/sci/ - Science & Math

What is Jacobian?

[math] textbf{UNANSWERED QUESTIONS IN POST ORDER} [/math]

>>12143905 || microscope
>>12145557 || anatomy
>>12145617 || Physics in India
>>12145698 || Math (career advice)
>>12147019 || college coursework advice
>>12147070 || physics (phenomenology)
>>12147485 || compsci/programming
>>12148393 || math
>>12149533 || electronics

Unanswered Questions from last thread (in post order)

>>12143905 || microscope
>>12145557 || anatomy
>>12145617 || Physics in India
>>12145698 || Math (career advice)
>>12147019 || college coursework advice
>>12147070 || physics (phenomenology)
>>12147485 || compsci/programming
>>12148393 || math
>>12149533 || electronics

>>12149873
an array of numbers

>>12149873
an array of numbers which describe how the function changes its inputs

>>12149887
I am curious if there is any statistics about the percentage of unanswered questions that remain unanswered. My guess it is close to 100% as usually if a question is not answered within an hour or so it will never be answered since it is either a stupid question or

>>12149892
>>12149895
so a tensor? lol everything is an array of stuff in math

>>12149896
last thread I would guess 1/3 to 1/2 of the unanswered questions from the previous thread were answered
a few people come into these threads from top to bottom and answer anything that they have expertise in, regardless of if it's been answered already or not.

thanks for removing my link to the physics book list you fucking faggot

>>12149911
it was a virus.

>>12149911
it was redundant, the wiki has like 10 different lists and anyone clicking on the thread will just ask for recommendations anyways.
it's time to drain! the! swamp!

>>12149867

>>12145557
first that you are a retarded weakling, second that alcool indeed destroy synapses (if my memory is correct) also smoking reduce cerebral plasticity
so you if you take care of your body in 3-5years you should be even better than before (or dead)

I always have a bunch of math questions in my mind. Many are silly but thats the way I learn. What is my best bet, ask here, create a separate thread or ask in /mg/? So far I tend to think that creating a thread is the best approach as it attracts more people.

>>12149925
anything but create a new thread.
>slow
>wastes space on the board
>attracts the most trolls

>>12149925
>ask in /mg/
I don't think mechanical engineers will be able to help you with any mathematical questions sadly

Reposting two questions OP skipped out of interest:
>>12149572
>>12149499
Honestly, for the first one, I wouldn't be surprised if the answer was something like "inspection lmao", "one of these five hundred methods lmao", or even "transform the nonholonomic system into a holonomic one lmao".
For the second one, I tried to parse some physics texts, and they don't explicit construct the dagger, but they also simultaneously claim that the grassman algebra is generated by (just) the [math]\theta _1 \ldots \theta _n[/math], in which case we should essentially have a funny involution on the grassman algebra which can actually be given explicitly in terms of the thetas, but that anticommutator just confuses me to literally no end.
>>12149919
>removing the serious advice written by actually competent people to keep the maymay 4chan advice
Really gets my nogging jogging.

>>12149867

>>12149533
well energy don't come from nothing, it come from chemical reactions (mostly) and if a chemical reaction create energy it mean that little atoms will dance and bang around.
and the more you have (the more powerful the device) the more noise you get
(this is heavy simplification)

>>12149925
/mg/ sucks, this thread is comfy and we read all the questions, thrown down your thoughts here.

What's the difference from finding the limit of negative infinity vs infinity?

>>12149933
bud if people are gonna come here for textbook advice they're gonna just click the first link (the sticky link) or ask a question in the thread.
also the sticky links to multiple undergrad textbook lists, it wasn't written by anyone here.

>>12149572
>is it possible photons emitted from BBR cannot be absorbed by any atom or molecule
yes and no.
taking what you asked literally, then some low-energy BBR photons might be below any atomic or molecular transition energy.
However, in order for them to have been emitted in the first place, something must've emitted them. There's no way to emit a photon that cannot be reabsorbed (by time reversal symmetry). This emission/absorption might be due to collective effects in the material. For example, vibrations between atoms or molecules in a solid. It's not technically a specific atom or molecule emitting/absorbing the radiation, but instead the energy might come from a quanta of vibration in the collective solid.

>>12149873
jacobian is unironically a tensor

>>12149919
No it wasn’t redundant, it had reviews of textbooks from actual physicists, and a large number of the books recommended there are not found on the wiki. Retarded fucking newfag nigger

>>12149972
so basically everything is a tensor? a number is a tensor, a function is a tensor (since in some vector space of functions it can be represented as a vector which is a tensor). everything. even zero is a tensor. a complex number is also a tensor since it can be represented by a vector. a matrix is also a tensor. i can't think of something that is not a tensor.

>>12149982
okay make the thread next time I'm done

>>12149982
You swear like tooker. No need to get emotional over some links in a short lived thread.

>>12149989
Calm down lad, we're talking about something that takes fifteen minutes of your time around once a week, are you really quitting because of one insult?

>>12149867
>>12149775
Someone pls help with this.

Okay so, triple integral of a density function provides the MASS? Or the triple integral of a function [that is not density] provide the DENSITY and then I have to find the volume to multiply it to get the mass?

>>12149899

>>12149911
What's the physics link, I'm taking physics right now and I'll need it

>>12150045
https://math.ucr.edu/home/baez/books.html

>>12150052
>>12150045
No you want this one:

https://math.ucr.edu/home/baez/physics/Administrivia/booklist.html#statistical-mechanics

>i’m taking physics rn
this is a book list for someone trying to learn undergraduate and graduate level physics. not for someone doing gen ed requirements. for the latter just use the assigned text for your course or something like Young or Halliday&Resnick. This list is only useful if you’re doing a full degree or the equivalent.
>>12149989
Make the thread correctly and I won’t aggro
>>12149992
shut the fuck up faggot i’ll fucking throw you through a plate glass window you fucking cuck

>>12150084
>https://math.ucr.edu/home/baez/physics/Administrivia/booklist.html#statistical-mechanics
This list is actually shit what the fuck? no griffiths EM for undergrad EM? Feynman lectures as the QM book?
I don't blame OP for not including this.

>>12149987
>a function is a tensor (since in some vector space of functions it can be represented as a vector which is a tensor)
if youre going with that then literally everything can be defined as 0 in some trivial vector space
saying a function is a vector removes all of its actual important parts

>>12150084
>this is a book list for someone trying to learn undergraduate and graduate level physics
Yea that's basically me

>>12150084
My physics class is just moving into Coulomb’s Law, do I go to the "Classical Electromagnetism" section of the page? Would it be wise to start with Feynman vol 2 first then into Berkeley?

>>12150167
You should use Griffiths electrodynamics, the standard introductory EM book, then into Jackson. Starting with either of those options would be a mistake and this is an example why this list is terrible.

>>12150249
"Introduction to Electrodynamics 4th Edition"
This? Is there anything I should watch out for while reading this?

is the fibonacci sequence considered chaotic (i might have a layman understanding of that word, so it might be the wrong word to use)? is it possible to predict a fibonacci number at any arbitrary point without having to do any other fibonacci calculations?

>>12150253
No, it's pretty much the gold standard for intro EM books. If you're just starting coulombs law I doubt you're ready for Jackson.
EM has a bunch of resources since it's a well-established field, don't be afraid to look up other sources for the stuff you're reading about if it isn't making sense as written.

>>12149987
Yes, and tensors are arrays of numbers.

>>12149899
It is even worse: Everything in math is a string of symbols.

