/sci/ - Science & Math

A force of 10 N stretches a spring 2 meters. A mass of 5 kilograms is attached to the end
of the spring and a damper which offers a damping coefficient of 0.6. The mass is
released from 1 meter above the equilibrium position with an upward velocity of 1 m/s.
Find the equation of motion.
5x'' + .6x' + 5x
5x'' because 5kg
.6x' because damping coefficient
5x because k = f/s = 10/2
Is this right? When I solve for the auxillary equation, I get something like -.6 + sqrt(99.64) i / 10
Then I would e^(-.6/10t)(c_1 cossqrt(99.64)t/10 + c_2 sinsqrt(99.64)t/10 which feels pretty wrong.

what do professors and teachers do when a student asks a question they don't know the answer to?

>>9340629
"I don't know the answer, I'll explain it tomorrow".

>>9340629
in my experience, most of the time the question is poorly phrased and built on a false understanding which confuses the lecturer. The lecturer would then offer to deal with it after class, or during office hours

>>9340629
-dismiss the question and insult the student
-ignore the question
-"That is a very interesting question anon"
-"I'm not sure but I will look into it" - finds an answer after class. This is the best outcome.

Very rarely will they directly admit that they don't know.

Why do some university math classes grade attendance? Please answer in whole and complete English sentences.

>>9340757
only classes that ever did this was first year courses. usually, in my math courses your attendance meant the difference between rounding the grade up from a B+ to A, of course if it was close enough to warrant it.

>>9340757
>Why do some university math classes grade attendance?
because you're going to a daycare, not a real university

>>9340625
yes that's right, now find an expression for x' and solve for the initial conditions

note that
[math] A \sin ( \omega t) + B \cos ( \omega t ) = \sqrt{A^2+B^2} \cos (\omega t - \tan ^{-1} ( \frac{A}{B} )) [/math]
if you want to make the expression look pretty

How do magnets work?

>>9340769
https://arxiv.org/pdf/hep-th/0012092.pdf

>>9340769
Literally magic

>>9340769
>charged particles moving in circle create a magnetic moment
>magnetic moments create a magnetic field and tend to align themselves with and follow external magnetic fields
>electrons have a magnetic moment linked with their quantum spin
>take an atom with an unbalanced outer shell
>almost all its electrons have the same spin
>they all generate a magnetic moment in a direction that depends on their spin
>add them up to get the magnetic moment of the atom (non-negligible since all electrons on the outer shell have the same spin)
>build something out of these atoms while assembling the atoms so their magnetic moments all point in the same direction
>your material has a non-null magnetization

so archimedian property removes the need for 'infinitesimals', but it in itself is an infinite process. what is the subtly here?

>>9340806
>but it in itself is an infinite process
No, it's not.

>>9340812
explain

>>9340757

They're trying their best to get as many of the students to pass the courses so they can get their funds and that's one of the tricks they came up with.

Thank god we don't have retarded shit like that here.

>>9340823
[eqn]\forall x\,>\,0,\,\forall y\,\geqslant\,0,\,\exists n\,\mathbf N,\,n\,x\,>\,y[/eqn]
How is this "an infinite process"?

>>9340833
there's an infinite amount of selection for n.

>>9340840
So?

Brainlet here, I can't understand Trig Identities for the life of me, do any of you have shit that would make learning identities not as confusing?

Didn't learn in class because I have class once a week and 3 lab hours, failed the fuck outta that test and now I'm finals with my dick in my hand.

example -3cosθ+3=2sin^2θ,
MyMathLab has like 18 confusing ass steps to do it

>>9340584
what the FUCK is 0/0?

>>9341008
>what the FUCK is 0/0?
In which wheel?

>>9340986
use unit circle ID on sin^2

get: 2cos^2x - 3cosx +1 =0

proof: think

>>9341012
>Stupid question thread
>Brings up wheel theory

>>9341012
>In which wheel?
what the FUCK are you talking about?

>>9341072
>he doesn't know

>>9341072
Refer to >>9341055

>tfw too much of a brainlet and don't know how to approach this problem

>>9341077
>>9341074
I don't understand. Goodbye, world.

Why was energy not uniformly spread across the universe at it's creation?

And DON'T say quantum fluctuations of the void.

>>9341088
sleep tight
*places paper on your grave*
http://www2.math.su.se/reports/2001/11/2001-11.pdf

>>9341094
you need the PHENOTYPE to tackle such questions, pea-brain. sorry.

Quick question. I'm at the point where I have a sum with the indices k=2. Do I have to set c_0 = 0 and c_1 = 1 for y_1 and c_0 = 1, c_1 = 0 for y_2?
Then I just get c_1*y_1 + c_2*y_2 ?
There are 2 examples in my book that does what I just mentioned, and then another where they just plug in values of k= 1,2,3...
It doesn't state why they do one or the other, they just do it.

>>9340986
All you need to know is:
[math] (\cos(x),\sin(x)) [/math] is the point at the circle of radius 1 and center (0,0) ( i.e. [math] \{(x,y) \in \mathbb{R}^2 : x^2+y^2=1 \} [/math] ) given that you travelled distance x on it starting at (1,0) and going counter-clockwise.
[math] \cos^2(x) + sin^2(x)=1 \\
e^{i x}=\cos(x) + i\sin(x) \\
\tan(x)=\frac{\sin(x)}{\cos(x)} [/math]

For example. What is the formula for [math] \cos(x+y) [/math] ?
[math] cos(x+y) + i\sin(x+y) = e^{i(x+y)} =e^{ix} e^{iy} = (\cos(x) + i\sin(x)) (\cos(y) + i\sin(y)) = (\cos(x) \cos(y) - \sin(x) \sin(y) ) + i (\cos(x) \sin(y) + \sin(x) \cos(y) ),
\\
\\ \text{therefore } \cos(x+y) = \cos(x) \cos(y) - \sin(x) \sin(y) \text{ and } \sin(x+y) = \cos(x) \sin(y) + \sin(x) \cos(y) [/math]
And this way you found the formula for Both cos(x+y) And sin(x+y).
From this, the identity for tan(x) easily follows.

