/sci/ - Science & Math

Does the degree of a self map induce multiplication for homotopy groups, or only for (co)homology?

~UNANSWERED~

Math
>>11674573
>>11688902 (Why wouldn't you just round as normal?)

Physics
>all the questions about light having momentum; still nobody mention's de Broglie's relation
>>11678300
>>11682547
>>11686409
>>11686498
>>11688483 (the gravitational interaction between planets is very weak compared to that with the sun. also, if they were to pull each other out of orbits, they would have done it long, long ago considering the age of the solar system)

Engineering
>>11675945
>>11685899 (watch https://www.youtube.com/watch?v=33vbFFFn04k and https://www.youtube.com/watch?v=DXvAlwMAxiA ; we wuz HOLES n' sheit. transistors are used in amplifiers and switches. You can't build a computer with just diodes.)
>>11689036 <3

Chem
>>11677257 (If the rxn is endothermic, the reverse is exothermic and rejects heat. Exothermic reactions are stifled when powered, from Chatelier's principle. Answer is no.)
>>11679387

/g/
>>11675712 (Use Octave.)
>>11684044
>>11688394

Stupid
>>11675612 (The game.)
>>11678443
>>11679096
>>11683564
>>11688521

>>11689319
For spheres, I should add. I know it does for one dimension, but otherwise I have no idea.

can someone give me intuition for adjoints of linear maps? reading axler and it isnt connecting

I have a problem /sci/. I can't use textbooks, I just can't Understand them, When I go on and try to learn some I feel like I'm just mindlessly reading.
And by the end when I try to recall something I just feel like I didn't even learned nothing.
I've figured that writing down EVERYTHING makes me remember, but It's Impossible to rewrite 5 textbooks in a Month.
I drink 6 cups of coffee a day since I started with textbooks, so IDK if that has something to.
Also, the way I learned stuff all through high school was by Youtube videos so that might affect as well.
I also can't take drugs like Adderall or those nootropics, Drugs are Illegal in my country

>>11689640
textbooks a shit
you, like me, are dependent on high quality lectures (visual) and demonstrations (hands on)
sucks, but at least you're living in the right time for it
>>>yootoobe
>>>libgen
>>>forums

>>11689909
I know but sadly there are some things that don't have quality lectures, so I need textbooks.

I've been studying unums/posits lately, and given the following:
>infty is defined as 1/0
>in shorthand, infty is written as /0, similar to +1 or -1
>the top half of the unum/posit circle is all positive whole numbers, while the bottom half is all fractions
What are the implications of the fact that the "whole number" 0 is on the bottom, while the "fractional" infinity, or /0, is on the top?
Does this imply zero is better written as [math]0 = /\infty[/math]? And that zero does not exist, except as an infinitesimal?

Do you collapse exponents from the right or from the left? Why?

What algorithms are used to generate the tool-path so that the CNC machine mills the desired shape. Any idea is appreciated. Does it maybe use some evolutionary algorithm or smth?

pic related.Video related
https://www.youtube.com/watch?v=jbIU7l_8pR8

>>11689206
>looking at covid growth rate with a friend
>i note the fact that italy has a log curve and brazil has exponential
>a random dude points out that its actually a gaussian curve
i got too cocky, /sci/bros...

How do I find the resonant frequency in any arbitrary RLC circuit?

Doing series right now, and in integral testing to show convergence, I don't understand why we need that the function of which we're taking the integral of (function based on our sequence) is decreasing, when before even doing the integral test we're supposed to take the limit [math]lim_{n \to\infty}a_n=0[/math] which already shows that the terms of our series are convergent. I understand this doesn't necessarily mean that our series is converging, but doesn't that kind of already show that the function that we're using to model our series is also going to 0? I'm confused as fuck.

I fucking hate calculus and I fucking hate the fact that they're making memorize this shit and I fucking hate the fact that I can't make any intuitive sense out of this shit
Why the fuck are these rules so unintuitive? How the fuck am I supposed to understand what they mean?

Would a sandstorm make the spreading of fire easier or harder? From one side it means low humidity and high winds, which should make it easier, from the other side sand is one of the best things to put out fire.

>>11692593
It would definitely put it out.
Just simulate it in your head.

How come I have less soot buildup on my pans after adding a bit of water to my denatured ethanol?

>>11690264
>what did he mean by this
>>11692477
>doesn't that kind of already show that the function that we're using to model our series is also going to 0?
A function [math]f[/math] such that [math]\int_a^{\infty}f(x) ~ dx[/math] exists does converge to zero at infinity, yes, but the inverse doesn't apply. See for example [math]f(x)=1/x[/math].
If that's not what you meant, feel free to elaborate.
>>11692584
>product rule
That's just the third term vanishing.
>quotient rule
That's just algebraic manipulation on the product rule.
>chain rule
If I play a movie at twice the speed, the characters move twice as fast.
Specifically, their speed at the time [math]t[/math] is twice the speed they'd have had at time [math]2t[/math] if I played the movie normally (because that's the same scene, obviously).

>>11692061
Find the impedance using Kirchhoff's laws, find the zeros of the numerator and denominator.

>>11692648
>That's just the third term vanishing.
What third term?
>That's just algebraic manipulation on the product rule.
How? Even so, it must have some meaning and a better reason than just shuffling some numbers around.
>If I play a movie at twice the speed, the characters move twice as fast.
>Specifically, their speed at the time t is twice the speed they'd have had at time 2t if I played the movie normally (because that's the same scene, obviously).
Yeah, that's obvious but didn't help at all. I don't see the connection.

>>11692584
>>11692685
Maybe watch the 3blue1brown video on them. They are great for intuition.

>>11692716
I did. Still didn't click because they only explain how to think of them, not why think of them that way.

Extremely stupid question about change of variables.

Consider the area in the first quadrant that lies between the parabolas [math]x=y^2 , x=4y^2 , y=x^2 , y=2x^2[/math]. I'm instructed to calculate it via the change of variables [math]x = vy^2[/math] and [math]y = ux^2[/math]. I calculated the Jacobian of [math]\frac {d(u,v)}{d(x,y)}[/math] and got [math]\frac {3}{x^2 y^2} = 3 \frac{uv}{xy}[/math]. But this can't be right - I need some way to get rid of the [math]xy[/math] term in the denominator, i.e. to get an expression solely in terms of [math]u,v[/math] in order to apply the formula.

What am I doing wrong?

>>11692685
>What third term?
[math]df \times dg[/math] in pic related.
>How
[math]\frac{f}{g} \times g = f[/math]. Thus, by the product rule, [math]\left ( \frac{f}{g} \right )' g + \frac{g'f}{g} = f'[/math]. Isolate [math]\left ( \frac{f}{g} \right )'[/math]
>Yeah, that's obvious but didn't help at all. I don't see the connection.
[math]g(t)[/math] is the function which gives you the in-movie time being displayed on the TV as a function of real time (so, for example, if I'm watching at twice the speed, [math]g(t)=2t[/math]), and [math]f(t)[/math] is the character's position as a function of in-movie time.
Then, the character's speed from your perspective is the speed he'd have had at the scene (that's [math]f'(g(t))[/math]) times the speed at which you're playing the movie (and that's [math]g'(t)[/math]).

>>11692804
>df×dg in pic related.
Oh yeah about that, how is it a legit argument to ignore df * dg just because it gets smaller much faster than the other two terms? As we approach infinity they should both be equally close to 0 and hence we can discard all 3 terms.
>[math]\frac{f}{g} \times g = f[/math]. Thus, by the product rule, [math]\left ( \frac{f}{g} \right )' g + \frac{g'f}{g} = f'[/math]. Isolate [math]\left ( \frac{f}{g} \right )'[/math]
Unintuitive and unsatisfying. Just like saying "it works because it works".
>Then, the character's speed from your perspective is the speed he'd have had at the scene times the speed at which you're playing the movie.
If I play the move twice as fast his speed is just 2 times bigger. That's only g'(t), nothing to do with f.

Can someone explain this to me? How exactly do I use this for error estimation?
This is the same as the Taylor's Remainder thing right?

>>11693128
h=f*g
dh is a small change in h, and so there is a small change in f and g. But if df is small, and dg is small, then df*dg is reeeaaaally small, much smaller than dh. So it drops out.

>>11693154
Yeah I know, I just tried to say the same thing and asked how that is a legit argument.
If I can get rid of df*dg just because it's reeeeeeeeeeeeeeeeeaaaally small, then I can make df and dg equally reeeeeeeeeeeeeeeeeaaaally small and drop out all 3 terms.
It's like the entirety of calculus is being taught as "trust me bro" without any formality and ways to resolve conflicts like these.

>>11693128
>Equally close to 0
What's the limit as x -> 0 of x^2/x?

>>11693174
>then I can make df and dg equally reeeeeeeeeeeeeeeeeaaaally small and drop out all 3 terms
what? no... dfdg is ALWAYS going to be much smaller than df and dg alone. That isn't possible.

>>11692781
You've miscalculated the Jacobian. Go through it again. What are u and v as functions of x and y? What are the partial derivatives? What is the determinant? The 'x's and 'y's should cancel out.

>>11693176
0, the same as the same limit of x, x^2 or x^3.
>>11693183
>dfdg is ALWAYS going to be much smaller than df and dg alone. That isn't possible.
As they both approach infinity they're both infinitesimally small. Comparing the magnitudes of one infinitesimal with another requires some serious justification other than just saying "no bro trust me it's smaller". We're dealing with infinity here, it's not as simple as just comparing two numbers.

Please at least tell me there have been people who had the same concerns as me, it's driving me insane. I just can't stop treating calculus as 'not-math' because of it. Dealing with infinity is not something I trust human mind to be capable of.

