with x1,y1 and x2,y2

I don't know how to get r without using real number.

>>8270541
Sorry it should be:
f(x) = ar^x, with x1,y1 and x2,y2

>>8270541
r^a/r^b=r^(a-b)

>>8270081
Yes. The second one is usually just used for vectors though.

>>8270661
So you're saying r = x2-x1th square root of y2/y1?

>>8270714
r=(y2/y1)^(1/(x2-x1))

12-8-32-28-?
Which of the following numbers complete the sequence: 112, 12, 76, 124

I don't get it, I feel so fucking stupid. The answer is 112. but I don't know why.

Been studying hard for my quantum exam on wednesday but when I look at previous exam questions I feel blank.

Feels bad lads

>>8271288
12 - 4 = 8
8 * 4 = 32
32 - 4 = 28
28 * 4 = 112

>>8271317
I hate how obvious they are once they are explained.

>>8270471
I was you a couple years ago, rather than following some linear progression like in school I think it's a lot more interesting to explore based on what you're interested in. Looking through wikipedia articles, getting books off libgen, watching youtube videos, checking out relevant stackexchange, all the free online resources for exploring math are great.

no time

>>8269969
check the charge of the first complex

2x cobalt II
3x sulfate

So that complex is supposed to be cobalt III

I have trouble. I finally understand what a derivative of some x is, it's a slope of a tangent line of that x on the original function. The formula goes like this [eqn]f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}[/eqn]. I understand how to get to it. I don't understand if it represents a slope of a tangent of a single point, how to actually plug in to solve the slope of a particular x, say 5, or how it is used for solving the derivative of a function? What is the difference between the derivative of a particular x, and a derivative of a function? Is the same formula used for both? How to plug to solve for each one?

>>8259781
How do I into diff equations if I barely passed calculus?

>>8271597
Practice till you get sick of it, then practice some more. Learn what different type of diff equations look like, i.e. learn their properties etc. so that you can recognize them easily. By making exercises you will learn and remember the methods used to solve them.

>>8271593

>Slope
https://en.wikipedia.org/wiki/Slope

>What is the difference between the derivative of a particular x, and a derivative of a function?
Deriving a function means that the x will stay variable, i.e. just x, not some value. This means that you will have a new function that allows you to calculate the slope of any point in the domain of your original function. When you're interested in the slope at let's say x = 2, you simply fill in x = 2 in f '(x). Note that the derivative of a function can be a constant as well.

Example: [math]f(x) = x^2[/math]

The derivative of the function (x stays variable) is: [math] f'(x) = 2x [/math]. If you want to know the value at x = 3 you simply do 2.3=6.

The formula you have there is simply the definition of a derivative. You'll rarely use it to really calculate the derivative. Most of the time you'll use it to prove some of the derivation rules.

>>8259781
test

>>8266233

Why?

from a good uni it actually gives the highest pay of all educations on avg.

Sup /sci/, i was wondering if anyone could help me with these 2 problems:

How many ways you can sit 5 people around a table, if two of them should never be together?

and

How many ways can seven friends sit around a circular table if 3 of them should always be together?

thanks in advance

>>8271693
5! - (number of ways to sit the two assholes together)

>>8271727
shouldn't it be (5-1)! - something because of the rotational symmetry of the table seats

like if you pick 12345 it's the same as 51234 etc

Can someone please help me in computing the integral:
[math]\int_{\frac{1}{x^3+x}}dx[/math]

Why can't I use partial fractions for solving this?

>>8259781
>>8271920

>>8271962
Integral is 1/(x^3+x) btw, sorry for messing up on LaTeXing it

>>8271661
Thanks! I understand a bit more now. By calculating the derivative of an entire function, instead of a single point, I can use the derived function to calculate the slope of ANY point that I wish, that is contained on the original function.

I think I finally understand derivatives. Just one nuance left.

If I have a slope of a tangent line, its meaning is basically for a change in [math]x[/math] there is a change in [math]y[/math]. [math]m_{tangent}=\frac{\Delta y}{\Delta x}[/math]. But for a tangent to be true, it must have a single point? Or is this the trick with the limits, which doesn't allow for a single point as it never actually reaches zero, so we have a secant that sort of "resembles" the tangent, but since it'll never become the tangent, it has two points that are so fucking close, you can calculate the change in time of ex. 0.000000000001? Did I see God, finally?