Now, about your problem, all you need is to use [math] \cos^2(\theta) + \sin^2(\theta)=1 [/math] and solve the quadratic equation in [math] \cos(\theta) [/math] .

>>9341008
It is not.

test

what's the most efficient way to input
>1+2+(4chan isn't letting me put ellipses here)+999+1000
into a calculator

>>9340584
Ok, so I'm reading some Larry Niven books and tides keep coming up.
I usually think I'm top of the science, but tides are fucking me in the head.
Explain me this

You have a spaceship. It's a hollow cigar. Rounded cylinder, right?
So it's orbiting a neutron star. Heavy heavy gravity gradient. The star is only just a bit above Sol in mass now.
The spaceship is orbiting a few dozen km above the surface.
The big thing is the tide. How do the tides act in such a scenario?
In the story, the spaceship, that cigar shape, orbits around the neutron star, passing close at the perihelion. The crewman finds on his approach that there is a "gravity" down to nose of the ship. It's gaining and gaining. Soon he'll be crushed against the hull at the bottom most point of the ship during the orbit.
But then he finds that the outer most point is undergoing the same event.
So he take shelter in the exact middle, with each extremity being pulled in opposite directions.

What I don't get is WHY
I thought tides involved too similarly massed bodies, like the moon and Earth.
How does a spaceship orbiting a neutron star experience tides?

>>9341148
Just do 1000!
That's what it is.

Also, use Wolfram Alpha. It's your cheat system for math

>>9341094
That's a good question.
The answer is the same as "Why is there more matter than anti-matter?"

>>9341148
1+2+3+4+5+6+7+8+9+10
= 10+(1+9)+(2+8)+(3+7)+(4+6)+5
= 10*5+5
= 55

Now do the same thing but for 1 to 1000

>>9341152
that's what i did and it gives me "error"
and when i do 10! it gives me 3,628,800

>>9341159
????

>>9341152
and how would i input this into wolfram alpha?

>>9341157
wow neat trick

1000*500+500 then?

i'm not so good with math dude
how would I do it for 29 then

>>9341164
i dont get it bro, i did it on my phone and it gave me the results that i told you
it gives me the product instead of the sum.

>>9341166
>phoneposter
KYS

>>9341150
You said it yourself: gravity *gradiant*. Tidal force is the difference in the effect of gravity over distanc. E.g. the moon's gravity pulls much harder on the side of the earth nearest to it, and much weaker on the opposite side of the earth. You get a high tide on both sides. A neutron star's extreme gravity has an extreme gravity gradient. It causes a noticeable difference in 'pull' over even small distances, meaning you will be stretched in the direction of the gradiant, and squeezed perpendicular to it. Just like the tides on Earth.

n*n+1/2

>>9341168
wat
im posting from my laptop

>>9341170
gradient*

>>9341170
No I get that
In my mind, if you're in a extreme gravity gradient, say a neutron star, then the tide force should be "horizontal" right?
Like ok, let's take the Moon as an example.
The closest part of the Moon wants to orbit at X speed due to its orbit.
But the farthest part of the Moon wants to orbit at Y speed.
Since they're both connected due to the, you know, actual fucking body of the moon, the closer part wants to orbit faster and the farther part wants to do it slower.
So there's a torsion between the close and far.

What I'm not getting is that why is that gradient pulling DOWN and not perpendicular to the gravitational force.

>>9341148
[math] 1+2+ \cdots + n= \frac{n(n+1)}{2} \\ \frac{1000 \cdot 1001}{2} = 500 \cdot 1001 = 500 \cdot 1000 + 500 = 500500 [/math]

>>9340584
Fe2O3 + ZnO = ZnO*Fe2O3
all solids
I need standard enthalpy of reaction (delt H, 298)

>>9341186
If the moon was a black hole, with all of its mass compressed into one tiny point, it would still cause tides on Earth. It has to do only with the inverse square of the distance between the closest and farthest sides of the Earth. The fall-off of gravitational force between those two points is what causes the Earth's tidal force. It has nothing to do with the size of the moon, only its mass.

>>9341202
Yeah yeah yeah
I said I understood that. Keep up

I'm thinking that in an orbit a tidal force should be orthogonal to the regular gravitational force, yeah?

>>9341204
The gradient, and thus the tidal force, would be toward/away-from the center of the neutron star. Either Niven's cigar is pointed toward the star (I just assumed that since it's the only thing that makes sense) or he's full of the proverbial poop.

>>9341213
Niven is often full o "proverbial poop" and he has said that in this story, he is partly.
What I'm giving a grievance isn't about the gradient.

Ok, so, in my knowledge (maybe I need to edify you too) the gradient should give a torsion effect. The bottom wants to go faster than the top. So the ship wants to tear apart.
But the issue is that in this story (and another), it isn't about the ship tearing apart, it's about the bottom wanting to go more down and the top wanting to go more up.
It's those directions that I don't understand

If Niven was any other writer, I'd say he was just a dumb pencil man. But Niven was at the core of the 70s Sci-Fi movement and that meant he went to all the NASA events and had all his work edited by real scientists.
The problem in this story isn't Niven. It's my understanding of it.

>>9341166
>1000*500+500 then?
You got it

>>9341222
Tidal force has nothing to do with rotation or orbit. If the Earth didn't rotate and the moon didn't orbit the Earth, there would still be a permanent tide on the Earth. It would just be stationary. It has only to do with the moon's gravity and the diameter of the earth.