>>11693226
>As they both approach infinity
?????????

>>11693226
They did and they inventend limits because of it
No such thing as infinitesimals unless you're doing nonstandard analysis

>>11693313
Infinity or infinitesimality, depends on the situation.
>>11693347
But if we limit ourselves to limits, the problem of product rule (and others) appears unanswerable. As we take limits of all the 3 terms, they are all 0 and drop out.

>>11689972
find the total impedance of the circuit, set the phase angle to zero (this is what resonance means), and solve for the frequency

Is the following correct?

>For a non-empty compact topological space [math]X[/math] there is a minimal non-empty closed subset [math]Z[/math].

Order the non-empty closed sets in the topology via [math]\supseteq[/math]. Then any chain [math]Z_1\supseteq Z_2 \supseteq ...[/math] (for simplicity I ordered with naturals, but you know what I mean), has an upper bound [math]\bigcap_i Z_i[/math] that is closed. Suppose it is empty, and consider the open sets [math]U_i:=X-Z_i[/math]. By assumption, they cover the space, so only finitely many cover the space by compactness. But then there is a maximal index [math]n[/math] such that [math]U_n=X[/math], and in particular, [math]Z_n=\emptyset[/math], in contradiction with the assumption. So by Zorn's Lemma, maximal elements exist, which in this context, theyre precisely minimal non-empty closed subsets.

>>11690761
i just want you to know that i really admire your tenacity, i wish i could answer your question

>>11689206
what software or website do you guys use to plot/visualize 3D functions?

>>11693918
https://www.desmos.com/calculator/emepjyzvcx
https://www.desmos.com/calculator/uduch2qikh
https://www.desmos.com/calculator/wbm8yakmvf
https://www.desmos.com/calculator/b2cu90g9lh
https://www.desmos.com/calculator/09eis0xgv6
These are not the be-all-end-all but are pretty useful, each with their own purpose (coordinate functions)

>>11693980
this is exactly what i needed, wolframalpha plot wouldn't let me turn the function

tyvm, anon!

>>11693750
It works, yup.
Kinda curious on one thing, tho.
>But then there is a maximal index n
What's the "maximal" for?

why is the derivative of [math]f(x)=3-\frac{12}{x^{2}}[/math] [math]{f(x)}'=\frac{24}{x^{3}}[/math] and not [math]{f(x)}'=-\frac{24}{x^{3}}[/math]?
and what does the [ ] of [math][g(x)]^{2}[/math] in [math]{\frac{f(x)}{g(x)}}'=\frac{{f(x)}'*g(x)-{g(x)}'*f(x)}{[g(x)]^{2}}[/math] mean? does it have to do with this?

>>11694026
Either think of that as [math]3 - 12x^{-2}[/math] and apply [math]D(x^n) = nx^{n-1}[/math], or note that your f would be constantly 12.

>>11694045
You know who you are, even if you deleted your post.

fucking latex.. take 2:
why is the derivative of [math]f(x)=3-\frac{12}{x^{2}}[/math] positive [math]{f(x)}'=\frac{24}{x^{3}}[/math] and not negative [math]{f(x)}'=-\frac{24}{x^{3}}[/math]?
and what does the [ ] of [math]{\frac{f(x)}{g(x)}}'=\frac{{f(x)}'*g(x)-{g(x)}'*f(x)}{[g(x)]^{2}}[/math] mean? does it have to do with this?

>>11694045
>>11694079

>>11694079
im looking forward to the third attempt

>>11694079
You know you can preview your post with the latex rendered, right?
Or is that not a thing if you don't have 4chanX?

>>11694079
take 3:
why is the derivative of [math]f(x)=3-\frac{12}{x^{2}}[/math]
positive [math]{f(x)}'=\frac{24}{x^{3}}[/math]
and not negative [math]{f(x)}'=-\frac{24}{x^{3}}[/math]?
and what does the [ ] of [math]{\frac{f(x)}{g(x)}}'=\frac{{f(x)}'*g(x)-{g(x)}'*f(x)}{[g(x)]^{2}}[/math] mean? does it have to do with this?
>>11694087
>>11694045
can you explain using words or this equation [math]{\frac{f(x)}{g(x)}}'=\frac{{f(x)}'*g(x)-{g(x)}'*f(x)}{[g(x)]^{2}}[/math]? i don't understand the deeper level of how this works
>>11694109
i did and it came out fine, don't know why it goes to shit when i post

>>11694024
Well, since the [math]U_i[/math] form a cover and [math]U_i\subseteq U_j[/math] iff [math]i\leq j[/math], taking any finite subcover [math]\{U_\lambda \}[/math] from this chain is equivalent to picking an [math]U_\mu[/math] that contains [math]U_\lambda[/math] for every [math]\lambda[/math], that is, [math]\forall\lambda:\mu\geq \lambda [/math], so [math]\mu [/math] is maximal in this sense.

>>11694109
the normal webpage has the renderer (albeit located in a different part of the reply screen)

>>11694120
fuck this shit
well if you guys can understand this cluterfuck ill appreciate it if you can explain why it comes out positive and not negetive

>>11694129
are you using umatrix or any similar browser extension by any chance?

>>11694129
OH is it broken on your end?
Oneechan breaks it

>>11694120
f constant -> f' = 0
g = x^2 -> g' = 2x
f'g - fg' = 0 - 12*2x = -24x

>>11694134
nope, i'd post a link to the original code but i'm retarded and lost my clipboard copying something else

>>11694123
Right.
In that case, I'd recommend phrasing it as "the maximal element [math]U_n[/math] of the finite subcover equals [math]X[/math]".

>>11694120
That the product rule; the formula for the derivative of (f/g) where f and g are functions of x. The brackets mean you square the whole function g(x). It's kinda redundant, but whatever. It can be derived with some fuckery, just the defn of derivative probably. OR, you can just never use it. Use the product rule and chain rules instead.
>first question
think

>>11694142
yeah i get [math]{f(x)}'-\frac{24}{x^{3}}[/math]
but according to the answers in my book it's wrong and should be positive 24
>>11694160
>think
i tried to figure this shit out for the last 15 minutes

>>11694160
that;s the QUOTIENT rule** fuck
>>11694177
i tried to figure this shit out for the last 15 minutes
f(x)=3-12/x^2. The constant drops out with differentiation, so I look at the second term. Use power rule.
[eqn] (3-12/x^2)'=(-12/x^2)'=(-12)(x^{-2})'=-2\cdot-12x^{-3}=24/x^3 [/eqn]

>>11694184
i don't know what equation you are using and how you get negative powers can you solve it with the f(x)'/g(x)' equation?

>>11694120
>>11694209
nvm i'm retarded i forgot to add the - to the f(x)

>>11694209
>i don't know what equation you are using and how you get negative powers
[math] (x^n)'=nx^{n-1} [/math]
>can you solve it with the f(x)'/g(x)' equation?
First, [math] \big[f(x)/g(x)\big]'\neq f'(x)/g'(x) [/math]. Let f(x)=-12 and g(x)=x^2 [eqn] \Bigg[\frac{f(x)}{g(x)}\Bigg]'=\frac{g(x)\cdot f'(x)-f(x)\cdot g'(x)}{[g(x)]^2}=\frac{x^2 (-12)'-(-12)(x^2)'}{(x^2)^2}=\frac{0+12\cdot 2x^1}{x^4}=24/x^3 [/eqn]
This is a hella fucking stupid way to compute a derivative

>>11694234
thanks, i forgot to add - to the 12 lol
what is the name of that x^n equation?

is the solution for [math]\frac{dy}{dx}=\frac{\sqrt{y^2-16}}{xy}[/math] defined for [math]y=4[/math]?

>>11694254
Books usually call it the power rule, I think https://en.wikipedia.org/wiki/Power_rule
>>11694261
That's a differential equation, and a disgusting one at that. 4 is a trivial solution, yes.

>>11694273
I'm asking because you get [math]\frac{y}{\sqrt{y^2-16}}dy=\frac{1}{x}dx[/math] when solving it, so [math]|y| \ne 4[/math].
Is this restriction still relevant for the final equation?

>>11694288
You cannot divide by zero, so yes

Will learning a new language keep my mind sharp heading into the fall semester?

Okay so I am just starting to touch on functions for my basic college algebra class. I don't really understand this.

>>11694422
answer is yes

>>11694432
Well I appreciate the promptness. Thank you.

>>11694422
Let f(x) = 9

f(1) = 9
f(2) = 9
f(3) = 9
f(pi) = 9
...
f(x) = 9

>>11694422
>>11694436
Do you understand why though?

>>11694471
Technically, not one bit. But I just finished a problem correctly that has the same pieces in motion so if I stare at that long enough with my other notes, I'll reverse engineer the concept internally. Or if anyone feels like helping a sped I would greatly appreciate that as well.

>>11694533
a function can't have two distinct points with the same x value, but can have any number of points with the same y value.

>>11694533
Sure. Are you familiar with sets? Like, think of them as bags containing some defined elements. Like all natural numbers, or the real numbers between 4 and 7, whatever.

Functions are relations between two sets. They asign every element of the first one, one and only one element of the second.

This is, an element of the second set can have many elements of the first associated with it, but elements of the first set can't have multiple elements of the second associated to it.

In the example you posted, of course, you can see this. Two distinct x can give you the same y. This can't happen in the inverse when we're dealing with functions.

BROS HOW DO I KEEP GETTING THIS ONE WRONG?
The correct answer is supposedly D but I can't get it right for some odd reason.
Here's what I did:
1) Got the series for the integral
2) Replaced it with the integral
3) Integrated each one
4) Evaluated each one (I just skipped this one because of the 0 lower bound)
5) Plugged in 0.5 to the first 4 terms, found out that the 4th term satisfies the <10^-3 inequality
6) Added the first 3 terms that had been evaluated at 0.5, get 0.4604166 which is not on the answer list.
What's going on bros, pls, it's raping my head.