>>12150259
the nth term in the fibonacci sequence is given by:
[eqn] Fib(n)= \frac{ \Phi ^n - \phi ^n }{\sqrt{5}} \\
\Phi \equiv \frac{1+\sqrt{5}}{2} \\
\phi \equiv \frac{1-\sqrt{5}}{2} [/eqn]

>>12150294
This assumes fib(1)=2
1,1,2,3,5,8,... Is better defined by:
[eqn]x_{n+1} = x_n + x_{n-1}[/eqn]

>>12150311
it is only true for n>1 so yes
also your form is pointless because the question asked "is it possible to predict a fibonacci number [...] without having to do any other fibonacci number calculations?"
I'm well aware that this is the definition of the series.

>>12150329
>series

>>12150353
sorry, function

>>12150353
>>12150376
Sequence Bro, also, there's no real distinction between sequences and series

>>12150012
Also, someone pls help with this, im always answering questions in these threads, trynna help anyone I can

>>12149925
Your questions are probably awful so don't waste the adults' time with them in /mg/.

>>12150434
>there's no real distinction between sequences and series
Yes, there is. A sequence is a sequence of numbers and a series is a sum of said sequence.

>>12149987
No. A tensor is not just an array of numbers. Stop. A tensor is very specifically a mathematical object which is a member of a collection of mathematical objects equipped with some very important operations. Without being able to make sense of these operations, i.e. outside of the proper context, an array of numbers is not a tensor. What are these operations? The most important is the tensor product. There's also a vector space structure. Indeed, there is some categorical formulation involving universal properties which captures what is a tensor and what is not (I believe the right place to look is "monoidal categories," someone correct me if that is wrong.)

What branches of math do I need to learn before I can learn representation theory?

>>12150022
The triple integral of the density function gives the mass. Think of it this way, the density function gives you how much mass is in each infinitessimal bit of volume in your object. Then integrating the density function adds all these little bits together to get the total mass.

>>12150084
>shut the fuck up faggot i’ll fucking throw you through a plate glass window you fucking cuck
lmao would be funny if posts like this would be accompanied with a picture of some cute anime girl

>>12150452
A series Is the limit point of a sequence of partial sums, series are simply a special case of sequences

>>12150434
Series cannot be defined without a group structure which respects the topology.

>>12150457
>tensor product.
is just a glorified martix multiplication of a column vector by a row vector.
also, that sounds like a recursive definition. tensor is defined via tensor product? it is like saying that numbers are defined via scalar multiplication?

>>12150476
This.

This is utterly amazing. log vs exp functions. What makes them look so similar? they both grow quickly when x<0 and then slow down asymptotically when x>0. Also notice the symmetry of one vs the other in the 1st vs 3rd quadrant. Why is that? Also what happens at 0,0? Why do they stop growing like crazy and begin to slow down asymptotically? What physical phenomenon is that? Why are they not symmetric relative to 0,0 but do look symmetric to each other's opposite side with respect to the dividing point 0,0?

>>12150476
I mean sure, they are still the limit point of a sequence tho, as I said, they're a special case.

>>12150517
Logs are the inverse of exponentials, that's why they share many similar features.

>>12150525
right but the inverse is usually rotated, such as sqrt(x) is the inverse of x^2 which is pretty obvious by just looking at the graph. but these two almost look like the same function despite being an inverse of each other. i would also throw in y=1/x here since if you shift and scale it, it would also somewhat align with these two.

>>12150434
you're asking for pretty specific career advice. I would recommend getting in contact with people who know you better, or forums for people who went to school in places for non-traditional places. it's very unlikely any advice here is going to be useful to your specific case.
you probably can't go wrong with anything you're considering. I doubt there will be a massive difference between the different options.

>>12150517
>>12150544
whatever you posted is not the exponential function. the log is the inverse of e^x, and if you look at these side by side it will appear "rotated" in the sense that you're talking about.

>>12150549
Well it is 1-exp(-x) which is a shifted exponential function. Also, look I added 1/x. It fits right in. Isn't that amazing.

>>12150554
>but these two almost look like the same function despite being an inverse of each other.
>log(x)
>1-e^(-x)
>inverses of each other

>>12150560
Ok they are not but why do they look so similar which was original question
ln(x)
1-e^(-x)
1/x
For example you wanted to model something that grows like crazy then slows down at some point. Which would you choose and why.

Why the fuck do I keep coming back here

>>12150587
You've got no self-control.

>>12150572
you pick which one you use based on their behavior far from 0, since they're all different.
1/x reaches an asymptote at both x=0 and x->nf
ln(x) reaches an asymptote at x=-1 but doesn't have one as x->inf
e^(-x) has an asymptote at x->inf but doesn't have one in the other direction

>>12150517
1. I'm fairly sure those graphs are y=log(1+x) and y=1-exp(-x).
2. Each is the reflection of the other in the line y=-x, i.e. mapping x'=-y,y'=-x:
y=log(1+x) => exp(y) = 1+x => exp(-x')=1-y' => y'=1-exp(-x').
3. They really aren't all that similar. log(x) has a vertical asymptote at x=0; exp(x) increase faster than x^n for any n, but is always finite.

>>12150547
>forums for people who went to school in places for non-traditional places
I can't find forums for these kind of stuff online. What do you mean by non traditional places?

Dude I just need to know what my financial options are, if I can get loans, if I can work part time, etc.

The best possible escenario would be going into a PhD straight away but I doubt that can happen and seeing the kind of research that's being conducted over there I doubt I'm even fully ready for that but idk honestly.

>>12150631
>financial options
will depend on each place you're looking at
with regards to phd, no 1st year phd student knows what they're doing. the work is above all of them. I would encourage you to look into this more, maybe reach out to a few professors that you'd be interested in working with

>>12150592
>>12150613
Yes ok but all three of them
log(1+x)
1-exp(-x)
1/x
have that "knee". It may even be at a slight different point or I could shift them around etc but it doesnt matter. All three of them "turn around" the corner after they reach that "inflection point" for the lack of a better term. So irst they grow fast and reach that "point" and then slow down. I understand they are all different but this the pattern they follow. I was wondering what is that "inflection point". Something to do with their derivatives, the way they grow? But the derivative at the "knee" is not zero, right?

>>12150587
Because you love us.

How do I move on after this brutal email?

>>12150662
respond and say you're in an abusive home environment where your dad yells at your mom constantly, drunkenly beats her during the day, and there's nothing you can do.
and then threaten to report the professor to the university for threatening you.

>>12150664
and accuse everyone of sexual harassment by dead naming

>>12150664
Id love to but I'm clearly talking to myself as I work thru the problems

Anyone here experienced with [math]\LaTeX[/math]?

Let's say I want to make a table with where the first column is a series of numbers going from 1, 2, 3... all the way to 25
Now let's say that I wanted to add a row in between rows 3 and 4 so know the new row is row 4, but now I have to change the numbers from the old rows 4-25 to 5-26 to reflect this change. Rather than having to individually change each row number one by one, is there a way to assign some sort of variable to the cells in the column such that [math]\LaTeX[\math] assigns the nunbers to them during compilation?

>>12150668
do you need to use the mic?

>>12150668
then say that. the professor sounds like a cunt, can they listen to what you're saying or just see that you're making noise?
just muffle your microphone with some sort of cover then. say you were talking out loud during the test and you won't do it again.

Anyone here experienced with [math]\LaTeX[/math]?

Let's say I want to make a table with where the first column is a series of numbers going from 1, 2, 3... all the way to 25.
Now let's say that I wanted to add a row in between rows 3 and 4 so know the new row is row 4, but now I have to change the numbers from the old rows 4-25 to 5-26 to reflect this change. Rather than having to individually change each row number one by one, is there a way to assign some sort of variable to the cells in the column such that [math]\LaTeX[/math] assigns the nunbers to them during compilation?

>>12150662
Based prof.