>>9341164
just realized the pic you posted is a product as well
factorials give you a product not a sum bro
you're making the same mistake i did lols

>>9341234
>If the Earth didn't rotate and the moon didn't orbit the Earth
How do you define this?
Whatever, that's some relativistic shit

I'm still talking about why the tidal force in this fictional fucking is vertical (i.e. towards the star) rather than horizontal (i.e. in the direction of the orbit) that I think it should be

I'm given the function y= 2/(3+x)
Using a geometric series, I need to find 2 power series centered at x = 0 and x= 1.
How do I start to solve this? Are geometric series the same as Maclaurin series?

I know that its not possible, but how would I formalize this into a mathematical proof?

>>9340986
Consider the matrix R(a) corresponding to a rotation by angle a:
[cos(a) -sin(a)]
[sin(a) cos(a)]

Note that rotation by a+b is equivalent to the composition of rotations by a and b: R(a+b)=R(a)*R(b)=R(b)*R(a).
=>
[cos(a+b) -sin(a+b)] = [cos(a)*cos(b)-sin(a)*sin(b) -(cos(a)*sin(b)+sin(a)*cos(b))]
[sin(a+b) cos(a+b)] [cos(a)*sin(b)+sin(a)*cos(b) cos(a)*cos(b)-sin(a)*sin(b)]
=>
sin(a+b) = cos(a)*sin(b)+sin(a)*cos(b)
cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)

Alternatively, use Euler's formulae and x^(a+b)=(x^a)*(x^b):
e^(ix)=cos(x)+i*sin(x) => e^(i*(a+b)) = (e^ia)*(e^ib)
=> cos(a+b)+i*sin(a+b) = (cos(a)+i*sin(a))*(cos(b)+i*sin(b))
= cos(a)*cos(b)+i*cos(a)*sin(b) + i*sin(a)*cos(b)+i*sin(a)*i*sin(b)
= cos(a)*cos(b)-sin(a)*sin(b) + i*(cos(a)*sin(b) + sin(a)*cos(b))

Put a=b to get the double-angle formulae:
sin(2*a) = 2*sin(a)*cos(a)
cos(2*a) = cos^2(a)-sin^2(a) = 2*cos^2(a)-1 (by substituting sin^2(a)=1-cos^2(a)).

To get the half-angle formulae, solve the latter for sin(a)/cos(a):
2*cos^2(a) = 1+cos(2*a)
=> cos^2(a) = (1+cos(2*a))/2
=> cos(a) = sqrt((1+cos(2*a))/2)
=> cos(a/2) = sqrt((1+cos(a))/2)

2*cos^2(a) = cos(2*a)+1
=> 2*(1-sin^2(a)) = cos(2*a)+1
=> 2-2*sin^2(a) = cos(2*a)+1
=> -2*sin^2(a) = cos(2*a)-1
=> sin^2(a) = (1-cos(2*a))/2
=> sin(a) = sqrt((1-cos(2*a))/2)
=> sin(a/2) = sqrt((1-cos(a))/2)

For anything involving tangents, just use tan(a)=sin(a)/cos(a). Where necessary, convert between sin(a) and cos(a) using sin^2(a)+cos^2(a)=1.

>>9341539
>I know that its not possible
Why?

can somebody quickly check if last row is same as other two?

>>9341608
i got the last row by adding log to each side and then migrated x from exponent to multiplier position and then divided it by log2
is this correct?

>>9341613
Yes.

You can check it with a calculator:
log(5)/log(2) = 2.321928094887362
2^2.321928094887362 = 5

>>9341673
thanks to the skies mate
teacher fucked me because she said when i wrote second step that i needed to do it further so i wrote third one instead and i thought i haven't done it correctly.
either way, both are correct lol

>>9341565
The junctions alternate between north-south and east-west in a chequerboard pattern. The one immediately north of the starting position is east-west. Each street is one-way; the junction at one end is north-south, the other east-west. It's only possible to enter a street from one end. The starting street can only be entered from the south.

Are the Feynman Lectures + Exercises good to learn physics?
I only studied physics in HS

>>9341737
Yes. Excellent, in fact. But then you'll want to study each area in more depth:
classical mechanics: Kleppner/Kolenkow
electrodynamics: Purcell
thermodynamics: Reif
quantum mechanics: Shankar
special relativity: Taylor/Wheeler

Then on to:
general relativity: d'Inverno
quantum field theory: Peskin/Schroeder

How do I study physics

I'm a brainlet and programmer. But I never went to uni. I've been working in software for 10+ years now.

I want to move abroad but most other countries do not welcome self-taught people as much as Germany does so I need a degree.

I signed up for computer science in October but the high amount of math is really difficult for me to learn since I can't quit my job.

Right now I am working 4 days a week, studying on 3.

What way can I find to memorize the amount of information more efficently? It's not that I don't understand the things, it's that I forgot most part of it after a day again

Is the answer to this not 0? Because if μ was 0 (and y was 0), it would satisfy the requirements of the equation.

Could someone please explain matrix puzzles to me?

Our professor was out on the day we were supposed to go over them. The substitute was an old Chinese man I could barely understand that wrote small on the far side of the whiteboard that seemed to assume we already knew most of the new stuff he went over.

I have no idea how to do these. I know the rows are numbered 0-4 and the, same with the columns (it's a computer class so we start counting at 0 instead of 1)

But after that, I have no idea. The homework is asking to give an assertion about the matrix. Pic related is what I'm talking about. It's not one from my homework, but it's a really similar one.

Really at the end of my rope here. I can't seem to find any videos or anything going over how to do these. I would really appreciate it if someone could go over making an assertion of these step by step, or if there is some youtube video to link that.

>>9342284
What pajeet wrote this problem?