>>11694793
Did you use the first three terms of [math]cos^2 x[/math]'s power series or the square of the first three terms of the [math]\cos x[/math] power series?

>>11694851
I integrated the first 5 shown in this picture, found out that the 4th term satisfied the inequality of < 10^-3 so I added the first 3 terms... I really don't know what I did wrong. If I had just evaluated the integral without replacing it with power series, I would get the same answer as well so I'm really just lost...

>>11694870
I've just checked with Wolfram and it says the value of the integral is 0.460368.
None of the options in the question are within 10^(-3)=0.001 of that, so it's probably a typo somewhere.

>>11694964
Thank you, a few of my friends got the same thing.
I really can't thank you enough desu, you and every other kind person has helped me since the beginning of the semester with dumb integral questions and then later on with series when I had previously failed this class and really helped in getting me back into shape.

Question about pumps.
Imagine a water pipe with a pump in the middle
Head of water increases before and after pump. What about head in the section of pipe before pump? What happens there?

i've been taught at my course that a markov chain random variable wise is, to simply put it, an random variable that depends on λ last states, i've wanted to read up more on this since the explanation on the course wasn't enough for me and so far, every article about markov chains says that they only depend on the last state, why is that?

I really hope this is the best place for a medical question if you can't get in contact with a doctor.

I have appendicitis. I was sent home with antibiotics by the hospital because they were worried I'd get corona if they operated. My stomach is bloated and I'd like to poop, but I'm constipated. without being funny, I think this is three days worth, and it's kind of a drag on my stomach. I know you're not allowed to take laxatives, but I'd really appreciate a way of relieving this tension.

Do I just wait for this to explode so I can call an ambulance? This is so fucked up. I had a friend when I was a kid who died from this, because our teachers thought it was just a tummy ache, I've been scanned and diagnosed, but I feel like I'm going to go the same way.

>>11694407
It can't hurt, but it's not ideal. Language learning is not as intense as sitting down and putting yourself through pages and pages of math.

Intelligence certainly helps you learn new languages, but one does not become more intelligent learning new languages- see multilingual gypsies. I can find nor remember any evidence to suggest it helps maintain intelligence either. I would give you more specific advice, but I don't remember studying linguistics after from that anecdote which felt familiar to me, so take it with a pinch of salt.

And I know what you mean - after a break, you do feel woolly. If you're studying something, study ahead if you're already familiar with what you learned last semester. That'll keep you sharp, and if you're worried about your education, that's a fair comprimise, I think. If you want to learn a language, though, you can still do that. Half an hour or an hour, every day, isn't much of your time.

How is this 0 and not 1.57? I've checked with other calculators as well and they all tell me it's 1.57 in radians, I've also did the work which got me pi/2 and that's 1.57

>>11696581
Who knows.
https://www.wolframalpha.com/input/?i=compute+the+angle+between+%280%2C+-7%2C+0%29+and+%284%2C+0%2C+-6%29

>>11692584
Then derive them yourself. Take the definition of the derivative and work out these expressions. Then you'll see and understand exactly why they hold.

>>11696197
Because that's how they're usually defined. They're processes which have no long-term memory.
It sounds like your course taught you a more generalized definition. The literature usually defines a Markov chain as the case when λ = 1. That's just standard convention.

>>11696581
You are right, it is pi/2. It should be obvious because u is along the y axis, while v is in the xz plane. They are trivially orthogonal.
I can only guess (hope) that the instructor accidentally put the inner product as the answer, instead of arccos(inner product). Either way, tell them and get your points back.

Just a lowly engineer but how the fuck did it solve this?

>>11696306
go to a different hospital, your doctors are retarded
force them to take you

How did he get radius of convergence of 1/5? If he cancelled everything out, it should be x/n which would then be abs convergent for all real numbers wouldn't it? The answer on the site also said 1/5 so I have no idea how they got it.

this is a really, really dumb question but what is the name for the sequence of numbers which form this triangle? my mind is throwing a blank.
1
11
121
1331
14641

>>11697422
Pascals triangle

>>11697424
Thank you.

The reason scientists say coronavirus wasn't engineered: "That analysis showed that the "hook" part of the spike had evolved to target a receptor on the outside of human cells called ACE2, which is involved in blood pressure regulation. It is so effective at attaching to human cells that the researchers said the spike proteins were the result of natural selection and not genetic engineering." (source:https://www.livescience.com/coronavirus-not-human-made-in-lab.html).). Wouldn't the evolved hook part be an indicator of a tampered virus. The hook part is specifically optimized to attack the human cell receptor ACE2. So apparently this virus was living among bats but for some reason evolved to to be really good at attacking to those ACE2 receptors which bats don't have? what in a bat population causes a selection pressure to evolve a hook that is best used on human cells. What am I missing?

>>11697422
>>11697424
ok 2nd question, is it possible to calculate the nth term of the oth sequence or must it be derived through building the triangle?

>>11697436
which scientists are saying it wasn't human engineered? as far as I can tell the evidence clearly points to massive gene cut and pasting with ties to billion dollar disease research labs.

>>11697439
Binomial coefficients. https://en.wikipedia.org/wiki/Binomial_coefficient

>>11697453
cheers

>>11697365
[math]5 \times 10 \times 15 \cdots \times 5n = 5^n n![/math]
Then the sum becomes [math]\sum_{i=1}^{\infty}(5x)^n[/math], which is geometric.

The proof I'm seeing scribbled on the background is autism.

Should a vector from say R3 be written as a row or as a column? The interplay between points, vectors, transformations has got me confused, and my professor is kind of a dick

>>11697557
You may have seen [math][x, y, z]^T[/math]. The vector is a column, but to save space it is transposed.

>>11697591
Prof said a vector colum is a vector in R1x3, not R3, whatever the fuck that means

Meanwhile doing a transformation for R3 uses columns so I really don't know what's up

>>11697600
the only time when you need to distinguish between row and column vectors is when you're talking about dual spaces. then vectors need to be columns and covectors need to be rows, otherwise stuff doesn't work.
every sane person thinks about vectors as of columns, precisely because linear transformations use columns. people write it however the fuck they want though, me included. but they always think columns.

For diagonalizable matrices, is its diagonal form always the same as its Jordan normal form? I can see this when the matrix has no degenerate eigenvalues, but if there are repeated eigenvalues, what ensures that each instance of that eigenvalue corresponds to its own [math]1 \times 1[/math] Jordan block?

how do dentists solder in your mouth without giving you 3rd degree burns?

>>11697852
>For diagonalizable matrices, is its diagonal form always the same as its Jordan normal form?
yes
>what ensures that each instance of that eigenvalue corresponds to its own 1×11×1 Jordan block?
diagonal matrix is trivially in a Jordan form, and Jordan form is unique. hence the statement

This is in the Schwarzschild metric. I just want to be sure about something, the time it would take the light signal to travel from [math] r_1 [/math] to [math] r_2 [/math] and the time it would take from [math] r_2 [/math] to [math] r_1 [/math] is the same, right?

A small part of me says 'no' because the photon would have to fight against the gravitational force when travelling from [math] r_1 [/math] and [math] r_2 [/math], but another part of me says this is nonsensical since photons always travel at the speed of light, the geodesic isn't changing, it shouldn't take a longer time.

>>11689206
Need help solving convolution integral.
I know intuitively what the result is but I just cant get it when actually solving the damn thing.

Let:
[eqn]rect(t/a) = \begin{cases} 0 & t < -a/2 \\ 1 & -a/2 \leq t \leq a/2 \\ 0 & t > a/2 \end{cases}[/eqn]

I need to find:

[eqn]rect(t/a)*rect(t/a) = int_{\mathbb{R}} rect(\tau /a)rect((t - \tau)/a)d \tau[/eqn]

Pls help senpai

>>11698525
Fuck, forgot a backslash

[eqn]rect(t/a)*rect(t/a) = \int_{\mathbb{R}} rect(\tau /a)rect((t - \tau)/a)d \tau[/eqn]

>>11698525
>>11698530
This is the kinda shit you have to properly grind out manually.
[math]rect(\tau/a)rect((t- \tau)/a) = 1[/math] and not zero if and only if [math]-a/2 \leq \tau \leq a/2[/math] and [math]-a/2 \leq t- \tau \leq a/2[/math]. Compute the intersection of the two intervals explicitly as a function of [math]t[/math] and figure out the length of said interval, which is your integral.

>>11698654
Oh right, forgot to mention this.
[math]-a/2 \leq t- \tau \leq a/2[/math] if and only if [math]-a/2 \leq \tau -t \leq a/2[/math].

Are there any macroeconomics books that use lots of math instead of fucking about with word games and analogies? I want something that's at least as rigorous as most books about calculus.

>>11698525
The integral will have 4 cases: t<-a, -a<=t<0, 0<=t<a, a<=t. For each case, partition the reals into 5 regions corresponding to splits at
1 τ=-a/2,
2 τ=a/2,
3 t-τ=a/2 => τ=t-a/2, and
4 t-τ=-a/2 => τ=t+a/2.
The four cases for t will determine the order in which these splits occur.: 3412, 3142, 1324, 1234. So e.g. if t<-a, you have -∞<t-a/2<t+a/2<-a/2<a/2<∞. In each region, both rect(τ/a) and rect((t-τ)/a) will be constant (0 or 1), as will their product, and the integral (for that region) will be either 0 or the difference between the bounds.