How did they convert theta = tan^-1 (9/8) to y=(9/8)x? I understand how they got the other two but I literally cannot understand how they did this.
I first broke up the tan^-1(9/8) = theta into 8/7 = tan theta but at that point I just got lost

>>12150637
>No first year phd knows what they're doing
You have no idea how encouraging this is.
Regardless, I'm looking at whatever is possible, I'm very content with doing a master's as long as I'm able to finance it in a feasible manner. (dude just sell drugs lmao obviously doesn't cut it lol)

>I would encourage you to look into this more, maybe reach out to a few professors that you'd be interested in working with

Ok I've heard this before but I don't know where to start. Do I just look into the departments and see who's doing what and email them explaining that I have an interest in what they're doing and what I wanna do?
Again, the phd option is the best case scenario but seems like it's the most out of reach one.

Sorry for all the questions and thank you very much for taking the time to answer, I honestly appreciate it.

>>12150732
[math]x = cos(\theta)[/math]
[math]y = sin(\theta)[/math

>>12150794
>[math]y = sin(\theta)[/math
[math]y = sin(\theta)[/math]

Should've previewed it...

>>12150688
As far as I know you'd have to do it individually or figure out a command for it.

I hate to ask, but is there any proof that this holds up? It seems like something very specific to the joint PDF used, no?

>>12150688
[math] \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex \latex [/math]

>>12150794
No
[math]x = r \cos(\theta) \\ y = r \sin(\theta)[/math]

>>12150688
[math] \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX \LaTeX [/math]

How do I convert the upper bound of θ = pi/2 to its cartesian form?

Is Bretscher a good book?

>>12150870
Have you drawn a picture of the region?

>>12150920
Yea it looks like a triangle, if I were to take the cosine value of both sides, it would 'close' it off which I assume is the correct choice of action. But is there a way where I wouldn't need to 'sketch' it? Like be able to tell without it?

>>12150926
Its just x=0.

>>12150938
Could you tell me how you got that? I've been stuck on dis for like a good 30 mins

>>12150770
you can always afford education. it's not that expensive
>Do I just look into the departments and see who's doing what and email them explaining that I have an interest in what they're doing and what I wanna do?
if you're considering a phd, you should have an idea about what field you want to work in. find people in these fields, reach out to them talking about how you find their research interesting and that you'd be interested in working with them (if possible). mention your background and relevant experience. ask to talk if you want to.

honestly, try this process out by emailing someone you're not ~super~ interested in first. that'll give you an idea of how the responses will be.
keep in mind during covid it'll likely be slow and unresponsive. don't be discouraged.
if you want to play the slow game, just say you'd have a couple questions about their research to ask them. come up with questions to ask.

>>12150952
If you want the method with all of the formulas, [math]r\cos\theta = 0,[/math] so [math]r=0[/math] or [math]\cos\theta =0[/math]. The first case only gives you the origin. The second case implies that [math]\theta = \pi/2, 3\pi/2,[/math] and I find that almost always, [math]r \geq 0[/math] when you are using it in multiple integrals, and it applies in this situation too. So [math]\theta = \pi/2[/math] is the positive y axis.

The thing that I would tell people is that when you measure [math]\pi/2[/math] from the positive x axis, you get the positive y axis, which has the equation x=0.

>>12150976
>you can always afford education. it's not that expensive
The tuition fee is not the issue. Living costs are. My parents have no way of sustaining me in europe during my masters and I honestly don't wouldnt want to place that burden upon them even if they could. I need a way to sustain myself whilst there, that would be a part time job or financial aid or whatever I can find (if masters).

Thanks for the advice regarding contacting profs. Ill put it to use, hopefully opportunities come out of it.

Again, thank you very very much!

>>12151032
I don't know much about the phd process in EU but you should get paid for it. It should subsidize a good portion of your living cost, if not all. I would look up what the systems are in the countries you're interested in.
You won't be able to get a 2nd job during a Phd or masters really. At the minimum it will be really hard and at the most it'll be outright prohibited.
You could always take out an educational loan for a masters, but this is also putting yourself in debt for a postgraduate degree, which you never want to do.

>>12151009
Ahhhh the second part made it a lot clearer for me thank you! Next time I'll just measure from the x-axis and then ask myself how I should label it, thank you.

What does it mean for a charge to be *quantuized*? As in it always have the same value? Or that it always have a positive or negative sign assigned to it? Or that it is also represented by the symbol e?

>>12151082
integer

>>12151082
quantized means there are discrete values that it can take on.
charge can only be in multiples of e (or 1/3e for quarks, but these are always bound). there is no way of having something with 1/2e charge

>>12151046
Yeah loans or jobs are for the masters. Most likely loans if I can access them.
Phds in sweden pay very well actually

>>12150835
I'm pretty sure that's from Ross, but what exactly do you want proved?

if i go to a psychologist and tell them im attracted to young girls, would they report me?

>>12151258
Depends on the psych but no
If you ever tell them you did something illegal. Then yes

is Mohr's circle considered a phase space?

>>12151246
Sorry I guess I should've asked it better:
How is it that we can approximate it to f_x(x)*sigma? Can there not be PDFs that even with little changes change their values so much that f_x(x)*sigma would be a bad approximation?

And it's from Tsitsiklis if you are interested

>>12151329
Continuous random variables have continuous cumulative distribution functions. So you can assume that the corresponding pdf is continuous. That is, in the equivalence class of pdfs, choose a continuous function corresponding to the derivative of the cdf(or rather, the Radon-Nikodym derivative of the probability measure if you're into that). If you are unable to, then the pdf will have jump discontinuities and then the random variable is not a continuous rv. This will control the amount of change you have in a small region.

>>12151329
Also, I recognized that book, so I thought it was from Ross, but I've read Bertsekas and Tsitsiklis's book as well. I would recommend that book over Ross.

I want to measure a position. The operator for position is
[math]\hat{x}\psi=x\psi[/math]
After applying the measurement, the vector state changes from [math]\psi[/math] to [math]x\psi[/math], which collapses the wave function. Nevertheless, the new state should still evolve according to Schrödinger's equation. The problem is, when I try to test it, I find the new state no longer satisfies the Schrödinger equation. When I try to do it, I get:
[math]ix\hbar\partial_{t}\psi=-\frac{\hbar^2}{2m}(x\partial_{xx}+2\partial_{x})\psi[/math]
What am I doing wrong?

>>12151370
Oh, so continuity is enough to warrant the approximation [math]\lim _{n\to \infty }\int _{a}^{a+n}f(x)\,dx \approx F(x)*n[/math], makes sense, thanks! Does this by chance have a name or so I could refer to?
>I have no clue how to word this for a google search, sorry
>>12151374
I see, thanks!

>>12151507
Did you write your limit correctly? The main thing that you have with continuous functions is that they are bounded on compact domains. That is called the extreme value theorem. Then [math]L \leq f(x)\leq M[/math], so [math]L\delta \leq \int_a^{a+\delta} f(x) dx \leq M\delta[/math]. By continuity, we may make [math]\delta[/math] small enough so that [math]M-L[/math] can be as small as we want, say for some [math]\epsilon[/math].

Followup question on >>12149499
Is there a mathematical reason that the complex numbers (as an algebra) have a notion of distance through the complex conjugate, but the Grassmann numbers do not?

>>12151557
That's a beautiful theorem and proof, thank you very much for all your help!

>Did you write your limit correctly
Oh I didn't, thanks ^^

We say RVs [math]X,Y[/math] are independent if their joint density equals the pointwise product of their marginal densities, [math]\rho_{X,Y} (x,y) = \rho_X (x) \rho_Y (y)[/math]. Is there anything interesting to say about the case when the [math]=[/math] is exchanged for either [math]\le[/math] or [math]\ge[/math]? (Where the inequality holds for all [math]x,y[/math] of course)

>>12149867
Are there any good books/articles about learning methods? I feel as if I'm doing it wrong.