>>9340584
Why the fuck do we even need this general?
The whole board is nothing but stupid questions.

>>9342299
My stats professor. I really don't know how to approach this problem. without just assuming y = 0, and μ = 0. Since X is normally distributed around μ i figure that would make it <0 1/2 the time (and >=0 the other 1/2)

>>9341895
>read book
>do problems
>get problems wrong
>think about it
>retry until right
pretty much it for anything undergrad

>>9342289
the fuck do you mean "matrix puzzle"? reducing to row-echelon form?

>>9342364
I have no idea. Like I said, I've tried searching how to solve these but nothing came up.
In the lecture notes, right under that one I posted it says
"Assertion:
Given an nXn matrix A, for row i from 0 to n-1, for column j from 0 to i, A[i,j] = 1" And there is a box on that same page which is this picture.

The substitute seemed to assume we already knew most of this stuff and how to do them so he didn't go into very much detail on anything. It's a beginner computer concepts course.

>>9342374
can you do this?

>>9342390
No. There were no variables of any kind involved in the lecture notes or with what the substitute did.

Here's another page from the lecture notes.

True/false: "Every nonempty, bounded subset [math]A\subseteq \mathbb{R}[/math] has a least upperbound"

Does bounded imply both an upper and lower bound? or just one?

>>9341008
Depends on the 0/0, some examples:
[math]\lim\limits_{n \to 0} \frac {n^2} n = 0[/math]

[math]\lim\limits_{n \to 0} \frac n n = 1[/math]

[math]\lim\limits_{n \to +0} \frac n {n^2} = \infty[/math]

[math]\lim\limits_{n \to -0} \frac n {n^2} = - \infty[/math]

>>9341008
0/0 = undefined

This is because of the axioms all the other rules are set up on. To divide a number strictly by 0 (and not a limit approaching 0), is not possible for the rules division is set up on

>>9342284
Yeah, it's 0. The only number with a single real root is 0 (I think?). Since a normal distribution is symmetric, p(0 < -X) = 0.5 is equivalent to saying the mean is 0

>>9342399
So you just want a formula expressing the elements of the matrix?
It is:
[math] a_{ij} = 1 \text{, if } i \geq j \\
a_{ij} = 0 \text{, if } i<j [/math]

>>9342501
No, that's not quite it.

What the homework is asking for is the assertion. Written like the example in >>9342399

What I don't understand is the process that you reach the assertion.

>>9342429
>0/0 = undefined
Wrong.

why isn't logic covered in high school? the usual "core" classes are algebra and trig. i would think that logic is arguably more relevant than trig, both for the layman and for someone who wants to move on to college or AP math classes.

>>9342529
>assertion
wtf is this choice of word your retarded professor picked... anyway it's literally what I posted, just rephrased:

For i from 0 to n-1
For j from 0 to i
A[i,j] = 1

And I assume that your proffesor assumes that the rest is filled with 0s.

>>9342400
>Does bounded imply both an upper and lower bound?
Yes.

>>9342551
What would the proper word for it be? I just want to know what to search to learn more about this type of problem.

I can't seem to learn very well unless I see a problem being worked out first.

Can anyone show me why the spectral radius of a Bounded Linear Operator is less than the norm of the operator?

>>9342400
False. Consider [math]A = \{0.9, 0.99, 0.999, \dots \}[/math] for example

What is frame dragging?

>>9342621
>A={0.9,0.99,0.999,…}
sup(A)=1.

>>9342635
But is it the least upper bound if it isn't reached?

>>9342642
>But is it the least upper bound if it isn't reached?
Yes. The difference between supremum and maximum is that a maximum has to be in the set you're considering, a supremum does not.

[eqn]x_{n+1} = \frac{1 + x_{n}^{2}}{2} [/eqn]
Diverges for [math]x_{1} = 2[/math] right?

>>9342736
My reasoning:

sequence is increasing (proof: think). suppose it does converge, then [math]x_{n+1}\to L \implies x_{n} \to \L[/math]. Take the limit and you get a quadratic expression: [math]\frac{1}{2}L^{2} -L + \frac{1}{2}[/math], which has solution [math]L=1[/math], but this is contradictory, since the sequence is increasing and [math]x_{1}[/math] is 2 > 1.

>>9342754
[math]x_{n} \to L[/math]*
[math]\frac{1}{2}L^{2} -L + \frac{1}{2} = 0[/math]*

(a) You are given the task of constructing a double-slit experiment for 5 eV electrons. If you want the first minimum of the diffraction pattern to occur at 5°, what must be the separation of the slits? (b) How far from the slits must the detector plane be located if the first minima on each side of the central maximum are to be separated by 1 cm?


I understand how to do a), Convert KE to wavelength, and do wavelength/sin(2*5deg)

How would I even approach b)? Should I construct a wave equation?

>>9342754
>Circular reasoning
PROVE the sequence is increasing, then your whole proof works. Otherwise it doesn't

>>9342765
>proof: think
I already did that, just too lazy to type out my induction proof

>>9342768
>induction instead of using calculus

>>9342764
it's just bragg diffraction for the first part my dude. Second part is just geometry, you have 1 side of a triangle and an angle you construct the rest.

is Lipschitz continuity what you get when mean value theorem and uniform continuity fug and make a baby?

I'm having some trouble with this problem. Let M be a compact, orientable m-dimensional manifold. If m is odd, then the euler characteristic of M is 0.

This is a differential topology class with not much algebraic topology content, so we can use for example poincare-hopf and homotopy invariance of degree, but no poincare duality, and only basic results related to the euler characteristic and betti numbers.

>>9342547
k lol

how the HECK do you show [math]f:\mathbb{R} \to \mathbb{R}[/math] by [math]f(x) = x^{2}[/math] is not uniformly continuous via the mean value theorem?