>>11698747
>he wants not science or math as rigorous as pure math
Lol

>>11698747
No way lmao.
Economics is suffering, get used to it.

>>11698654
>>11698667
This doesnt get me anywhere.
Ffs what Im I doing wrong?

I graduated last semester.
I can't go back for a minor at my university.
Are there things like certificates for math?
I wanna learn something while this pandemic is happening but my university wont let me unless I go back for a dual major and I don't think the pandemic would last that long.

I know how to use a Vernier caliper. But what's the purpose of the second carriage connected to the graded one? There's a screw that holds it to the body and a screw that adjusts its separation from the graded carriage.

>>11698921
If you just want to learn, your university probably has the option to take a limited number of non-degree credits on your own dime. While I was waiting for admission to a good private university, I took classes as a non-degree student at the public university.

>>11698990
Yeah but I wouldn't get a degree or anything.

>>11698995
Look for post-bacs or REUs if you want something more organized

Is the expected value of the distance to the nearest leaf in a full binary tree given by:
[eqn] \sum_{i=0}^{n-1} (n-1-i)\frac{2i}{2^{n-1}} [/eqn]

or did i fuck up? i couldn't find this online anywhere

thx

>>11689206

Let [math] y^i = \gamma \circ x + \beta [/math], for [math]i = 1..n[/math]. I am given a scalar-valued function, [math]L(y^1, y^2, ... y^n)[/math], and wish to calculate the derivative with respect to [math]\beta[/math]. Would the correct expression for the derivative be:

[math] \frac{\partial \mathcal{L}}{\partial\beta_j} = \sum_i^{1,n}
\frac{\partial\mathcal{L}}{\partial y^i} \cdot
\frac{\partial y^i}{\partial \beta_j}
[/math]

I think this is correct, but am unsure about how to take derivatives when a function takes in a vector (or series of vectors, in this case). From what I know about the chain rule, this warrants the use of a sum, but I'm not entirely sure

>>11699137
I've rewroked the secret formula, it is now:
[eqn]
\sum_{i=0}^{n-1}i \cdot \frac{2^{n-(i+1)}}{2^n-1}
[/eqn]

can someone help me with this question please
"the multiplication of three positive numbers, two of which are identical numbers, is a^3 (a>0).
what should the numbers be in order for their sum to be minimal?"

and what difference does the (a>0) make?

>>11698747
Quantum Field Theory for Economics and Finance

>>11699291
> "the multiplication of three positive numbers, two of which are identical numbers, is a^3 (a>0).
> what should the numbers be in order for their sum to be minimal?"
IOW, minimise x+2y where xy^2=a^3.
Solving xy^2=a^3 for x gives x=a^3/y^2. Substituting into x+2y gives a^3/y^2+2y. Differentiating w.r.t. y gives 2-2a^3/y^3. This is zero when 2-2a^3/y^3=0 => 2a^3/y^3=2 => 2a^3=2y^3 => y=a, which corresponds to the minimum of x+2y. IOW, all three should be equal to a and their sum is 3a.

> and what difference does the (a>0) make?
It's unnecessary to state it. The product of 3 positive numbers is always positive. Note that if negative values were allowed, there would be no minimum.

An non-ideal Rankine cycle with reheat that uses water as the working fluid has a net power of 119 MW.

Steam enters the HPT @ 10 MPa, 500°C while at the LPT after it's been reheated it enters @ 1 MPa, 500°C.

The steam exits the condenser at a pressure of 10 kPa.

The isentropic efficiency of the pump is 95% and that of the turbine is 80%.

Calculate:
A. The quality of steam, or the temperature of the steam, if it's superheated, at the exit of the turbine.
B. The thermal efficiency of the cycle
C. The mass flow rate of the steam

in pic related, you can see what I think is the solution for A.

is it even close to being correct ?

as for b and c, what formulas will I have to use?

finally, a more general question, how many fucking efficiencies are there in thermodynamics?

I don't get how graphs 3 and 5 are not isomorphic to one another, they both have the same number of vertices of degree 3, 2 and 1.

>>11700730
No.
It's hard to tell because they're in ebin hexagon form to save space xD, but graphs three and five are isomorphic to pic related, which are clearly not isomorphic.

>>11700870
Graphs 3 and 5 both have 1 vertex with degree 3, 2 vertices with degree 2, and 3 with degree 1. Therefore they are isomorphic.

what's wrong with my thinking?

>>11700870
is this correct? i kind of get why there not isomorphic, but what furhter stipulations are applied beyind what I mentioned here?>>11701026

My book implied only the criteria i mentioned matter for determining if spanning trees are isomorphic. but i see that clearly the graphs you've show cannot be mapped to each other to form the same 'shape'

please explain me as if you were talking to a 8 years old child how the fuck does all that shit about ion channels work in neurons
i understand that neurons after a high enough of a signal, get a potential way higher potential in their membrane than in their nucleus and release a spike but i don't get all this talk about exchanging ions through channels and etc
fucking hell i don't even fucking know what an ion is

>>11701026
>what's wrong with my thinking?
Sometimes I can give clean, simple explanations for why something doesn't work.
In this case I can't. It literally just doesn't work.
The best I can do is some garbage like "Just because a map between graphs preserves degree doesn't mean it's an isomorphism."
>>11701154
There are all sorts of criteria, but I'm not a graph theorist, so I couldn't really give you any references.
For example, if we had an isomorphism between those two graphs from earlier, it would preserve vertex degree. So it sends the vertex with degree three to the other vertex with degree three.
Now, if we remove the degree three vertex from the graph on the left, we have three connected components, two with one vertex, one with three vertices.
If we remove the vertex with degree three from the other one, we have two connected components with two vertices, and a single connected component with one vertices.
However, an isomorphism of the entire graphs would induce an isomorphism of the two subgraphs, and thus bijections between the vertices of the connected components. But that's impossible.

what's that site called to find books and articles, it starts with a g and ends with .io

>>11689206
Need help with this.

This is for an applied math data analysis class, the book were using has us prove that given a data matrix [math]X[/math] we can compute de distance-between-individuals matrix using the following formula:
[eqn]D = diag(XX')1_n + 1_n diag(XX') - 2X'X[/eqn]
Where diag(A) is the vector containing all the diagonal elements of A and 1_n is the column vector filled with n ones (ie 1_3 = (1,1,1)')

The thing is, this formula is wrong, so our task is to prove its wrong which I already have and to correct the wrong formula.
Im stuck on the correction part.

The distance matrix D is the nxn matrix which in the position Dij has the euclidian distance between the individual i and the individual j.

Generally, for a data matriz [math]X[/math] composed of n observations measured in p variables:

[eqn]D(X) = \begin{bmatrix}0 & p-norm(x_2 - x_1) & \dots & p-norm(x_n - x_1) \\ p-norm(x_1 - x_2) & 0 & \dots & p-norm(x_n - x_2) \\ \vdots & \vdots & \ddots & \vdots \\ p-norm(x_1 - x_n) & p-norm(x_2 - x_n) & \dots & 0\end{bmatrix}[/eqn]

Where [math]x_i[/math] is the ith row of the data matrix

>>11701206
open a book on general chemistry and read it.

>>11701567
So far ive gotten that
[eqn]D(X) = diag(XX')1_n + 1_n diag(XX') - 2XX'[/eqn]
At the very least makes algebraic sense but its not in any shape or form the correct distance matrix.

>>11701154
>>11701262
>There are all sorts of criteria, but I'm not a graph theorist, so I couldn't really give you any references.
Criteria like this (basically all the different forms of "isomorphism preserves any graph property") are what you look for in those problems, but it's worth pointing out that they're all _negative_ criteria; you check it and if it fails you know the graphs are NOT isomorphic, but you can't guarantee if the graphs are isomorphic this way.
For two isomorphic graphs there's no (known) way of showing this much better than just rolling up your sleeves and finding an isomorphism by hand. No one knows a usable set of stipulations where you can just say "I checked every property on this list so they're isomorphic". Determining graph isomorphism is one of the oldest problems of complexity theory (and interestingly enough it's one of the rare problems still stuck in limbo between P and NP-complete)

>>11701575
i hate chemistry

>>11701567
Anyone pls???

>>11701567
>>11701781
If the data comes as a collumn vector [math]x[/math], then the solution should be [math]|1_n x^T - x 1_n^T|[/math].
I'm currently trying to figure out what bullshit am I supposed to do to generalize this to data matrices.

>>11701567
>>11701891
Never mind, the trick is completely different.
So, we'll use [math]||x-y||^2 = ||x||^2 + ||y||^2 - 2 \langle x, y \rangle [/math].
The matrix [math]A[/math] has collumns [math]A_i[/math] and entries [math]A_{i, j}[/math].
[math]||A_i - A_j||^2 = ||A_i||^2 + ||A_j||^2 - 2 \langle A_i, A_j \rangle [/math].
For the last term, we notice that [math][A^T A]_{i, j} = \langle A_i, A_j \rangle [/math].
Then, we add in [math]diag (A^T A)1_n^T[/math], which is the matrix whose i-th rows is constantly [math]||A_i||^2[/math], and [math]1_n diag(A^TA)^T[/math], the matrix whose i-th collumn is constantly [math]||A_i||^2[/math].
So [math]D(X)= - 2 A^T A + diag (A^T A)1_n^T + 1_n diag(A^TA)^T[/math]
That should be it, I think.

>>11701949
Forgot to mention that the individual entries in that are all squared.