>>8271982
1/(x^3+x) = 1/x - x/(x^2+1)

Could anyone give me a pointer on how I would start these questions? I couldn't do these proofs to save my life so I really have no idea how to do it

how can i rewire my brain to be autistic at math

>>8272549
Fingers in the nearest electric outlet. That's how we all did it.

>>8272495
>lel cs major detected

A) Unwrap the definition
(1/xn) converges to 0 iff for all deviations ε>0 you can find a N for it such that the distance from 0 is smaller than the deviation past N i.e. |1/xn-0|=|1/xn|<ε when n is bigger than N
Lets invert that:
1/ε < 1/|1/xn| = |xn| for n>N
By the definition of a sequence diverging to ∞ with M=round_up(1/ε) we know that we can find a N to do this (and since xn is forced to be positive by M, we can drop the absolutes.) QED

B) Unwrap the definition
(1/yn) converges to ∞ iff for any big ass number like your mother's weight M>0 you can find a N such that fuckers in the sequence are even fatter than your momma M i.e. 1/yn>M when n is bigger than N
Lets invert that:
1/M ≷ 1 / 1/yn = yn
But wait, yn could be negative getting the opposite result.

Counter example: y_n = -1/n

Im supposed to find the (a)s for which the linear system has:
(i) 1 result
(ii) no result
(iii) infinite amount of results

So I got put it in a more comfortable format:

x + 2y - 3z = 4
0 - 7x + 14z = -10
0 + 0 + (a2-16)z= a-4

for (iii) pretty obvious that a = 4 so that 0=0

how do I get (i) and (ii) though?

>>8272748
the x in (II) is supposed to be a y

>>8272748
I figured that using a=-4 will make (III) 0=-8 so that would be (ii).
Is (i) all (a)s except of 4 and -4 then?
I guess so,uff. Sorry for spamming

>>8271316
I know that feeling man

Hello,
someone mind telling me what I have to do for this one?

Translation:
Find for the solution set L(A,0) of the homogenous linear equation system A*x=0 a base and give the dimension of L(A,0).

>>8271783
Yes, but you divide by 5 to mod out by the symmetry. Hint: There are 5 places where the jerk on the left can be seated.

>>8272101
I'm a physicist so my personal understanding of mathematical concepts might not be mathematically pure as I'd like it to be.

I see limits as a way of predicting what happens when you approach a point, without ever really reaching that point. Though when you have a limit that converges, i.e. [math] \lim_{x \rightarrow a} \in R[/math], and a is in your domain, then you can simply say at point a the value is w/e. You can actually reach this point. When a is outside the domain, well you obviously won't be able to reach it, but you can still use the predictions from the limit. The difference is only that in the first situation (a in the domain) you can say e.g. f(a) = 2, but in the other situation (a outside the domain) you can't say f(a) = 2. You have to say [math] \lim_{x \rightarrow a} f(x) = 2 [/math]. So yes, it is possible to get a tangent when the conditions are right. Otherwise a secant will be used as an approximation and a "prediction" for a possible tangent.

This will also express itself in derivatives. Take for example the function f = |x|. (Make a drawing of it). You can calculate the derivative everywhere except for x = 0. The reason for this is the fact that [math] \lim_{x \rightarrow 0}[/math] doesn't exist. The reason for this is because the limit differs depending from where you approach. If you approach from the left you'll get -1, and from the right you'll get 1.

Idk if my explanation helped or not. Feel free to ask if something wasn't clear.

>>8272462
So when you are dividing it up:

It is = A/x + (Bx+C)/(x^2+1)

??

>>8272903
oopsie

>>8272909
Use Gaussian elimination. It's literally the only technique.

>>8272913
I figured I should use it. But I'm not sure what exactly I am supposed to do in the first place

If I have a pump which says it needs 12V and 3amps on the label but I only need to run it intermittently can I run the pump from a 12V 500mA power supply with some capacitors that charge up between uses of the pump? And what would that circuit diagram look like?

>>8272917
You can add up two rows (or multiples of two rows) to create a new linearly independent row. Then you take that new row and replace one of the old ones with it. Try and get as many zeros as possible.

>>8272932
I know how it works but I don't understand how doing that would help me with the scope

>>8272905
so (5! - something) / 5?

>>8272940
You can't come here and ask for homework answers when you clearly haven't thought about the problem at all. Even worse, someone told you exactly what to do and you still want more. I think it's time to read the fucking textbook and use your brain.

Why is there not a B_y component?

>>8272957
yes

>>8272965
I didn't ask for answers. I asked WHAT I am supposed to do (not even how). I was wondering what 'L(A,0)' means in that context. Thanks for your help though

>>8272908
Yep.