>>9342562
It's the general idea of how to create certain matrices by using loops.

>>9342609
You want operators on infinite dimensional spaces as well.

>>9342917
Fucking google it you brainlet
'x^2 not uniformly continuous proof mean value theorem'

https://math.stackexchange.com/questions/2260254/prove-that-fx-x2-is-uniformly-continuous-on-any-bounded-interval

Please assist

>>9342635
Wrong, it's actually 0.999...

>>9342969
What have you tried?

>>9342959
but my domain is unbounded

>>9340584
Excuse me, is this the thread for posting stupid questions?

>>9342969
I'm trying to apply method of characteristics along with 1D wave equation, u(x,t)=F(x-ct)+G(x-ct) but I'm not really sure how to apply the boundary conditions to get a analytical solution. I should have paid more attention in class.

>>9342362
What if I never get them right?

>>9343010
McDonald's is always hiring.

>>9342997
[math]
\text{You want to show that } \exists \varepsilon >0 : \forall \delta >0 : \exists x,y : |x-y|<\delta \land |f(x)-f(y)|>\varepsilon \\
\text{Let } x=\frac{1}{\delta} \text{ and } y=\frac{1}{\delta}+\frac{\delta}{2} \\
\text{Then obviously }|x-y|=\frac{\delta}{2} < \delta \\
\text{Mean value theorem says } \frac{f(x)-f(y)}{x-y} = f'(a) = 2a \text{ for some } a\in (x,y) \\
|f(x)-f(y)| = 2 a |x-y| = 2 a \frac{\delta}{2} = a \delta > x \delta = \frac{1}{\delta} \delta = 1 \\
\text{Pick } \varepsilon =1 \text{ and you are done.} \\
\\
\text{Now how did I pick x and y this way? Well, you have this: } |f(x)-f(y)| = 2 a |x-y| \text{ so first of all it would be nice to have } |x-y|=\frac{\delta}{2} \text{ so that we get } |f(x)-f(y)| = a \delta \text{, and } y=x+\frac{\delta}{2} \text{ seems like a reasonable choice}.\\
\text{Since } a>x \text{ we get that } |f(x)-f(y)|> x \delta
\text{ , and since we want to have } a\delta \text{ always greater than some fixed number } \varepsilon \text{ we just pick } x=\frac{1}{\delta} \text{ so that } x\delta \text{ is always greater than } 1=:\varepsilon
[/math]

I need to model 1-D Fickian diffusion through two separate membranes with initial conditions, boundary conditions and clearance. While I understand the general solution for diffusion across a single membrane, I'm not quite sure how to add the boundary condition and second membrane into the formula.

I was planning on using a system of PDEs but I'm struggling to find anything related to this on the internet, though I know it exists since I did similar stuff in a Biotransport class. Can anyone point me in the right direction?

>>9343143
>and since we want to haveaδalways greater than some fixed numberε
meant xδ
And obviously, you consider the interval [x,y] to be contained in the positive reals so that you can remove the absolute value from a and make things simpler.

>>9341152
Surely adding consecutive numbers is more to do with triangular numbers? Factorial is multiplication-based.

All this banter in Star Trek about Class M planets and Class J fas giants etc etc really astronomy terms or just Sci Fi
Shorthand?

>>9342399
the numbers in each row of your matrix correspond to the coefficients in a polynomial in m variables where m is the number of columns. its a condensed form of a system of linear equations.

>>9342400
yeah this is the axiom of completeness. Bounded is a definition, it means upper and lower bound.,

>>9342621
youre retarded.

>>9343185
It's just sci-fi wanking, but it seems like a pretty decent way to quickly convey information on a planet.

>>9343185
If you’d actually read the chapter and not skipped to the picture page you’d know it’s real but a bit more prolofically used in Treks time than today.

https://en.m.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram

>>9343151
anyone? I feel like a fucking brainlet

>>9340584
I want to do Electrical Engineering, but my shitty college doesn't offer engineering in any form.
>Choose a different college
Just humor me please

Would a B.S. in Mathematics (Pure) or Mathematics (Applied) be better for eventual entry into engineering?

>>9343366
applied math is what you want

expect to get comfy with: linear algebra, differential equations, basic analysis, vec.calc + multi-var, and programming .

>>9343379
oh, maybe minor/joint major in physics or something, that's pretty important

>>9343379
>>9343384
Thanks. I'll break out my dad's old "Ordinary Differential Equations" and brush up on my calculus. I fucked up college years ago but made it through multi-variable calculus once before; time to refresh I sold my Stewart book.
Never was a big fan of physics, but I hate chemistry more so since engineering fields use more of one or the other, I'm glad it's physics.

>>9343398
>Spoilers don't work on /sci/
Well why the fuck does the shortcut work, Hiro.

>>9343398
here's my unfinished intro ode notes: https://www.mediafire.com/file/y3x444ex72c9sp2/2260.pdf , if you want a kind of 'cheat sheet'. not very rigorous but covers a good bit of ground.

should probably learn some python/c++ maybe a bit of matlab too, you can do some useful things with those

important thing - don't chew too much off, you'll get overwhelmed. until you enroll, just keep the learning to a manageable rate, you don't want to get burnt out.

>>9343366
Why don't you transfer to a school with an engineering program?

>>9343379
>applied math is what you want

No, applied math is just the watered down courses for future highschool math teachers.

>linear algebra, differential equations, basic analysis, vec.calc + multi-var, and programming

Everyone does those core courses.

>>9341787
Wrong on almost all accounts.
>classical mechanics
Landau-Lifshitz
>electrodynamics
Jackson
>quantum mechanics
Ballentine
>quantum field theory
Weinberg

Can someone explain to me why for questions that involve something like P(2 ≥ x), I must add up the probability of every number before and including 2, whereas questions that involve P(2 >x) do not require it?