Any UK/british lads have any recommendations for high school physics books?

>>12152111
i shouldn't say "High School" but Secondary School

Why is there no hand holding in math classes? why are the "real" textbooks so terse? How do they learn stuff? 90% of what they seem to "just know" is not covered in any of the text books. Mos text books give you definitions with little explanations and then immediately demand proofs "as an exercise". WTF

>>12152197
you can just email your prof. most of them aren't work to rule assholes who tell you that their job is to give 1 lecture per week and grade exams.

>>12152197
I might be retarded but I'm pretty sure that it's done so you can't learn on your own so you're dependent on an "expert", who you can only learn from by enrolling in his class for lodsofemone.

How does one find the constants of motion when energy is not conserved? Specifically, when the change in energy is dependent on the state. Pic related.


Is it possible that certain photons emitted by blackbody radiation are unable to be reabsorbed by any atom or molecule?

Guys how do i solve 55?
The result should be (4,3)
But if i put y=3/4 in the upper equation and then simplify it for the quadratic equation, i get a fucked up root ( i get 6.51950199 wtf)
I don't know where i went wrong, pls halp

>>12152440
>But if i put y=3/4
It says y=3/4*x

>>12152446
3/4x*

I still don't know where i went wrong

>>12152464
Post your procedure

How do i convert kilowatts to newtons?

>>12152472
[eqn]P = F \cdot v[/eqn]

>>12152472
You don't. KW and N don't measure the same physical quantity.

>>12149867
>table of 1 to 10, not 11 to 20
really?

I'm trying to put all relationships between units and formulas on a diagram. This is the core basic skeleton and I will progressively add more complex stuff.
Do you think it is a good idea?

>>12152494
with a particular focus on chemistry, if it wasn't already clear haha

>>12152498
Well, I think some of your students will find it helpful

>>12152507
I would like to use it for people learning but also for me once I start adding complicated stuff like electrochemistry or chemical engineering equilibriums etc.

>>12152440
ill help you but first you have to prove youre not chinese

>>12152494
I like it.
>>12152440
[math](x - 1)^2 + (\frac{3}{4} x - 7)^2 = 25[/math]
This is a quadratic equation and can be plugged wholesale into wolframalpha.
https://www.wolframalpha.com/input/?i=solve+%28x+-+1%29%5E2+%2B+%283x%2F4+-7%29%5E2+%3D+25
>>12152298
See >>12149955

>>12152579
if that guy turns out to be a chink i swear to christ anon ill never forgive you

>>12152579
>I like it.
thanks, I like to think in terms of relationships when possible. I also did this one and I hope to merge it with the other.

>>12152555
Checked

Pls help, the the site the other anon sent cost money, i searched for online servers and found nothing that helps, that's why i asked you guys.

As the other anon showed, at some stage it gets multiplied by 25 so it becomes 25x/16^2 - 25x/2 + 50 = 25

I don't know what step i missed along the way.

>>12151370
>>12151597
Sorry, I found a mistake. Continuous random variables can have probability density functions with jump discontinuities. Example is the exponential random variable. Still, the discontinuities form a set of measure zero, so the bad points doesn't really matter in terms of the estimation. This is always a thing you have to keep track of in probability theory and other things that use measure theory. Pretty much every theorem is true up to a set of measure zero.

>>12152654
wolfram doesnt cost money

OK this may be funny to you but it is not funny to me. I am reading Gravity by Misner and I don't understand much. Are there any gaps I need to fill if I am basically only familiar with high school level math, i.e. up to basic calculus? I also watched some youtube videos about vectors in general. I picked this book because it describes a lot of things "in words". But it is the formulas and the drawings that I don't get.
For example whats up with statements like this:
>Curvature manifest itself as gravitation
But I believe it is exactly the opposite:
Gravitation manifests itself as curvature. I mean how can curvature cause "gravitation" lol. It is obviously gravitation that distorts everything. Was he drunk when he wrote that?

>>12152654
Alright, alright, I'll spoonfeed you.
[math](x - 1)^2 + ( \frac{3}{4}x - 7)^2 - 25 = x^2 - 2x + 1 + \frac{9}{16}x^2 - \frac{21}{2}x + 49 - 25 = \frac{25}{16} x^2 - \frac{25}{2} x + 25[/math].
Solve it with Bhaskara.

I need to solve distance needed to stop the car, starting velocity is 75km/h, brake power is 430kw and mass of the vehicle is 14245kg. How to?

Guys pls i got lost at this equation and wolfram doesn't show me the step I'm missing without being able to pay money for it.
After i put y=3/4x in the left equationg i get x^2+9/16x-2x-7*3/4x-7*3/4x+50=25
I'm doing something wrong at this stage but I'm not sure what it is

>>12152695
bro fuck off, you were in the last thread where anons answered your question, and like three more answered in this thread. this is clearly trolling

>>12152704
was that when anons started a long autistic investigation about writing right to left etc? what was that about?

>>12152694
What governing equations are you working with?

>>12152707
yes, people thought that he was arabic or some shit LMAO

>>12152694
It originally has [math]14245 * 75^2 / 2[/math] kinectic energy. It loses kinectic energy at [math]430 kw[/math]. That's just a linear equation.
Fucking units tho.

>>12152720
that cant be right, arabics are good at algebra

>>12152730
yes taleb seems to be ok

>>12152734
He is not an arab, he is european, you imbecile. He is Nicolas. 100% euro.

If the official IS unit for mass is the kilogram, should we actually call tons kilokilograms and grams milikilograms?

>>12152743
if a Lolita was a unit of measurement, would a thousand of them be a kilolita?

>>12152704
>>12152579
>>12152682

Thank you guys and sorry for my autism, at the part where you open (3/4x-7)^2 i get +9/16x^2-42/8x instead of 42/4x, i accidentally add the base 4+4 instead of realizing that you just leave 4 at base and you get 42/4x, aka 21/2x.

Again thank you anons you helped me alot

>>12152743
kk is a thing. posers and wannabes use it all the time when discussing their astronomical salaries.

>>12152695
(x-1)^2+(y-7)^2=25
=> (x-1)^2+((3/4)x-7)^2=25
=> (x^2-2x+1)+((9/16)x^2-(21/2)x+49)=25
=> (25/16)x^2-(25/2)x+25=0
=> (1/16)x^2-(1/2)x+1=0
=> x^2-8x+16=0
=> (x-4)^2 = 0
=> x=4
=> y=3

>>12152694
The whole kinetic energy of the car has to dissipate into the brakes. Assuming constant brake power:
[math]E(t_0) \stackrel{!}{=} E(t_{end}) \Leftrightarrow \frac{1}{2} mv^2= P_{brake}\cdot t_{end} [/math]

>>12152743
Just another reason why SI units are retarded along with everything else that came from the "enlightenment"

>>12150292
This is just a philosophical stance called formalism.

Is there a text equivalent to Gravitation but on SR?

>>12151411
I think I see the confusion, and there's a lot going on here.
Think about a state that is fully localized in position, corresponding to a position eigenstate for position [math] x_0 [/math]. What would this look like? It would be a dirac delta centered at the point that [math] x_0 \rightarrow |x_0 \rangle = \delta (x-x_0) [/math] . If this isn't obvious let me know and I can go through why that has to be the case.

If we're talking about measurements and collapse, then you need to represent your wavefunction in the same eigenbasis as your operator. Well, things get a little shitty here, but you can naively say that your position-space wavefunction is given by [math] | \psi \rangle = \int dx \delta (x-x_i) \psi (x) [/math] (which I get is a bit of a circular definition but hopefully you get the idea so I don't need to go through 5 lines to arrive at the same answer).