>>11701026
Count the geodesic distances for each point.
Graph 3 has 1 node from which the other nodes are at distances 1,2,3,4,4, 1 node from which the other nodes are at distances 1,1,2,3,3, 1 node from which the other nodes are at distances 1,1,2,2,2, 1 node from which the other nodes are at distances 1,1,1,2,3 and two nodes from which the other nodes are at distances 1,2,2,3,4
I'm sick of writing this out neatly.
Graph 5 meanwhile: 12233 11122 11223 11223 12334 12334

>>11689206
I don’t get irrational numbers

>>11701594
I didn't realize I was working with _negatives_, that sums it up perfectly, along with everything else you said.

well put and thanks a bunch! if my book did mention this, it was way too subtle

I need sum help. Can somebody tell me about a book that explains the process of building the real numbers set through cauchy sucessions of the rational numbers? All i can find is normie popsci shit. I would like to really understand the process and im going to have a very long summer

is so called "model reduction" a meme?

why is so many people regard computer-science as an autistic major? if autism is related to technical prowess why is it not applied to other discipline like electronics perhaps? is it a meme? enlighten me.

>>11702226
>Cauchy sequences construiction of the reals
I recall that Bishop's Constructive Analysis did a modified version of that. I think Tao's books did it too.

>writing out the question I pondered about made me realize my errors
Thank you for existing sqt :)

>>11700321
anyone

do drivers in Braess's paradox when choosing the road to take, take the fastest route as a whole, or only look at the fastest road that's next to them?

>>11700321
>B. The thermal efficiency of the cycle
Find the specific enthalpies at all points in the cycle just like normal and apply the definition of thermal efficiency: net work out/heat in
>C. The mass flow rate of the steam
You're given the power output. You already know the enthalpies so you should now the specific heat delivered during the boiling process. Mass flow rate = power/change in spec. enthalpy.
>how many fucking efficiencies are there in thermodynamics
Dozens, probably. Thermal, isentropic, and CoP are most important.
>>11695405
>Head of water increases before and after pump
? Usually it steadily decreases along the length of the pipe and spikes at the pump. Suppose two long pipes with steady flow and joined with a single pump in the middle. The graph of head as a function of distance would be a downward sloped line that discontinuously jumps up at the pump, and immediately after the pump it starts to drop again. The slope of this line is a function of reynold's number and internal surface finish+roughness of the pipe.
>>11702037
Ask a question

>>11689206
Okay I need help with statics anyway pic related

I keep getting -11880 Nm
for moment around point C when watched from what is in front force wise
and this shows 14880 Nm how?

it should be Mc=-FDy *3m=-3960*2m

Is learning Algebra from Apostol a dumb idea

>>11703535
post the original problem with dimensions

>>11689206
how do I get the highest moment under distributed force part?
do I really have to go every 0.1 move to see which one is greater or is there a shortcut

>>11703618
see
>>11703540

>>11703618

>>11703637
see >>11703635 >>11703540

>>11703526
was the way I tried to solve A correct?

>>11703641
>>11703635

>>11703646
the other red is axial force is -8000

>>11703537
I've just flipped through it.
The pre-calc part is not particularly well written, but it's workable, yes.

>>11689206
>>11703618
>>11703646
doesnt matter got there step by step
now I need help with this
I am pretty sure I got FBy and FAy correct but I am having trouble with the angle force

The book I'm reading computes these fibers without further word, however, I want to find a geometric interpretation of them, or something of the like. They seem to look like there's a satisfying explanation of their shape.

>How to interpret the fiber of the generic point? How can I think of it being char 0, while the others are char p?
>How to interpret the fact that (most) fibers are affine lines?
>How to interpret the singular fiber at char 2? I can imagine it has something to do with the fact that 2^2=2x2, but I've read that you can think of [math](y)/(y^2)[/math] as giving tangent or "analytic" information.

What GPA do I put on a resume?
My overall GPA is 3.26 (came from 2 year college), however my current GPA in University is 3.62.

>>11704107
Whichever makes you look better, obviously

>>11704107
>What GPA do I put on a resume?
neither, who the fuck does that

what the fuck happened here

Is solar energy possible or is it a meme? I'm asking because I heard African countries have the most solar rays coming into their countries compared to elsewhere

>>11704542
reverse LEDs

>>11704542
it's possible but we don't really see an avenue to making it more efficient than nuclear.
if battery tech was better and energy transportation was more efficient then lackluster solar efficiencies wouldn't be as bad, but you can only build them in certain situations and their electricity production is very unreliable, so unless you have massive battery arrays then you can't keep up with changes in demand when there's a lack of sun.

>>11704504
I assume you mean the 3rd equality.
They're summing over variables that don't play a part in the probabilities of events x or z, it is a generalization of the second term but for extra conditions.

say you're picking a random number 1-100
x=number is a multiple of 5
z=number is even

then for the conditional probability of p(multiple of 5|even number) you wouldn't care about conditions such as:
y=number is a square, number is odd, etc.

however in order for this to be true, the summation over y must indicate that you're summing over y is true and y is false.
so the numerator on the far right would read:

probability of x AND y AND z plus probability of x (AND NOT) y AND z
which just defines the probability x AND z, p(x,z)

>>11689206
Does calculus need a really strong background on trig functions and the sort? I am with fine many of the other topics than that in precalculus, trig I just did not put too much effort into.

>>11705670
calculus and trig are two different fields. however, a lot of the problems you'll do in calc will involve trig and once you start going into 2-D calc then you absolutely require trig.

>>11705677
Thank you very much anon

>>11689206
How hard is it actually to get into PhD programs at MIT/Stanford/Harvard/etc? Do I need to be a literal genius or are good grades/GRE/some research experience enough?

>>11705698
I don't consider myself a genius by any means and I did really well on grad apps. you conveniently listed the only 3 schools that rejected me but I got into a better program for what I want to do anyways.
what field are you in?

>>11705698
>>11705709
I'll post my advice anyways and if you come back I can tailor it to your experience.
getting into a top PhD program is 90% about your success in research. this can often include papers, presentations, or a dissertation but really boils down to your rec letters and research experience.
"some" research experience is not enough. they are admitting you into the PhD to do research, not for your ability to do well in classes. I recommend 3+ years of research experience minimum, and try to keep it in one or two labs/groups so that you're able to get maximal depth and the letter writers will have more to say about you. this also increases the odds that you'll end up on a paper.
of course, there are a lot of factors. you need to apply to schools that have specific groups that align with what you want to do. for example, one of top schools in my field is CU Boulder. you wouldn't think to apply there if you're just applying to the name of the school. and the schools can tell when you do that; probably 50% of people applying to Harvard/MIT/Stanford/etc. shouldn't even be doing that because their research interests don't align.
here are some general tips that are almost as important (or even more important) than getting a 4.0 gpa:
>talk to professors that you're interested in working with EARLY to establish a connection
I cold-emailed 4 profs and got 4 responses without even including too much about myself, just that I was interested in their work. I currently work with one of them now.
>establish a good relationship with your current research advisor
>ASK THEM for advice on where to apply
this will often be because they know where your skills will transfer best AND ALSO what places will know their name and thus their rec letter will be more meaningful.
remember that getting into a good PhD is a lot about making good contact beforehand. but the stuff about research still comes first, you need the research experience to back it up

>>11705709
>>11705885
Thanks for the advice anon. My field is CS. I just finished my freshman year, and I'm starting a summer research position at my school next week. I'm not sure if it's the exact subfield that I'm interested in, but it was the best opportunity that I had available to me.

>>11706022
try to get into the field you want asap. its best to start early. i can field any other questions as well

>>11705565
uh oh thanks
what do i google to see what the equalities that you speak of look like?

I have a pretty dumb field theory question: I am trying to show that [math] \Q(\sqrt[3]{2}, i) [\math] is not a normal extension of [math] \Q [\math]. What I have so far is that the polynomial [math] x^3 - 2 [\math] is irreducible over [math] \Q [\math] and has one root [math] \sqrt[3]{2} [\math] in [math] \Q(\sqrt[3]{2},i) [\math] but not all others, namely [math] \frac{-1 \pm i\sqrt{3}}{2} [\math]. So I have to show that [math] \sqrt{3} \not\in \Q(\sqrt[3]{2},i) [\math], but I am not sure how to do this. I have tried giving an argument with degrees of the extensions but that hasn't worked.

I have a pretty dumb field theory question: I am trying to show that [math] \Q(\sqrt[3]{2}, i) [/math] is not a normal extension of [math] \Q [/math]. What I have so far is that the polynomial [math] x^3 - 2 [/math] is irreducible over [math] \Q [/math] and has one root [math] \sqrt[3]{2} [/math] in [math] \Q(\sqrt[3]{2},i) [/math] but not all others, namely [math] \frac{-1 \pm i\sqrt{3}}{2} [/math]. So I have to show that [math] \sqrt{3} \not\in \Q(\sqrt[3]{2},i) [/math], but I am not sure how to do this. I have tried giving an argument with degrees of the extensions but that hasn't worked.

>>11706194
I don't understand your question. I meant the 3rd equality in terms of the 3rd term in the expression, the far right one. Am I misinterpreting you?

>>11706333
yeah nvm i'm retarded, shouldn't be here at this hour, but i've got it now, thanks

Does caffeine act as a preservative in foods/beverages?

I started Mountainbiking a few months ago and i have troubles jumping with both wheels in the air. Can someone explain me how this works on a physical level?

>>11706221
Let [math]K = \mathbb{Q}(\sqrt[3]{2}, i) [/math]. It's clear that [math]K[/math] has degree 6 over [math]\mathbb{Q}[/math]. This is because we have the tower of field extensions [math]\mathbb{Q}\subset \mathbb{Q}(\sqrt[3]{2}) \subset \mathbb{Q}(\sqrt[3]{2})(i) = K [/math]. The first extension has degree 3, and the second extension has degree 2. Hence, the degree is [math] [K : Q] = 6 [/math]. For contradiction suppose that [math]\sqrt{3}\in K[/math]. This implies that [math]K[/math] contains the extension [math]L = \mathbb{Q}(\sqrt{3}, i)[/math]. Note that the degree of [math]L[/math] over [math]\mathbb{Q}[/math] is 4, but 4 does not divide 6, which is the degree of [math]K[/math] over [math]\mathbb{Q}[/math]. This is our contradiction

>>11706499
>This implies that K contains the extension L
God I'm so retarded. I spent a good two hours on this... Thank you for the help.