>>9341787
>special relativity: Taylor/Wheeler

0/10

If someone was around lead as a child are the effects able to be seen later? Say if you had a brain scan they would be able to tell that the person was exposed to lead earlier in their life?

Math undergrad here. I'm just curious, what's the highest level of math used in physics? Even if it's only applicable in some arcane area. I'm just curious if/when math stops being applicable to physics.

>>9341540
nice

>>9343646
New fields of maths are constantly being developed to study general properties of of physical theories.
>Ginzburg-Landau [math]\rightarrow[/math] Singularity theory
>String theory [math]\rightarrow[/math] Twistors/tt*-geometry
>Theory of Defects [math]\rightarrow[/math] Topological Quantum Field Theory
>Quantum mechanics [math]\rightarrow[/math] Quantum algebra
>Quantization [math]\rightarrow[/math] Geometric quantization
>Conformal field theory [math]\rightarrow[/math] Vertex algebras
>Yang-Mills [math]\rightarrow[/math] Equivariant cohomology
>Critical phenomena [math]\rightarrow[/math] Quantum integrability
>Quantum field theory [math]\rightarrow[/math] Local von-Neumann algebras
>Renormalization [math]\rightarrow[/math] Renormalization (the math one)
And of course there are also fields that see (relatively) unexpected applications in physics:
>Feynman path integrals [math]\leftarrow[/math] Theory of moduli spaces
>Feynman diagrams [math]\leftarrow[/math] Graph theory
>Wilson loops [math]\leftarrow[/math] Quantum loop groups
>Partition functions [math]\leftarrow[/math] Knot invariants
>Minimal coupling [math]\leftarrow[/math] Theory of sheaves
And so on.
Bottom line is that there is virtually no limit to how deep maths can go to suit the needs of physics.

>>9340757
College obviously needs to be structured like high school still. I would have benefited from that probably.

Asked /g/ but no response, so here.

Okay, so I started in some programming languages like C++ and Python. I have Programming: Principles and Practice Using C++, going through the book and take notes/ answer exercises. Watched some Python youtube videos, understood concepts like for loops, classes, arrays and some other basic stuff but whenever someone gives me a unique problem, I'm at a blank. I seriously don't know how to start a problem. This is especially apparent in C++ because I find it way harder and trying to think how I implement dynamic arrays and classes like an idiot and mess around until I get frustrated and give up.

I guess all this time I've been memorizing. How do I actually learn? It's been few months but I feel like I'm learning things incorrectly

>>9343750
You should attempt the exercises in the books without looking at the answer first. I used to do this too and still do if I'm totally lost or the process isn't introduced yet. For programming, you really need to step back and think abstractly about what the question is asking, then use the tools in your mental toolbox to solve them.

>>9343750
What I found to be great is use python and just try to make neat things. Web scraping in python, as well as web servers (raspberry pi with web server gives wireless control of anything you hook up to it).

For c++, I made games with irrlicht. It's a 2d/3d graphics/game engine. Fun to mess around with.

>>9343754
I've never actually did it like this so I might redo some of the questions then. Thanks

>>9343760
So just working on a project basically? I always thought that I don't know enough to have a project, especially since I started recently. Guess I need one anyway

>>9343772
What do you want to automate in your life? I made a python app to punch me in at work because I was too lazy to do it myself.
Im also making a program to send files to another computer using tcp.

Hope that helps!

I'm using electrolysis to oxidize iron (so I can eventually make ferrocyanide (and eventually cyanide so I can kill myself))
There is always an ugly thick oxide layer on the rods I'm using (as to be expected) and large "fingers" coming off the end.
How important is removing this layer to expose fresh metal?
Will the oxidation stop if I don't continue to agitate the rod to clean off the oxide buildup, or will it slough off enough on its own to continue to oxidize the metal?

>>9343733
Ok that's cool. I thought that might be the case, but I was having trouble finding anything on Google that wasn't describing the bare minimum to get through a physics undergrad. Thanks anon

Does anyone care about the general GRE or just the one for your subject? Are you expected to take both?

Can I ace finals in Number Theory, Abstract Algebra, Real Analysis, and The Mathematics of Secondary Financial Markets if I have a week to prepare and haven't done any of the work nor showed up to lecture all year?

>>9343915
Are you just meming or what? I see these posts on /sci/ all the time and I can't imagine what kind of person willfully enrolls in a school and then neglects their education to this extent.

So the Lambert W function is defined such that if
[math]x=y e^y[/math] then [math]y = W(x)[/math].
For [math]x=y (e^y+1)[/math] there a way to find y in terms of the Lambert W function (and other elementary functions of course)?

I'm struggling finding extrema for a function with two variables.

I took the first partial derivative for both, and the three second ones. Everywhere I look, notes, youtube, textbook when we go back to find points to test using the first partial derivatives we can factor something out or we end up with the function in terms of one of the variables.
I'm starting with
[math] f(x,y) = x^3 + y^3 + 9xy + 6 [/math]
so my first partials are(I think)
[math] f_x(x,y) = 3x^2+ 9y [/math]
[math] f_y(x,y) = 3y^2+ 9x [/math]

When I set those to zero I can't seems to pull anything out and when trying to set them equal to one variable or another they just cancel, is this really just as simple as x = y = -3? As a test point?

Probability question
if there's a 1% chance of a person being autistic, and I get a random group of 100 people, what are the odds of ONE of them being autistic?
What about if it's a group of 50 or 200? what's even the formula you'd use for this

>>9344062
Exactly 1?
.01 * .99^99 * 100 = 37%
One event with a .01 probability, 99 events with a .99 probability and 100 possibilities for which person is the autistic one.