A/B+C/D = (A*D)/(B*D)+(B*C)/(B*D) = (A*D+B*C)/(B*D).

If B=x and D=(1+x^2), A*D is going to have an x^2 term, so B*C need a -x^2 term to cancel it, so C needs an x term (i.e. it can't be a constant).

>>8272920
Realistically, no.

3 amps = 3 coulombs/second. 1 farad = 1 coulomb/volt.

If you can tolerate the voltage dropping by 1V over the period the pump runs, you'd need 3 farads of capacitance for each second the pump runs.

Most capacitors are a small fraction of a farad. 10,000uF (1/100th farad) is a fairly large capacitor.

You can get supercaps up to a few farads but those are typically no more than 2-3V, so you'd need 4 or 6 in series, which also reduces the capacitance by 4 or 6. So you'd need e.g. 36x 1-farad, 2-volt caps to make a 1-farad, 12-volt cap. and 108x such caps to make a 3-farad 12-volt cap (enough to run the pump for one second).

It's much cheaper to just get a 12V, 3A PSU.

If for some reason you were limited to 12V, 500mA, you'd use batteries rather than capacitors.

>>8272967
Rollers have a degree of freedom along the surface thus they only carry force perpendicular to the surface. A B_y component would move the rollers. As this is a statics problem, whatever motion that might have happened happened a long time ago.

>>8273173
Thanks anon for saving me the time looking into a dead end, I will just find a properly rated power supply as you suggested.

>>8273201
Thanks Anon, I realized that looking at some textbooks. My teacher just sent that exercise without naming rollers a single time.

>>8273082
bump
Am I supposed to find the matrix X where A*X equals a zero matrix?

>>8273082
They've literally defined what L(A,0) means in the question. You've got to work on your reading comprehension, anon. ;^)

>>8259781
what the fuck are you doing in that pic

thats not how you integrate

but since you only do integrals in high school I guess that explains it

I don't know if this is a stupid question but why are components added in notations for equations for points, vectors, planes, etc.? as opposed to components in parentheses
(x, y, z) ---> x + y + z

Don't know if this is appropriate here, but I have a botanical question:

Do young spruce tips contain digestible carbohydrates? I know they're edible, but I want to figure out new modes of preparation.

>>8273364
...what?

>>8273261
You're being asked to find the null space of A, which the (infinite) set of vectors x such that A*x=0.

If A was full-rank (non-zero determinant, invertible), the only solution to A*x=0 would be x=0. The fact that this is presented as a problem worth solving implies that A isn't full-rank.

In such a situation, there is some set of vectors x0,x1,x2,... such that any linear combination x=k0*x0+k1*x1+k2*x2+... is a solution to A*x=0. If there are N such vectors, then those vectors are a basis of an N-dimensional space which is the null space of A, and the nullity of A is N (for an MxM matrix, if the rank is R and the nullity is N then N+R=M). A full-rank matrix has a nullity zero, i.e. the only solution to A*x=0 is x=0.

By linearity, if A*x0=0 and A*x1=0, then A*k0*x0 = k0*A*x0=0, A*k1*x1=k1*A*x1=0 and A*(k0*x0+k1*x1) = A*k0*x0 + A*k1*x1 = 0+0 = 0.

So you need to find a set of linearly-independent vectors which satisfy A*x=0. Which basically means using Gaussian elimination to reduce the matrix to a triangular matrix (row-echelon form), which will result in some all-zero rows. The number of all-zero rows is equal to the nullity of the matrix.

>>8273364
What?

Are you talking about a plane equation, which is a linear equation in the coordinates? E.g.
kx*x+ky*y+kz*z=k

Or representation of a point as a linear combination of the axes? E.g.
x*X+y*Y+z*Z
(where x,y,z are scalars and X,Y,Z are vectors representing the axes)

This isn't homework, it's a practice test I'm studying.

I got a 19 in math on my ACT, so I had to take a remedial math class last year in college. At my school, to get into college algebra you have to of had a 22 (I believe) on ACT, pass an entry test (what I'm trying to do) or complete the lower level math class, which my advisor said would just go back over what I learned in remedial. I did very well in the remedial class, if that means anything.

However, in my remedial class they did not go over any problems similar to this one. I do not want to know the answer, the sheet says it at the bottom: D.

What I want to know is how you get to that answer, so that I can replicate it for similar problems.