(fuzzy logic) can someone explain me or point to a article that explains where do these things i circled in yellow come from? i get the theory behind fuzzy logic but not really the calculations like this
something i forgot to mention is that altitude belongs to [0, 200]; velocity to [0, 20]; force to [0, 100] but i'm not sure if or how that affects the exercise

exceedingly stupid question I know but why exactly dont laxatives help weight loss, do we have a solid idea of why precisely something like laxatives wouldnt reduce total caloric absorption or do we only have studies showing it doesnt work? im not planning on taking any for that reason obviously, but i started eating prunes to deal with some issues i started having after i went on antibiotics, and the question came to mind. secondly, am i at all likely to develop a dependency on the laxative effects of prunes?

What's an easily digested, simple, intuitive book on number theory

>>>/wsr/816682
Completely off-topic, I know, but it's been months.

>>11706975
they make you shit out all your water weight. you have minimum 5 pounds of weight that is highly variable based on your fluid intake, and laxatives push it all out.
this is not real weight loss though because you'll get it back over time.

>>11707915
yeah i gathered but it also accelerates the passage of matter through the tract. my question is more on how digestion actually works in this case in order to be unaffected by a dramatic shortening in processing time.

>>11707947
you don't get nearly the nutrients you need and can easily become nutrient-deficient. laxatives are not meant to be taken regularly for this reason, along with the dehydration.

why is the bohr model used, imaginary electron orbits etc., when it doesn't really happen like that in nature?

>>11708066
Is it used, tho?

>>11708066
my guess is that it's because the boomers who design the curriculum have a hard time believing that kids can understand anything more complex, and so think that teaching them something that's largely wrong but gets a lot of the ideas right is a better trade-off. when in reality kids are the best target for the complex ideas because they soak up information.
I understand how it might be "easier" to do it this way but it does seem weird to me that we're still teaching something that is blatantly wrong.

I've recently been seriously self-studying for the first time and it's proving to be frustrating. Discipline issues aside, sometimes I stumble onto a roadblock and can't surpass it through rereading or looking for answers/suggestions online, just moving on knowing I couldn't do that exercise or understand that part kills me inside.

>>11708490
>just moving on hurts my feelings
you are not a genius, do you expect to be able to teach yourself advanced topics without any help and also solve every problem with no challenges along the way? How often do you abandon exercises and what type of problems are you tripping up on? Sometimes you are specifically being filtered by end of chapter problems, othertimes they're simply there for the amusement of select students and not actually intended to be solved by most people even those perfectly capable of doing most of the rest of the text. My rule of thumb when working exercises is always at least 50% have to be doable and correct distributed across each section of the end of chapter exercises; that is, if they are obviously partitioned according to the topics covered in the chapter about every other exercise in each "sub-section" should not only be doable but I make sure to attempt them. If its a subject I care more about like something related to my actual studies then I push that up to >75% but for larger/shittier textbooks that's not feasible. If you're just self-studying seriously consider whether you are attempting too few or too many exercises and try to intuit whether the author has included them as a strict challenge for bored students or an actual integral test of knowledge of the chapter's contents.

>>11707985
yeah, same as the first 10 results of google say. laxatives bad. what im curious on though is what actually goes on, and why we can both become nutrient deficient from it and not succeed in loss of body fat.

is hydrogen bomb without fissile material to ignite, possible?

>>11708490
make use of /sqt/ and stackexchange

group theory: We can embed [math] S_n \leq S_{n+1} [/math] by fixing [math] \sigma(n+1) = n+1, \sigma \in S_n [/math]. The original question asked: how many proper subgroups [math] S_n \subseteq H \subseteq S_{n+1} [/math/ are there? In the picrel, how do we know [math]H[/math] contains such a cycle [math]c[/math] with [math]c(b) = c(1) = n+1[/math]?

Can anyone walk me through this proof?

>>11709553
In particular, how do know that we can have [math] b=1 [/math]? Also what would be the "suitable permutation [math] \sigma [/math] "?

>>11709553
We have [math]c \in H[/math] but [math]c \notin S_n[/math] is a permutation.
You construct the transposition [math]\sigma = (c^{-1} (n+1), c(n+1))[/math] and compose [math]\sigma \circ c[/math].
We compute [math]\sigma \circ c (n+1) = c^{-1} (n+1)[/math] and [math]\sigma \circ c [c^{-1} (n+1)] = n+1[/math].
Because of those computations, we can set [math]\sigma ' (n) = ( \sigma \circ c ) (n)[/math] if and only if [math]n \notin \{ n+1, c^{-1} (n+1) \}[/math].
>>11709571
>how do know that we can have b=1?
It's just reindexing.

>>11709743
>It's just reindexing.
I mean, from the fact that [math] S_n < H [/math] all we know is there is some permutation c that "moves" n+1, i.e. [math] c(n+1) = a \neq n+1 [/math]. Isn't that guy claiming that we can have the permutation c satisfy [math] c(1) = n+1 [/math] ?

>>11709743
But thanks for the other explanation. That really made sense.

>>11709792
No, it's just the good old renumberino.
Alternatively, consider that [math](a, c)^{-1} (a, b)(a, c) = (b, c)[/math] and use that to move the [math]b[/math] to [math]1[/math].

>>11709812
Do you mean that, in the case our first choice of [math]H[/math] containing cycle [math]c = (a~\dots~b~~n+1)[/math] doesn't give us [math]b = 1[/math], we simply choose another [math]H'[/math] where we "swap" [math]b, 1[/math]? Sorry, but I'm trying to make sure I understood everything before I move on.

>>11709820
No, you reindex.
You seem to understand extremely explicit computations, so I'll just give you one.
[math]b = c^{-1} (n+1)[/math], just to fix notation.
Then, [math]( \sigma ')^{-1} \circ [ \sigma \circ c] = (b, n+1)[/math].
So, because all of those three on the left belong in [math]H[/math] , so does [math](b, n+1)[/math].
Then, [math](1, b)^{-1} (b, n+1) (1, b) = (1, n+1)[/math], by the formula here >>11709812 , and then [math](1, n+1) \in H [/math] .
The formula is proved by simple computation. In other words, you check it manually for [math]a[/math], [math]b[/math] and [math]c[/math], i.e. [math][(a, c)(a, b)(a, c)](a)= [(a, c)(a, b)](c) = (a, c) (c) = a[/math].

>>11709833
I get it now thank you

>>11707323
My preference is for Burton's Elementary Number Theory

>>11708661
Probably not. The thing about a "bomb" is that the machinery tends to stop working fairly quickly, so you have a very short window in which to run the reaction. This is why gun-type fission devices have such low yields (Little Boy had a yield of 1%, i.e. 99% of the U-235 was just vaporised without undergoing fission).

Can somebody correct my mistake or confirm I am correct? If we have some pointed spaces [math]X, Y[/math], define [math]X \rtimes Y = X\times Y/ *\times Y[/math]. If we look at the projection [math]\pi\colon X\times Y \to X\rtimes Y[/math], let [math]E_\pi = \{ (x, y, \gamma) \in X\times Y \times (X\rtimes Y)^I \ |\ \gamma(1) = \pi(x, y)\}[/math] as usual. Then we can look at the fiber of the map [math]E_\pi \to X\rtimes Y, (x, y, \gamma) \mapsto \gamma(0)[/math], and this will be [math]F = \{ (x, y, \gamma)\in E_\pi\ |\ \gamma(0) = [* \times Y]\}[/math]. Now the question goes, am I wrong if I say that this forces [math]\gamma[/math] to be an element of [math]\Omega(X) \times Y^I[/math]? It can do whatever it wishes in [math]Y[/math] but it has to be mapped to the basepoint of the half smash. I don't even know anymore.

>>11710013
Why are you assuming that [math]\pi_X (\gamma(1)) = *[/math] ?

>>11710064
Am I? I literally don't know what I'm doing.

Trying to wrap my head around Navier Stokes and fluid dynamics simulations.
I keep seeing a term called "advection," described as the fluid's ability to carry ink, dust, particles etc. with it. When you simulate turbulence, is this advection what's being plotted? Is that what the colored pixels represent?

>>11710077
There's a canonical projection [math]\pi _X : X \rtimes Y \rightarrow X[/math], right? It exists because you haven't identified any [math](a, b)[/math] and [math](c, d) \in X \times Y[/math] with [math]c \neq a[/math], correct?
So the map [math]f: F \rightarrow \Omega X [/math] you're using is [math]f(x, y, \gamma) = \pi_X ( \gamma)[/math], right?
In that case, I don't see why you're assuming that [math]\pi _X ( \gamma (1)) = \pi _X ( \gamma (0)) = * [/math].

>>11710136
I'm not using any maps. I tried to use common sense, but I don't know.

I want to simulate this heat transfer condition on Ansys Fluent, could someone please direct me to an appropriate tutorial? The one I'm following right now (https://www.youtube.com/watch?v=fLgFkd_oLMc)) seems to only apply for interior pipes that don't connect outside of the "box"

>>11689206
Just had a lecture on Bell's inequalities, and it sounds like a very intricate way to prove a basic principle of the world. What I cannot wrap my head around is this might mean the universe is nonlocal (i.e. action at a distance exists) while faster-than-light communication is still impossible. Is there a basic (not necessarily easy) way to understand this, without working through some particular thought experiment? For example, time dilation is much better understood than the "ladder in a barn" thought experiment. Thinking of it in this way obscures the deeper and more general consequences. I'm wondering if the impossibility of FTL communication in a nonlocal universe can be understood similarly.