>>9344059
There will be two points which solve both partials being zero, (0,0,6) and (-3,-3,33). You can use the second partials to find whether or not these are extrema (http://tutorial.math.lamar.edu/Classes/CalcIII/RelativeExtrema.aspx)), or just look at a graph.

>>9344073
Thanks, I'm still not sure what methods besides just sort of looking at it and seeing it I was supposed to use to get x = -3 or x = 0 as test points, I'll ask my professor to go over it in class.

>>9344078
So, you have 3x^2+9y=0 and 3y^2+9x=0. You can solve the first one to get y=x^2 /3, and substitute into the second to get x^4 /3 +9x = 0. This can be factored to get x(x^3 + 27) =0, giving the solutions x=0 and x=-3.

>>9341078
Look up colligative properties, the freezing point depression is expressed as

deltaT = Kf * b

I don't know how dumb you are so

The lowering in temperature (for freezing point) = freezing coefficient * molality

>>9344081
I really need to practice factoring, it just doesn't jump out at me. I had y= (x/3)^2 scribbled on the side of the page but I wasn't really sure how to substitute it in. Thanks again, that makes perfect sense.

>>9343646
All of it. Physics is limited because we don't have enough.

>>9343750
>but whenever someone gives me a unique problem, I'm at a blank. I seriously don't know how to start a problem.

It takes most people a while before they can start breaking down problems into parts that can be done by loops, arrays, structures, etc. Things start clicking for most people when they get into data structures.

Stick to one language (C++) and branch out when you're comfortable at programming. It really is like a foreign language, it becomes more natural the more you practice it.

>>9343750
Read Cormen and practice solving project Euler problems

>>9344059
f(x,y)=f(y,x), so consider a change of axes: g(u,v)=f(u+v,u-v) = (6u-9)v^2+(2u^3+9u^2+6). The first term has an extremum at v=0 (minimum if u>0, maximum if u<0). The second term has extrema at u=-3 and u=0; the leading coefficient is positive so u=-3 is a maximum and u=0 is a minimum.

So the point u=-3,v=0 (x=-3,y=-3) is a maximum, u=0,v=0 (x=0,y=0) is a saddle point.

>>9344123
> practice solving project Euler problems
Project Euler is fundamentally about the math, not the programming. You're looking for mathematical properties which reduce the amount of calculation required.

The (very) few problems that are more programming than math are probably far too hard for someone who's still struggling with the basics.

>>9344062
Exactly k of them being autistic:
https://en.wikipedia.org/wiki/Binomial_distribution

P(At least one is autistic) = 1 - P(exactly 0 being autistic) =
[math] 1 - \binom{n}{0} (0.1)^0 (0.99)^{n-0} = 1-(0.99)^n [/math]

>>9344181
They don't seem to be struggling with programming, but with algorithms

>>9344059
>When I set those to zero I can't seems to pull anything out and when trying to set them equal to one variable or another they just cancel, is this really just as simple as x = y = -3? As a test point?
No dude, you can write y completely in terms of x in one equation and then replace it in the other equation.

Is there a general formula for solving two quadratic equations
[math]
a_1 x^2 + b_1 y^2 + c_1 xy = d_1\\
a_2 x^2 + b_2 y^2 + c_2 xy = d_2
[/math]
?

>0/0 =/= ∞

okay big boy, it's sleepy time now.

>question about finding the center of mass of an object
>spent a good time of the exam on it with no success
>tfw couldn't figure out all i had to do was to integrate, divide by 2 and find (x,y) at that value
>tfw brainlet

I have a month to become an expert in human physiology, what do?
I've been reading Guyton and even if it's amazing in quality of content, it has too much detail. Is Costanzo a good alternative? If so, should I go for the BRS edition or the normal one?

>>9344272
https://en.wikipedia.org/wiki/Center_of_mass#A_continuous_volume

It's very intuitive.

I am having problems with the torques, the coefficient between the wall and the ladder mu(static). The entire thing is in static equilibrium, I am trying to get the value of tan(alpha) only in values of mu. From working from the torques I get that tan(alpha)=(|N_1|-|N_2|)/(|F_1|+|F_2|). It asks for it when the system is at a point of slipping so F_1=mu|N_2| and F_2=mu|N_1|. Also |W|=Mg. Can anyone help me here, because I feel as though I am completely wrong and there is no way to simplify it in only terms of mu.

>>9340769

If light has no mass then how do black holes attract light with gravity?

>>9344473
>light has no mass
False.

>>9344484
>Photons have mass
False

>>9344486
>False
False

>>9344242
Change of coordinate system to get one of the equations in standard form (x^2/a^2 +/- y^2/b^2 = 1). That gives you one variable in terms of the other. Substitute into the other equation, rearrange so that the square root is on one side, square both sides. You now have a quartic in one variable, which can be solved algebraically or numerically.

>>9344493
>That gives you one variable in terms of the other.
But those are the transformed variables.

>Substitute into the other equation
Substitute the transformed variable. That makes no sense.

>>9344242
forgot to add the terms [math] e_1 x , f_1 x , e_2 y, f_2 y [/math]

>>9344518
[math] e_1 x , f_1 y , e_2 x, f_2 y [/math] *

Any chicks here? Is /sci/ boys club?

>>9344473
It has mass, it's just negligible. "infinitesimal" would be the technical term.

Does linear (in)dependence only apply when all the constants are 0?
So if all the equations don't equal 0, the system is linearly dependent?

>>9344663
I'm pretty sure that not even you know what you are asking about.

brainlet here. have a intermediate algebra final exam on friday.
whats the best calculator that can help me solve problems. was using my phone during the semester but he said its ban for the final

also were using something called scantron

>>9344668
If you have a system like:
2x+3y = 0
-4x+y = 0

Obviously a solution is x=y=0.
But what about:
2x+3y = 2
-4+y = 5

Does the fact that the constant vector isn't 0 mean that the vectors are automatically linearly dependent?