So, if you measure your wavevector and measure a value [math] x_0 [/math], your wavefunction "collapses" into the infinitely-localized state [math] \delta (x-x_0) [/math], which has eigenvalue [math] x_0 [/math]. However, this is only in the ideal case. In reality, you cannot collapse to a perfect delta function, you'll actually get a "highly localized but not infinitely localized" position wavefunction as a result of a position measurement. To work with these you need to use statistical quantum mechanics, and their logistics depend on your measurement scheme.

The reason that we can get away with saying [math] \hat{x} \psi = x \psi [/math] is because, for operators with continuous spectra, we're only ever interested in "intervals." When we want to calculate things relating to position, we want to know "the probability that the particle is found in the interval [a,b]," since "the probability that the particle is at x=a" is exactly 0. Thus, we actually integrate the result of a position measurement over an interval, which has the same effect as integrating [math] x \psi [/math].

>>12152298
I already answered the second question
>>12149955

>>12150465
I think you could start out with just linear algebra, basic group theory and ring theory (maybe some topology for compact groups), but rep theory was one of those subjects like number theory where the requirements gradually expand until they become literally everything.
>inb4 how basic is the group and ring theory
Serre recalls in his Linear Reps of Finite Groups what's an abelian group and how you do products of abelian groups,

>>12149867
Can someone pls explain ordered pairs to me? I don't understand what the set notation is supposed to mean. As in;
[math](a,b) = \{\{a\},\{a,b\}\}[/math]
I get no meaning from the curly bracket part

>>12152886
Should I read an abstract algebra book for both ring and group theory or should I read separate books on the topics?

>>12152922
Just read a normal abstract algebra book.

>>12152913
An ordered pair must be a set for some reason that we don't care about. The only thing you need to understand about the right hand side is how (a,b) is different from (b,a). This is, that the RHS is actually an ordered pair.

>>12151989
Give this a go

>>12152955
Yes I get this. What I don't get is why the curly bracket notation represents this difference.

>>12152940
Thanks for the advice, fren

[math]R =\langle \{ ax^b : a \in \mathbb{C}, b \in \mathbb{Q}^+ \} \rangle[/math] (complex polynomials on one variable with nonnegative rational powers) works innit? Not noetherian because we can just get the ideal generated by a smaller [math]b[/math], but the spectrum satisfies the condition because it only has only one non-trivial prime ideal, right?

>>12152913
>>12152984

"{ }" brackets are roster notation for sets and the elements contained within them, so "{a}" is the set containing the element "a"

elements of a set in roster notation aren't ordered so { a , b , c } is equivalent to { a , c , b } . we would like to be able to order elements of a set and an easy way to do that is to use cardinality. { a } has a cardinality of 1, and { a , b } has a cardinality of 2

How come these 2 integrals provide the same answer but in different signs?
The only different between the two is the lower bound for theta, the first being 3pi/2 and the second being -pi/2, aren't they both the same point but expressed differently? And if I were to go from 3pi/2 and -pi/2 to pi/2, wouldn't they both be going in the same direction of the right side?

>>12153058
The first one gives you a region in the second and third quadrant. The second one gives you a region in the first and fourth quadrant. The reason why is because the theta can keep track of the angle measurement, so even though you are integrating at the same points, it knows that [math]\frac{3\pi}{2}> \frac{\pi}{2}[/math] and can keep track of that. That's why you can integrate from 0 to [math]2\pi[/math] and get something nonzero.

Also, the top integral is not the negation of the bottom integral. Look at it carefully.

What's a good Master's Degree to get after a BSc. Applied Mathematics?

>>12153181
Statistics

>>12153222
Best job opportunities for MSc. Statistics? Is there any chance to work in AI if I ever have the interest to do so? Also, outside of projects, what are the best ways to show that I have programming/computer knowledge without having a degree in CS?

>>12153181
ML shit, stats, bioinformatics are all worth money to employers

>>12153181
MBA

>>12153240
>bioinformatics
Seems interesting. Can I get into this field without any knowledge on Biology?

>>12153181
dick lickin'

Guys this is the last one i promise, what do you do in an equation like this one? If i simplify the lower one i get 2y^2=18/3x^2
Do i multiply this by 3 and the upper equation by 2 and then insert 6y^2=54/9x^2 to the upper one?
I did that and i got a huge mess.
The result should be (0,-3) (0,3)
Sorry for the repeat questions i just really suck ass at this and this is the board that can help

>>12153249
Yes

>>12153256
>this is the board that can help
not this time, Chang

>>12153256

Do a=x^2, b=y^2 giving you easier linear equations.
then just keep im mind you get 2 solutions for each x,y when taking roots

>>12153233
The big thing is machine learning, which involves many fields, including statistics and CS. If you're more into CS and AI, why not do that?

>>12153275
You mean insert a=x^2, b=y^2 randomly to one equation to get a quadratic equation?
>>12153264
Lol what's with this Chinese meme

>>12153372
>You mean insert a=x^2, b=y^2 randomly to one equation to get a quadratic equation?
No, substitute in both equations, to get a pair of linear equations. Why would we be asking you to do something "randomly"?

>>12152971
Thank you.

>>12152824
I think I get what you're saying. Say I get away with saying [math]\hat{x}\phi=x\phi[/math] because after the measurement I get something other than Dirac delta, for example, a rectangular step function (which is a simple enough case), in such a way that I get the same expected value as the Dirac delta but with some uncertainty on position. In this case [math]x\phi[/math] should solve the Scrödinger equation for the valid interval of x (e.g. the interval where the rectangular step is nonzero). The question is, if I apply the Schrödinger equation to [math]x\psi[/math] instead of [math]\psi[/math] should I expect to recover the original Schrödinger equation? And if no, why?

>>12153489
Every [math]\phi[/math] is just [math]\psi[/math], goddamn dyslexia.

>>12153445
I did that to the first equation and i got a quadratic root of - 3 and 9/4

Did it with the second equation and got some messed up root.
You meant that if we take for example the first equation and set a=4 b=3 c=-27?

>>12153040
Wtf are you saying? Cardinality is an equivalence relation not an order relation.

To define an order you need to define >, < and ≠

>>12153489
have you learned angular momentum? it's much easier to think about this in terms of angular momentum if so.
part of what's hindering your understanding is you can never be in a position eigenstate, simply because you can't construct a delta wavepacket.
but what I think is most confusing is the fact that, when you make a measurement, your final state is not the state that you think it is. let's define [math] \psi \text{ , } \phi [/math] to be the initial wavefunction and the "collapsed, pseudo-delta" wavefunction (ignoring the fact that this makes no sense, because a real treatment requires statistical QM like I mentioned before). Following the observation of the position, you have something more like [math] \hat{x} \psi = x \phi [/math] for some phi that depends on what position you measure, since your original wavefunction is not an eigenstate (and never can be).
What's worth noting is that this x is NOT a variable -- observables are always real numbers, and you're observing a position. the "x" in [math] x \phi [/math] is a c-number (just a number) that corresponds to what position you measure when you make the observation. your final state is thus described by [math] \phi \text{, not} x \phi [/math].
This wavefunction is distinct from your original state, since as you know a measurement of something that is not an eigenstate doesn't return the same state (otherwise the initial wavefunction would be an eigenstate). It obeys the schrodinger equation in the same sense that everything in QM does, though. I'm not sure what you mean by "solves the schrodinger equation," that's like saying "this trajectory solves newtons laws of motion." The equation dictates the state, not the other way around.