>>11689206
STATICS
How do I find the force in the other two sticks
I found T3 but it seems there is too many unkowns for the other 2 above it to solve

>>11689206

>>11689206
any book recommendation on linear algebra more specifically on the topics of eigendecomposition and singular value decomposition?

>>11710464

Method of joints. Write sum of forces in X and Y for literally every joint and solve with some symbolic maths package

If you're actually trying to get work done instead of do homework (or you want to check answers) use the right tool for the job https://ei.jhu.edu/truss-simulator/

>>11689206
How do I calculate the amount of fuel needed to get a spacecraft to take off from a planet and reach a certain orbit.
Can I just plug in the orbit velocity, specific impulse, gravitational acceleration of the planet and dry mass into the Twiolkovski equation and solve for the missing mass?
Kind of seems like there's something missing there.

>>11689206
What is the name of the flow diagram I’ve seen lately? Something where there’s a large block on the left that splits into smaller categories as it moves to the right? It’s usually used for something like “Companies I applied to” > “Companies I Interviewed With / Ignored” > ...

>>11711558
No. For a start: when escaping gravity, delta-V isn't just the change in actual velocity. You also have to add g*t, i.e. the amount of extra delta-V that you would get if gravity wasn't holding you down. Also, it doesn't account for aerodynamic drag (which matters if you're taking off from a planet with atmosphere).

How do I cram topology and complex analysis efficiently? Read notes? Solve exercises?

>>11711842
Work a lot of problems. Use Schuam's Outlines and other textbooks. I find reading notes a waste of time really as most books explain shit just as well.

Is the probability of choosing an exact real number between 0 and 1 equal to 0 since there are infinitely many real numbers packed in between 0 and 1? If so, what does it mean to choose a "random number" between 0 and 1?

if i put a finger really close to my eye, why do things seem to slightly bend near it's outline?

>>11711779
Things like this?

>>11689206
I just finished a differential topology course (we covered everything up to de Rham cohomology pretty thoroughly) and was thinking of learning some differential geometry. Which books would you guys recommend? Does anyone have experience with Loring Tu's diff geo book ?

Hello. I'm having some trouble visualizing how exactly the small signal model for transistors works (BJT, JFET, MOSFET). In particular, I got a problem like pic related except I'm at low frequency and can replace the capacitors for open circuits. I understand, based on what I found online, that once the transistor is properly biased, I can replace the transistor symbol for the small signal four port network equivalent circuit, and then make my DC sources zero.
This is the step I don't understand... Making sure my transistor is properly biased means, I imagine, making sure that saturation has been reached, that is that drain voltage is higher than the saturation drain voltage. But I don't see why I can then just set all DC sources to zero. Is it because I don't care what the DC voltage is, and only care about the small oscillating signal on top of it? And for the analysis is the same whether that small signal is oscillating around zero than around any other DC voltage value?
Thanks.

>>11712004
if you're talking about a computer picking a random number, they don't have infinite decimal precision. so it approximates a random number when in reality it's just one of 2^64 numbers possible or whatever
I don't know computers so I don't know the exact precision they can reach

>>11712004
>Is the probability of choosing an exact real number between 0 and 1 equal to 0 since there are infinitely many real numbers packed in between 0 and 1?
Yes. This is called "measure zero", specifically any individual number has measure zero in that context.

>If so, what does it mean to choose a "random number" between 0 and 1?
To explain that you need to look into probability distributions.
While talking about individual numbers becomes meaningless in that setting, talking about subsets can be meaningful.
E.g. what is the probability that the number is between 0.36 and 0.447 can be answered meaningfully.

>>11712047
diffraction
now make a pinhole with your fingers and look through it

>>11712250
>Does anyone have experience with Loring Tu's diff geo book ?
Yeah. It's pretty good. Nicely covers the Weil homomorphism and connections on principle bundles stuff.
If you're the same dude who asked in /mg/, I recommend Petersen for Riemannian geometry.
Chavel is also good, but somewhat schizophrenic.

>>11712004
> Is the probability of choosing an exact real number between 0 and 1 equal to 0
Yes. Also, see:
https://en.wikipedia.org/wiki/Almost_surely

if there is 4 base types in dna and amino acids are made of three bases why is there only 21 amino acids when there is 64 possible combinations? what would happen if you put a combination that doesn't correspond to any amino acid?

Can someone explain the statement "The axiom of choice implies the existence of sets which we are not able to construct."?
Specifically, what is meant by construct? Something like this: https://ncatlab.org/nlab/show/constructible+universe ?
I hear this or similar phrases thrown about all the time but it doesn't really make sense to me and I agonize over that.

>>11713830
you have redundancies or ones that code for stop codons.
something something certain things are easier to transmute and thus having redundancy protects against mutations.

>>11713830
There is redundancy, some sequences code for the same amino acid.

>>11713830
tangentially related, but some genetic engineers will actually replace one of the redundant acid encodings with a new artificial amino acid

>>11709861
this one looks pretty great. thanks!

Can you help? a gaussian sphere shell of radii R is cut in two by a square plate of 10R long sides is loaded with s uniform superficial load. Whats the flux though the spere? can it be found?

Seven loads Q are set in the corners of a regular octogone, at ditance "d" from the centre. A load q=q/2 in brought from a point in the infinite to the centre of the octogone. Whats the work done agaisnt the electroestatic force?

>>11715240
"The flux through a closed surface is proportional to the charge enclosed

>>11698967
Fine adjustment. If you lock the second carriage to the body of the caliper, then you can use the other screw to finely adjust the distance of the graded carriage. It's useful for fine measurement, but I've never used it.

How do I calculate the capacitance of a non-parallel plate system?

>>11715642
That's a complicated problem. I think you would need to use computer simulations to determine that.

What does this mean? I'm sorry, but I'm an ESL and I can't really decipher this "Principle of Qualitative inference".
Does it mean that I should look for arbitrary "qualitative" properties of a theorem/problem/formula? What kind of "qualitative" property should I find?
It sounds like a solid advice but also seems too abstract to me.

Should I learn the history in my physics book? Literally 3/4 of the content is pure history and when did the X dude came up with Y.
I just fucking hate to memorize shit.

How do you cope with loneliness? How do you deal with knowing that literally no one apart from your parents cares if you are alive or you are not? I don't even have efrens anymore, I wish I had cool friends to talk to about thing we like. I feel so lonely. Not really /sci/related but I don't like to post in shitty boards like /r9k/ or /adv/.

>>11716813
bro just be yourself bro just talk to people in your class bro just go out with them bro it's ez asf bro

yeah I don't fucking know

let me know if you find a way

>>11716818
I actually made some "friends" in classes a couple of years ago but it's been a lot since last time I leaved home, now I just go to uni to take exams and I don't talk to anybody there. Going out makes me feel like shit in the long term.

>>11716827
Dedicate yourself to your craft. Pour all of your life into your craft and ascend to a level that only few have reached. This will allow you to rise in status and your life will become better.

>>11716827
I'm in my first year in this uni, having dropped out of my previous one.

being with first year again is kinda odd, I had just started making "friends" and acquaintances just before the corona bs shit hit the fan.

they even asked me to do that semester group project together, and for the first time in my fucking life the others are actually doing a good job at what they were supposed to do.

however, i don't think this is going to go any further, i think they just consider me as a "uni friend" that they hang out with in between classes etc

>>11716857
and then end up working at a min wage entry job for 5+ years

>>11716813
>How do you cope with loneliness?
By having friends.

>>11714637
I'm gonna give a really shitty answer since it doesn't look like anyone's giving a good one.

Assume that the axiom of choice isn't trivial. That is, it guarantees the existence of at least one choice function which, without the AoC, cannot be shown to exist (which in particular means it can't be constructed).
Then this function is a set whose existence is implied by AoC but cannot be constructed.

Of course, the whole non-triviality thing is the independence of choice from ZF.

Quantum physics in the end means that ultimately there are no infinitesimals in reality, right?

But it seems wrong to think of space as Lego bricks. After all we should have already observed their borders in that case, right?
And there would also be different ways to split space into equal(ish) chunks.
Are there any results on how space and time are structured at that level?

yes, I'm retarded. How do I calculate initial velocity when this is all the data I'm given?

>>11715642
Solve Laplace's equation given that the potential on the surface of the conductors is constant. Apart from certain idealised geometry, you have to do this numerically.

>>11716986
So "constructible" sets are just the ones which can be proven to exist in ZF? That seems really arbitrary to me.
So is there some other condition to be able to call a set "constructible" that just happens to be fulfilled for every set which can be proven to exist in ZF?
Does that condition coincide exactly with the one given in https://ncatlab.org/nlab/show/constructible+universe ?
And how do constructible sets relate to definable sets? I think I've also heard it said that AC implies the existence of sets which can't be "explicitly defined" or something.
nLab seems to have a rigorous for "definable set" as well, but I can barely understand anything on that entire site, it reads like schizo rambling to me.

>>11717569
Never mind, I think I figured most of it out, though feel free to correct me.
ZFC implies the existence of sets which aren't definable.
The question of whether a non-constructible set exists is independent of ZFC.
What had me confused is that often when people say "constructible" they really mean "definable", both these terms taking the more or less rigorous definition on nLab or Wikipedia.

>>11718003
That's what I think is meant, yes.
But again, I'm responding because no one else is.