They only briefly went over parabolas, but there were never any questions similar to this one. I would really appreciate it if someone could help me understand how to solve questions like this.

>>8273551
just obtain the maximum value of that parabola

and the roots

now you have the 3 points, and you can calculate the area

>>8273572
actually, you don't even need the maximum

since the maximum is clearly the same as x=0

>>8273551
e z p z

height of triangle is 7 because the maximum of 7 - x^2 is 7 (x^2 can only be 0 or higher, so you want x^2=0 to get the maximum)

then you want to solve 7 - x^2 = 0 because that's where the intersection with the x axis is (y = 0), rearrange it so it's 7 = x^2 and you get x = (+-) sqrt(7), so the base is 2*sqrt(7) because you've got one on each side

then the area of the triangle is base * height / 2 = 2*sqrt(7) * 7 / 2 = 7*sqrt(7)

>>8273551
use the intercepts of the parabola to find the dimensions of the triangle. From there use the simple formula of a triangle's area

>>8273595
>>8273613
>>8273572

Thanks a bunch! So, would it be applicable to use that method in >>8273595
to solve a similar problem if it came up on the actual test? Like I said, my teacher did not go over anything exactly like this, and problems pertaining to shapes have never been my strong suit.

>>8273487
I think I'm asking about the latter. I don't understand why you would represent them in that kind of way.

How do you find AD*AB?
I know that the answer is 3, but I don't know how to get there. I've been looking at this shit for like 2 hours. Starting to think I'm retarded.

>>8273551

>>8273664
Thanks! I'll save this so I can study it some more.

I need to reduce [math]4ln{2}\times2^{ln}[/math]. Apparently, [math]2^{ln}[/math] is [math]1[/math], but idk how to get to that solution.

>>8273484
Appreciate it!
I got the solution: v= (-t,0,t,0) (t being a real number), and no matter what t I choose A*v is always 0, cheers

>>8273658
can you read and understand this anon?

>>8273697
e^0 =1 <=> ln(1) =0

2^ln(1) =2^0 =1

on a frictionless surface, can a car take off?

>>8273742
no

>>8273739
Thanks anon! I couldn't understand everything you wrote there but got the idea and could solve it.

>>8273761
No problem :'^)

>>8273712
That's only one dimensional; A actually has nullity 2 (i.e. the null space is 2-dimensional), so you need 2 linearly-independent vectors.

One such solution is (1,-1,0,2) and (-1,0,1,0), i.e. for any a,b, x=(a-b,-a,b,2a) satisfies A*x=0.

>>8273795
Thanks alot, got it

>>8273742
yes, the exhaust could provide thrust

>>8273742
Aren't you basically flying the entire time considering the ground is frictionless?

>>8273741
Yeah, realized that as soon as I posted. [math]ln[/math] without a digit confused me, then I just realized if there's nothing, it's 1. Thanks.

>>8272906
I'm afraid I'm still as confused as I was before. So you can't really tell if what I wrote in my post is correct? I guess I might've misunderstood in that case.

>>8262128
a lot of people helped invent the computer, not just engineers. It had contributions from years of math, physics and engineering.

Hey /sci/

Is there anyway to differentiate between particles that have had their wave function collapsed and those that haven't?

For example, a researcher generates a stream of 10 electrons and randomly measures the spin of 4 out of those hundred along the way.

The stream is sent next door to another researcher who has to figure out which electrons have been measured in the same order, not just the number of electrons that have been measured.

ie: If it was the 3rd, 6th, 7th, and 10th electrons, he needs to find out it was the 3rd, 6th, 7th and 10th etc.

Collapsing the other 6 electrons' wave functions is permissible as long as you figure out the order of those that were collapsed in the first room.

>>8274008
You are not wrong. I just wanted to point out that it is possible to get a real tangent.

Thread soon ded, regardless:
How do ions separate in water, specifically when you dissolve NaCl into water? Do the positive ions and negative ions separate to opposite ends of the container?
Not sure where to find an answer to this, any links would be gud if an anon cares to help that much

>>8259781

I was reading about LIGO detecting gravitational waves and the article said it made a sound. How did they pick up the sound seeing as how sound can't travel through the vacuum of space? Not that I don't believe them or anything, I'm just curious.

can you make a circle out of straight lines?

>>8274396
You could zoom in on any curve and it will appear as segments being joined together so I believe that you could make a circle out of segments. I'm not sure about lines though.

>>8274227
Okay, thanks! Think I won't be able to understand details until I get a good grasp of the basics though.