I'll end with what this looks like in practice. When you measure the position of a delocalized object, it localizes to approximately a point (probably more like some really narrow gaussian) in position space, given by a wavefunction you need to determine separately

>>12153554
(cont.)
The wavefunction that it collapses to will depend on what value of position you measure, the specifics of your detector, and the potential that your particle is in.
This collapsed position-space wavefunction will then evolve according to the schrodinger equation. It will spread out quite quickly, with dynamics given by the time dependence of the schrodinger equation (aka it is NOT a steady-state solution). The spread at the beginning will happen much quicker, because your position uncertainty is very low following measurement, meaning your momentum uncertainty gets higher and thus your particle has a wide momentum spread and smears out faster accordingly.
Like when someone records a slow-mo video of dropping something in a pool of water. When the resulting splash is at the peak, think of that as the "collapsed" position wavefunction. This peak spreads out quickly following this.

>>12153508
I mean try solving the system:
4a + 3b = 27
3a + 2b = 18
for "a" and "b".

Is this guy right?
https://www.youtube.com/watch?v=iU59S5JDpSU

>>12153629
judging by the title, yes

>>12153622
If i subtract the first equation by the second one, and assume that x=0 i get the anwser (0,3), that is one of the correct answers, the other anwser should be (0,-3), but i have no idea how i should get it because even if i insert y=-3 in the equations i don't get 0.

>>12153651
You do know that (-3)*(-3) = 9?

>>12153629
He's right except at the very end. Space is infinitely divisible.
Zeno's paradox just shows that if, an infinite amount of points fit inside a line segment, an infinite amount of events can happen in a finite time frame.

>>12153665
How do i find the y=- 3?

>>12153554
>What's worth noting is that this x is NOT a variable -- observables are always real numbers, and you're observing a position. the "x" in xϕ is a c-number (just a number) that corresponds to what position you measure when you make the observation. your final state is thus described by ϕ, notxϕ.
This particular statement is what I didn't get before, everything makes sense now. Thanks a lot, anon.

Many, many years ago I had exceptionally boing lecture n physic. Lecturer droned that linear forces (F ~ distance-between-objects) and inverse-square forces (F ~ 1/(distance-between-objects)^2) are somehow distinguished. What is so special about them?

>>12153818
[math] F \propto x [/math] leads to oscillating motion (spring, pendulum), describes harmonic potentials
[math] F \propto \frac{1}{r^2} [/math] leads to bound "orbits," describes attractive forces (gravity, electromagnetism)

both are important because they're pretty much the most interesting and common types of forces, as the motion that they describe is periodic and doesn't blow up to infinity or die out to 0 over time.

Would {0} technically be closed under addition?

Would I be able to see or hear or feel anything if two hydrogen atoms spontaneously fused in front of me?

I've started to re-learn maths at age 22 after I dropped out of Cs degree.
I was a horrible student in high school when it came to maths.
What is the best way for me to learn mathematics, are there any books for a person like me(already tried Khan academy, but I hate videos)?
Can I still become a mathematician?
Literally starting from scratch here.

>>12149867
could you explain the abstract in baby words please im retarded

>>12153941
Nevermind I'm fucking stupid, of course it's closed under addition since 0+0=0

>>12153701
Starting with:
[math]4x^2 + 3y^2 = 27[/math]
[math]3x^2 + 2y^2 = 18[/math]
For convenience, substitute "a" for [math]x^2[/math] and "b" for [math]y^2[/math], giving:
[math]4a + 3b = 27[/math]
[math]3a + 2b = 18[/math]
Subtract 2 times the first equation from 3 times the second equation gives:
[math]a = 0[/math]
Filling this in to the second equation gives:
[math]2b = 18[/math], giving [math]b = 9[/math].
By our definition of "a" and "b", this says [math]x^2 = 0[/math] and [math]y^2 = 9[/math]. So x=0, and either y=3 or y= -3.

>>12153941
I know it's called stupid questions, but this might be pushing it a bit.

>>12153961

No, you would instantly become deaf and blind

is there such a thing as a half dimension? like R^1/2 or something similar

>>12153961
Don't think so.
https://www.physlink.com/education/askexperts/ae534.cfm
Twenty seven million electron volts is about 0,000000000001 calories according to google.
>>12154083
Look up Hausdorff dimension.

>>12154083
Some fractals have a dimension of 1/2

>>12153974
got you cover anon
https://4chan-science.fandom.com/wiki/Mathematics
https://4chan-science.fandom.com/wiki/Math_Textbook_Recommendations

>>12154083
R^1/2 should stand for a space X such that X^2 = R. I doubt that's possible. non-integer dimension is a thing though, fractals ale like that.

>>12154083
https://en.wikipedia.org/wiki/Hausdorff_dimension
https://en.wikipedia.org/wiki/Koch_snowflake

>>12153961
the fusion energy of two protons is 1.442 MeV or 2.3E-13 Joules. this energy goes into the kinetic energy of the products, including a positron that is produced. this positron would annihilate an electron, producing an extra 1 MeV of energy that is split between two photons.
human eyes can (arguably) see single-digit numbers of photons, but this is pushing it. you'd need a room that's the blackest black and even then you'd see nothing most likely.
most of the energy would be carried away by a neutrino in the form of kinetic energy, which you wouldn't see.

my guess is no, you wouldn't notice anything. unless the positron annihilates an electron on your body, but I don't think humans can feel this (source anyone?)

>>12154123

Good answer, thanks. It's always boggled my mind how much energy comes from atoms just through sheer numbers

>>12154026
So i don't really find the - 3, i assume that the other y is negative 3 because the x's are 0? Thank you so much, thanks everyone, even the one who called me a chink
You got no idea how much you helped me

>>12154026
But 4a times two is 8a, and 3a times 3 is 9a, how is subtracting them gives us a zero?

>>12154250
You are right, that's why an a is left over and we get a = 27*2 - 18*3 = 0

>>12154264
Fuggggg thx mate

Trying to reinforce my understanding of vector valued functions vs vector spaces
Top example: R-> R^n space curve (r is usually time), 2D example: the blue position vector is the OUTPUT
Bottom example: R^n -> R^n, the blue vector is THE INPUT (the argument given as (x,y) ) and the values are the green vectors, correct?
So basically with vector value functions, we have one function per coordinate such as f(t) and g(t) and their output are a pair of numbers (x,y) that give us the tip of the position vector.
But for vector fields, x an y are given to us directly and we do something with them: f(x, y) and the output is the new vector.
Any inaccuracies in my understanding? I want to be sure I am 100% correct.

>>12154096
>>12154100
>>12154120
>>12154121
holy moly, i never thought of fractals like that. this video explains it very nicely if anyone else is interested: https://www.youtube.com/watch?v=gB9n2gHsHN4

thanks a bunch, anones. i wish i was math-smarter.......

>>12149933
>"transform the nonholonomic system into a holonomic one lmao"
Realized one day later that I wrote this instead of "transform the time-dependent hamiltonian into a time-independent hamiltonian".
>inb4 something something energy isn't the hamiltonian yada yada yada
See https://www.degruyter.com/view/journals/phys/5/3/article-p313.xml if anyone's interested for whatever reason.

>>12153240
>>12153249
>>12153233
>>12153280
I'm concerned about a lot of recent developments where things such as AI farming your personal information and pushing things like personalized advertising. I know that everything has the potential to be used unethically under the wrong hands, but it's really difficult to see how AI can be used without being unethical.

Believe me, I really am interested in the idea of machine learning and AI but not for the purposes of allowing big corporations invading people's freedoms. Can somebody prove me please prove me wrong and that I shouldn't be too focused on the extremes and that there are ethical uses for AI?

>>12154327
Yes,

f: R -> R^2 can be written as f(t) = (g(t), h(t)), where g, h are R -> R.

f: R^2 -> R^2 can be written as f(x,y) = (g(x,y), h(x,y)) where g, h are R^2 -> R

Is it true that if [math]| x_{n+1} - x_n| < \frac{1}{n}[/math], then [math]\{x_n\}[/math] converges?