I had to calculate the thermal efficiency of a non-ideal Rankine cycle with reheat and it came at around ~31%.

Isn't this a little too low for a Rankine cycle with reheat? Should it be at around ~40%?

>What will be the solubility of CsClO4 in a saturated solution of CsClO4 and KClO4 ? Data:
Ks(KClO 4)=1,05·10^-2 ; Ks(CsClO4 )=3,95·10^-3

Since CsClO4 will precipitate before KClO4 does, I shouldn't even care about its solubility constant right? I should just apply the formula for the solubility of CsClO4.

Is this wrong?

what's the error I should associate to a time independent counting experiment (say, a simulation of rolling a dice and counting the occurrences of 1)? in my old error analysis book only the time dependent case is described (sqrt of the number of occurrences)

>>11720592
shit I haven't taken gen chem in like 8 years

>>11723573
assuming it's a relatively likely event, such as rolling a 1, then you use the standard deviation for binomial distribution
[math]\sigma=\sqrt{np(1-p)}[/math]
where n=number of trials, p=probability of success (rolling a 1)

>>11717057
no, our current theories assume space is not quantized, otherwise lorentz invariance is broken. there are theories which assert otherwise but they are not currently the belief.
planck length is not a "fundamental length unit" but rather just the length of minimum usefulness because below that we cannot study [with current technologies]

>>11723840
unfortunately I don't know the probability distribution of my event (in fact I'm writing a simulation precisely because I don't want to deal with the mess that the exact formula would be)
should've given out all the info on the first post, my bad, I'm simulating the probability of drawing card x and y in a pool of N cards with M copies of x and y in it.

>>11717057
>infinitesimals
That is a long hurried concept which has been buried, rightfully, in mathematics for about 100 years.

I wouldn't even know what a real world analog would be? Infinitesimals are just a bad way to describe limits.

>But it seems wrong to think of space as Lego bricks.
Basically any physical theory models space as continuous rather than discrete.

>we should have already observed their borders in that case, right?
No? Why would that be the case?

>And there would also be different ways to split space into equal(ish) chunks.
No? Why would that be the case?

>Are there any results on how space and time are structured at that level?
A billion, but ultimately everything we learned is that "we can't know".

>>11723849
>[with current technologies]
No, that isn't how this works. We can't study anything unless QM is, on a very basic level, wrong.
Just like we are not going to go faster than light unless relativity is fundamentally wrong or just like "free energy" is impossible unless thermo dynamics is fundamentally wrong.
This isn't an issue of technology, like the maximum speed a car can reach, it is a fundamental barrier.
To quote Wikipedia:
"It is the smallest distance about which current, experimentally corroborated, models of physics can make meaningful statements."

>>11723792
LoL hopefully I'll be in the same position as you in 8 years, don't really understand why I have to take it

>>11723898
I've never had to work with standard deviation of things without replacement, but try here:
https://web.ma.utexas.edu/users/parker/sampling/woreplshort.htm

>>11723906
>No, that isn't how this works.
I meant with current knowledge. I'm future-proofing my post in case in 100 years people dig up this archive with knowledge of another ultrashort-range force that can circumvent this.

>>11723906
>bad way
works_for_me.png
>"we can't know"
As in we don't know, or actually we can't (possibly) know?
>No? Why would that be the case?
I do realize that due to Heisenberg there isn't really anything to be done, but shouldn't there be measurable symmetries appearing through the homogeneity of space?
Which would then allow to come up with a rough idea of how space is shaped. What the final building blocks actually look like.
>No? Why would that be the case?
Instead of 1x1x1 blocks, it could also be, for example, rhombi. Whatever solid is capable of filling space ad infinitum without gaps.

>>11724032
even if space _were_ discrete, we're a very very long time from being able to make any measurements even close to this level.
to answer all of your questions: we don't know, there are a lot of possible ways to come up with things that would "work" to answer your question but without being able to observe them in some way they're all equivalent.
it's like string theory: it might work as a theory, but we cannot test it so we can't say whether it's true or not. you could imagine coming up with equivalent theories that are untestable but also unfalsifiable

>>11715776
Please help.

>>11710464
I solved it faggots no tnx to you guys on sci

>>11723992
thank you, I'll have a look

>>11716857
Too depressed for that shit, I can barely do anything.
>>11716895
>that reddit spacing
you deserve no friends faggot

>>11715776
>Does it mean that I should look for arbitrary "qualitative" properties of a theorem/problem/formula?
I think he means you're supposed to look for qualitative cases.
For example, if you have that [math]|f(x)| \leq |g(x)|[/math] you have in particular that, whenever [math]g(x)[/math] is finite (a qualitative property), then [math]f(x)[/math] is also finite, and if [math]f(x)[/math] is infinite, then [math]g(x)[/math] is also infinite.
>What kind of "qualitative" property should I find?
Corner case evaluations and sometimes obvious inequalities. For example, if you have [math]a = b+c[/math] and you know that [math]b \leq 0[/math], then you know that [math]a \leq c[/math]. This is the kind of stupid stuff which sometimes turns out to be important to prove non-existence results.

For the proof, try [math]|a_k b_k| \leq \max (a_k^2, b_k^2) \leq a_k^2 + b_k^2[/math]

Can anyone answer >>>/g/76109260

can someone please post that meme pasta usually in the form of arithmetic between burgers or fruit etc.
i've seen a version floating around here for years that includes an integral, looking for a version of that.

>>11724371
I made one a few weeks ago and posted it on here, I think this will make you happy anon

>>11724388
This is pretty good but I really would prefer the calculus one

>>11724352
:)

>>11724352
>>11724567
No idea.
Probably some particularities with how your machine computes powers.

>>11724587
Lol what, it literally works out the exact result

>>11724605
>it literally works out the exact result
Did you check by hand?

>>11723898
just believe in the hart of the cards bro

When factoring -3^(k+1), shouldn't I get "-3^k * -3" instead of -3^k * 3? If it was -3^2 it would be -3*-3, after all.
Saw -3^k *-3 in the solutions for something I'm doing.

>>11724889
[math](-3)^(k+1)=(-3)^k(-3)^1=(-3)*(-3)^k[/math]
solution likely has a typo

>>11724917
Thanks, it got me worried for a while that I had forgotten basic rules.

>>11724959
unless you're studying non-commutative algebras, you're good senpai

>>11724300
Thanks anon. That really helps.

I was a very large baby (11 lbs). Is there any correlation between a baby's birth weight and the baby's father's birth weight?

>>11685899
read this

When I was in high school I remember a class where we had to find how to make an "" optimal open box"" with the maximum possible volume by cutting 4 squares like pic related then folding the paper an using tape.
I do not remember the name of the equations to do that, can somebody help me please?
also, why isn't always the "smallest squares removed" the box with the largest volume?

>>11725669
this would be a class of optimization problems

a related problem: you have 20 meters of fencing to design a fence with the greatest contained land area.
your logic would be to design a fence with near 0 width and almost 10 meters of length (10 meters * 2 sides = 20 meters). but the area of this is almost 0 ([math]\sim 0 * \sim 10 \approx 0[/math]
instead, what if the side lengths were 5? then your circumference is still 20, as this is the amount of fencing you have, but your contained area is 5*5=25 meters^2.

generally you want the most "square" object in these problems.

How should I approach solving an equation of motion
[eqn] \ddot x = F(x) [/egn]
where [math] F = -kx [/math] when [math] -a < x < a [/math] and outside this region [math] F = -C/x^2 [/math], where [math] k [/math] and [math] C [/math] are constants. I also have initial conditions for [math] x [/math] and its first time derivative.
This would be easy if [math] F [/math] didn't have these different expressions in different regions. If it's not possible to do on paper, what numerical method would work?

How should I approach solving an equation of motion
[eqn]\ddot x = F(x)[/eqn]
where [math] F = -kx [/math] when [math] -a < x < a [/math] and outside this region [math] F = -C/x^2 [/math], where [math] k [/math] and [math] C [/math] are constants. I also have initial conditions for [math] x [/math] and its first time derivative.
This would be easy if [math] F [/math] didn't have these different expressions in different regions. If it's not possible to do on paper, what numerical method would work?

>>11725752
Have you ever heard of an "ordinary differential equation"?

>>11725769
Yes but I only know how to solve simple separable equations and 2nd order linear equations.

>>11725772
>2nd order linear equations.
But this *is* a linear 2nd order equation.
What you have to do is, solve it on (-a,a) and then use that solution to get an initial condition for the areas [a,infinity] and [-infinity, -a], where you have to solve an, admittedly, non linear differential equation. This is assuming that the "initial condition" is given for something inside of (-a,a).

>>11725795
I don't quite understand what you mean. If the initial valiue for x is in (-a,a) the problem reduces to a simple harmonic oscillator and the particle or whatever is never going to leave (-a,a). I'm more interested in solving this in the case where x(0) > a.

>>11725817
>I'm more interested in solving this in the case where x(0) > a.
Then you do the exact same process in reverse. Solve the DE in the area where x(0) is, then use that solution to get initial values for the rest.

>>11725827
Thanks. I'm fucking retardedd.

What am I doing wrong... I get -3699.99N for T6 when it should be a positive value...

>>11726405
i took right as positive for x forces and up for y forces

>>11724352
Note that lim[n->∞](1-1/n)^n = 1/e

>>11689640
Assuming the textbook is agreed not to be shit, you can do it as follows.
Read a word. Repeat. Read another word. Repeat both. And so on. Gradually drop the beginning of what you repeat, so that it doesn't take too long.
While this may seem crude and useless, it's an useful way to deal with material you are not able to get on the spot and you really need to know it. You will eventually find a way to make sense of it as you learn more and as you now got virtually limitless amount of time to analyze it.