>>12154484
ah, thats even better and clearer, thanks.

>>12154504
No.
Set [math]x_n = \sum _{i = 1}^n \frac{1}{2i}[/math].

>>12154522
Thanks.

How do inverse trig functions work?
For real tho

>>12154553
sin(x)=y
arcsin(y)=x

>>12154522
You actually don't even need the 2 in the denominator; the regular harmonic series does the job.

>>12154559
This.

>>12149955
>There's no way to emit a photon that cannot be reabsorbed
So black body radiation is not a continuous spectrum?

hello sci, 1 question. suppose I pick a point on [0,1] at random uniformly and I cut the interval at this point. Let R be the random variable that is the ratio of the shorter length to longer length, what is the cdf of R? How the f do i find it?

>>12154596
black body radiation is continuous. but there's no such thing as a perfect black body, only things that get really close to it (stars). doppler broadening helps to smooth out the spectrum too, so technically you can emit a photon that doesn't correspond to an absorbable energy in the rest frame, but when you move the absorber then it can be shifted to resonance.

>>12154611
nvm this question is dumb

>>12154675
I mean, not really?
You want twice the inverse of [math]f(x) = \int _0 ^x \frac{t]{1 - t} dt[/math], I think.
Kind of a pain in the ass.

>>12154701
[math]f(x) = \int _0 ^x \frac{t}{1 - t} dt[/math]
I'm starting to think I should buy a better keyboard.

>>12154611
Define
[eqn]
R = \begin{cases} \frac{X}{1-X} & X \leq \frac{1}{2} \\ \frac{1-X}{X} & X> \frac{1}{2} .\end{cases}
[/eqn]. Then we have the cdf of R is
[eqn]
\mathbb{P}(R\leq a) =
\mathbb{P}(\frac{X}{1-X}\leq a) + \mathbb{P}(\frac{X}{1-X} \leq a).
[/eqn] Then
[eqn]
\begin{align}\mathbb{P}(\frac{X}{1-X}\leq a) &= \mathbb{P}(X \leq a(1-X))\\
&= \mathbb{P}( X\leq \frac{a}{1+a} ).
\end{align}
[/eqn] The last one you can figure out because you should know the cdf of X. Then do something similar for the other case.

>>12154675
Screw that, I already typed it.

>>12154705
>>12154701
i've never seen a frame around misgendered latex. is this something new?
is this something new?

>>12154743
>misgendered
wtf? must be autocorrection
i mean mis-rendered

I NEVER understood how the FUCK anyone is supposed to easily find explicit formulas for recursive sequences when they shove so many factorials and weird equations up their asses that you have to plot out 50 points before you have a chance to find a pattern. WHAT THE FUCK AM I MISSING

>>12154752
associative thinking skills, I was really bad at it before I took analysis and got gud by being forced to spot the pattern or lose points on quizzes/assignments.

>>12154761
Analysis separates the boys from the men.

>>12154761
>>12154773
>literally in analysis now
a-am i gonna make it anons...

>>12154779
do more exercises, go to office hours, go to study groups with your talented classmates, go to tutoring with the unsympathetic grad students. Ask questions here when you're stuck. Study. Don't be a fucking faggot, take your performance into your own hands.
>>12154773
This, desu

>>12154779
Where are you at right now? Topology of [math]\mathbb{R}[/math] is usually the first real filter people encounter. That being said, if you can make it through Analysis I, you're pretty golden for the rest of your degree (assuming it's math).

>>12154773
>a first-year undergrad course separates boys from men
anon, I...

>>12154790
Analysis is usually when people that get A's in calc and diff eq find out they're hard working idiots. It's the first big filter for mathematical reasoning at the uni level

>>12154801
Lower level calc and diff eq hardly qualify as math, t b h.

>>12154478
bump

scalar: magnitude
vector: magnitude and direction
tensor: magnitude and direction and ????

>>12155129
magnitude and direction and orientation

>>12155129
A tensor is a generalized vector space.

Can wearing headphones all the time actually change the shape of my skull...
?

>>12155186
Are your headphones made out of two ton cinderblocks?

Why am I paying 50k for an online degree when I don't even go there?

i am helping homeschool some children and successfully got the 9 year old to do long division. im stumped where to go from here. just been giving him the same numbers in + - * / and seeing if he can connect the dots. this is also on top of their mandatory schooling. any suggestions?

>>12155407
Do you do it for free?

>>12155423
no, they pay me in their undying loyalty

>>12154784
>>12154790
Analysis was brutal to take in my first year. I suppose it wasn't that hard as a subject as much as the scoring was incredibly bloody. Get three topics, say cantor sections, limit of a sequence and criteria of convergence, you have three hours to basically recreate the entire lecture on each from scratch. You either write everything perfectly or you fail, if any theorems or proofs covered are missing, fail, etc. 2/3 need to be completely accurate to pass. If you had shit luck it could be 20+ pages to write. Best way to pass was just to memorize as many complete topics verbatim and pray you'll get those.

>>12155407
roots, logs, trig, complex numbers and euler's identity
and the fundamental theorem of calculus

Let X~exp(0.75) be the delay in transmission from client to server. If X=x, let Y~N(2+x,1) be the time of the reply.

What is the density of Y?

Attempt

I understand that independence does not hold as knowing X (Y) gives information about Y (X). I thought that since summing a number to a normally distributed random variable increases the mean by that number, then Y could be the sum of X and another RV~N(2+x-x,1)=N(2,1).

>>12155639
What you are looking for is the convolution of a normal and an exponential distribution:
https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution

This does not have a closed form (the erfc stems from integrating a normal density over the part where it is positive), but the basic idea is that your Y can be written as Y = X + Z, where Z~N(2,1), and then manipulating the (conditional) densities until the expression in the wiki-article is obtained.

>>12155713
Ok, I did reach that point by setting up the convolution.

I am glad I guessed well.

I actually posted this on reddit and they answered:
"Have you learned about conditioning and conditional probability? To approach problems likes this, you could use the law of total probability to rewrite the probability P(Y=y) as ∫P(Y=y|X=x)P(X=x)dx, which is a function of y only. This gives you the exact distribution of y although in this case the integral is kinda ugly."

>>12155723
Well, "kinda ugly" is an understatement. What is the context of your question?

>>12155713
>>12155723
Many thanks, by the way.

The answer i got on reddit threw me off quite a bit because it seems to treat the RVs as discrete for some reason but then calls it an "integral".

>>12155726
It's in the chapter that deals with Multidimensional RVs.

>>12155727
This "P(Y=y|X=x)" notation is a bit misleading as you said, but it can be understood as a shorthand for a regular version of a conditional probability distribution at a point, and in many cases (such as this) it can be written as a density (just like P(Y=y) can be understood as the density at a point y).

>>12155739
I understand, so
P(Y=y) = ∫P(Y=y|X=x)P(X=x)dx
becomes
is the integral of the conditional density of Y given X=x multiplied by the density of X?

If so, how do the computations proceed?
Is this the same as the convolution method?

>>12155126
Perhaps stuff like brain-implants for amputees could use some form of machine learning decode brain activity into input to a device.
Further, autonomous transport may require good image-recognition facilities.

>>12155739
>>12155757
forgot to thank you.

>>12154553
sin(x)
You know the angle and want to learn its sine value

arcsin(x)
You know a sine value and want to learn from what angle it originates

>>12155757
You are correct. In this case, [math]f_{Y \vert X}(y \vert x ) = \frac{1}{2 \pi} \exp (-(y-2-x)^2)[/math] and [math]f_X (x) = 2 \exp(-2x)[/math].
Thus, [math]f_{Y}(y) = \int_{\mathbb{R}_+} \frac{1}{\pi} \exp (-(y-2-x)^2 -2x) dx[/math].
This is essentially the same as a convolution, perhaps change of variables is required to get an identical expression.
One could proceed by then completing the square to obtain a normal density in x with mean (y-3) in the integral, multiplied by an exponential function of y. The integral then does not have a closed form and can, as far as I know, not be simplified significantly.

>>12155785
Thank you very much, but "fX(x)=2exp(−2x)"
gets me confused.

Is it not 0.75*exp(-0.75x)?

>>12155813
Oh yeah sorry, I misremembered the parameter.

>>12155815
Your answer was extremely helpful, thank you again

>>12154327
This anon gave me a good answer >>12154484
but I'd like to clarify something. In both cases we get the "tip" of the vector. But for the space curve R->R^2 the output is a position vector originating in (0,0) whereas for the vector field it is a displacement vector that originates at (x,y). But it is not obvious from just looking at the formula that just gives us the tip. Could it not be a position vector in case of a R^2 -> R^2? Or is it an arbitrary choice so we just assume it is a displacement vector?

>>12155545
Now try the same in 2020
>corona shit
>lectures online
>fucking zoom
>lecturers don't do shit, don't explain anything
>automated tests online
>place an extra space, buggy software rejects the answer
>have to contest results all the time
>window crashes in the middle of the test
>proctored tests, bitch is watching you for 2 hours
>pay $$$ for this self study shit
I imagine they will eventually improve the software but the online bullshit is here to stay for sure.
This is the end of education as we've known it in the past.

>>12155850
Pedagogy will always be practiced irl as well

What do I need to know to study strange attractors? Just basic difference equations? How do I find my own attractors, maybe with matlab or something?

>>12155850
fwih this year it's basically a given that teaching will be a mess. Hopefully it'll be less retarded by next year.

Remember to send anonymous death threats to the bursar if they don't slash/refund tuition.

>>12155129
and dimension >= 2x2xn where n is rank (or order).

>>12155862
no threats, i will just show up in person and rape them

>>12155838
> In both cases we get the "tip" of the vector
You're imposing a geometric interpretation, but this isn't necessary. A curve in N-dimensional space is a function from R->R^n, but its derivative is also a function from R->R^n. Conversely, a function from R^n->R^n could be a spatial transformation or it could represent some arbitrary property (e.g. wind velocity as a function of position).

>>12155129
that's a retarded way of thinking about things. it's ok for a high schooler, but get this out of your head immediately if you want to learn things properly.

How do I conceptualize something like kg⋅m2⋅s-2?
What does it mean to have 5kg*m^2/s^-2?
5kg of mass accelerating through a square meter every second?

>>12149867

Can anyone explain the calculation done at the bottom of this image for me prefixed by #

I understand why there are two conflicts, and one nonconflicting overlap, but what is going on with remainderOf(1002 div 1000), the remainder of 1.002 is 2?

and what does quotientOf(1.002) / how do I get 1

I feel dumb. What's wrong with this "proof"? Let A be a square matrix, different from the identity matrix. Then (I-A)x = x only if Ax = x, i.e. x must be the zero vectors. Hence (I-A) is invertible.

It obviously doesn't work, there's a lot of counterexamples, but I don't see the issue with the proof.

>>12149867
Hello if anyone knows physics, statics please check my work if it is correct.
1. I needed to find the weight of block Q necessary to keep the system in balance

I solved it and then tried to validate it thru reversing it but I still need someone to confirm it

>>12156062
>(I-A)x = x only if Ax = x
wrong

>>12155998
how do you think about scalars and vectors?

>>12156043
bump

>>12156043
That's just energy.

>>12156111
Yes I know that it's the Joule in SI base unit form. But I'm trying to get my ahead around how to imagine it.

>>12155975
Yes but even we drop the geometric interpretation, for the vector field we input a vector (x,y) and get a new vector (x2,y2). How do we then calculate its magnitude? If we apply whatever metric is defined for that vector space, for example the dot product, we would get the magnitude relative to (0,0) unless we specifically agree that the vector's origin is at (x,y). So we still need some sort of a convention to distinguish the result as being a displacement vector relative to x,y, not a position vector relative to (0,0). I think that reasoning should be applicable not to just geometric applications but to an arbitrary vector space that has a basis. Technically nothing prevents me from defining a vector field as an f -> R^n to R^n that eats a position vector and spits out another position vector, right? That sounds like a linear transformation, desu.

>>12156213
a mapping R^n -> R^n can be interpreted either as sending points to points (transformation of the space, look up diffeomorphism), or sending points to vectors based at these points (vector field). it depends on the context. vector fields and diffeomorphisms are totally different ideas which just happen to be encoded by the same mathematical object. the distinction becomes apparent when you work on manifolds instead of just R^n.

>>12156242
>sending points to vectors based at these points (vector field).
OK, thats what I wanted to clarify. So it is the definition of the vector field that imposes that rule: the resulting vector necessarily originates from that point.

What is the closest known R CrB variable star to Earth?

>>12156043
Look up the unit definitions.
A joule is the work produced by a force of 1 N applied to an object that moved on 1 meter in the force's direction.
A newton is the force that produces an acceleration of 1 m/s2 for an object weighing 1 kg.

>>12149925
Hey I feel the same. Even have a little notebook for all my dumb stuff.
I'd rather ask here tho, seems more active, but you lose nothing asking twice, even if you get bullied

>>12156267
Are there really branches of mathematics that talk about vectors have an origin, as if they were little arrows?

>>12155407
> same numbers in + - * /
Stop this immediately and use proper notation for division.

I'm not sure if I understand what you are asking but I'm assuming you want to know what you should teach them. First and foremost, make sure they know how to do arithmetic with all types of numbers, i.e. integers, fractions, decimals. Once you get past this, work on having them understand the basic laws such as associative, commutative, distributive, etc. Do not skimp out on vocabulary and force them to learn the vocabulary.

If you can get past that stage, work through Gelfand's Algebra booklet. It's less than 100 pages but contains a lot of information that is accessible once you know arithmetic.

>>12151601
Think about what happens when you integrate over the entire range of values for X and Y. For both the joint density and the product of the marginal densities this integral should be 1. So the integral of the difference is 0. So if the difference is non-negative everywhere, for example, it can only be positive on a set of measure 0.

>>12156372
I think all branches of mathematics that deal with euclidean vector spaces. Most vector fields represent physical phenomena in non-affine Euclidean 3D vector spaces. So surely one could come up with the definition of a vector field R^n -> R^n that takes a position vector and returns a position vector.

>>12156051
Image seems to be using a "div" operator that returns both an integer quotient and a remainder, so that if r=remainderOf(x div y), and q=quotientOf(x div y), then x = q*y + r.
Since 1002 = 1*1000 + 2, remainderOf(1002 div 1000) = 2 and quotientOf(1002 div 1000) = 1.

>>12150106
Griffiths is bae, such an enjoyable book to go through

>>12150106
>>12156555
Griffith's proofs are cringe. Feynman is based.

>>12149867
how do i calculate the required electric field to pull apart Na+ and Cl- on salt water? i thought even a weak field could do it, since the water has already broken them up

>>12149982
Now make a new thread, faggot.
You have 10 minutes.

>>12157429
>You have ten minutes
>58 minutes ago
Ummm, sweetie?

>>12152494
Maybe make n, m and M a triangle with n= m / M?

>>12157429
>implying

>>12158164
well, good, thank you and fuck him

>>12158164
although you typically add a link to a new thread

>>12158247
What for?
Surely you don't leave the thread open the entire day and instead look it up every couple hours on the catalog, rendering forward links moot.