>>9344676
You mean the vectors [math] \begin{pmatrix} 2\\ -4 \end{pmatrix} , \begin{pmatrix} 3 \\ 1 \end{pmatrix} [/math] ?
Your systems can be written
[math]
x \begin{pmatrix} 2\\ -4 \end{pmatrix} + y \begin{pmatrix} 3 \\ 1 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix} \\
x \begin{pmatrix} 2\\ -4 \end{pmatrix} + y \begin{pmatrix} 3 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}
[/math]

>Does the fact that the constant vector isn't 0 mean that the vectors are automatically linearly dependent?
Do you know the definition of linear dependence and independence?

>>9344529
>Any chicks here?
Yes.

>>9344242
You can express one d as a multiple of the other so that the LHSs are also multiples of each other. You can then solve the resulting homogeneous equation in 2 variables using the quadratic formula.

Would a hypothetical universe where the unit of temperature (degrees Kelvin) is doubled, and the value of the Boltzmann constant is halved, be observationally indistinguishable from our current one?

Where can I start with math? The farthest i've gone is grade 10 mathematics, couldn't go on not due to being a brainlet but because my school was heavily pushing me towards an english program.

>>9344473
The black holes don't "attract" light, at least not in the usual sense. The mass of the black hole curves the space around it, and the light being "attracted" to the black hole is just it following a "straight line" (geodesic) in curved spacetime.

>>9344676
>>9344711
Anyway.
Two vectors u,v are linearly dependent if you can write 0 as a linear combination xu+yv of u and v other than the trivial one where x=y=0.
That is if your first system has a solution other than the x=y=0, then your vectors are linearly dependent.

In general, if you can write a vector b with two different linear combinations of u and v, then u and v are linearly dependent since:
x1 u + y1 v = b = x2 u + y2 v ==> (x2-x1)u + (y2-y1)v = 0 (the coefficients are not both 0 since the combinations were assumed to be different)
That is if your second system has more than one solution, then your vectors are linearly dependent.

Also, If you system is n by n (has as many equations as variables) and you it has no solution for some b, then your vectors are dependent again, but this needs some work to be proven.
That is if your second system has no solution, then the vectors are dependent.

How similar is Discrete Math to Linear Algebra? I just finished my Discrete Math course with an A- and i made me like math a lot, debating picking up a math minor now.

>>9344510
You apply the same transformation to both equations. The transformation is chosen so that one of them is in standard form (the other will be an arbitrary conic).

Assuming my computer uses 300 watts constantly. Does it generate the same amount of heat as a constant 300 watt electric heater?

>>9344830
https://www.pugetsystems.com/labs/articles/Gaming-PC-vs-Space-Heater-Efficiency-511/
Holy shit, someone tested this!

What is the scientific explanation for the attraction to the feet of females?

>>9344841
The brain-overlap theory.

>>9343014
Pls no bully

water that contains specific levels of certain metals like manganese or lead can have neurotoxic effects. Now if im making tea with an herb that is very high in manganese, which is often the case, why is that manganese less bioavailable or/and less dangerous than manganese polluted water from some village in china ?

>>9344916
are you in uni or self studying? If you're in uni, go to your professor's office hours you probably pay a hefty bargain for that opportunity. If you're self study then post the problems here, someone will help walk you through eventually.

how do you guys study to non-math disciplines? i find it harder memorizing things than solving any kind of numerical or logical problem
the method i currently use to study these things is write it down, but this doesn't make me feel safe enough... so, any suggestions?

>>9344975
>how do you guys study to non-math disciplines?
i don't

>>9344975
we don't

>>9344975
>how do you guys study to non-math disciplines?
Why would you?

>>9345018
basically because the university said so lmao
its tanenbaum book about operating systems, btw

>>9345032
>basically because the university said so lmao
Which university for brainlets do you go to?

>>9345032
looks interesting enough, just do it

do many examples and counterexamples to gain intuition like in math

>>9345036
ive read more or less 100 pages, the book is really nice and easy to follow, ive wrote down some interesting topics in a handbook which i read from time to time, but i just don't feel confidence because it feels like too much stuff

>>9345035
you would probably not know it since i'm not from US

>>9344800
Not at all similar but it's an absolutely essential course for math.

>>9345077
So which main math course introduces set theory, induction proofs, and logical propositions? I thought induction proofs was a Linear Algebra thing.

>>9345046
>it feels like too much stuff
you probably aren't required to have complete mastery over all that shit then. that's fine. learn the main principles, collect the main examples, and be able to implement what you're expected to.

>>9345081
I learnt those topics in high school so I think they come under pre-calculus. Most introductory courses where they're required will probably have a quick review of the topics at the beginning. Even Munkres's Topology has an introductory chapter on set theory and induction iirc.

>>9345081
>>9345119
But if you want to study it in depth you'll have to take a course on set theory.

>>9345081
>So which main math course introduces set theory, induction proofs, and logical propositions?
You didn't do some naive set theory and induction in discrete? What did it cover?

>>9345137
yeah we did. But at my school, Discrete math is a Computer Science class. We have a MATH 3300 class called "Introduction to High Mathematics" so I'm guessing this is the Math Major equivalent course. In Discrete at my school we focus on Boolean Algebra and Bitstring concepts when introduced to recursion/Fibonacci and all.

can someone check my workings. summarizing due to time constraints.: (mainly just need to know this is the right idea)

[eqn]f(x) = \begin{cases} x^{2}\sin(\frac{1}{x}) &\mbox{if } x\neq 0 \\ 0 & \mbox{if } x=0 \end{cases} [/eqn]

>[math] f[/math] is continuous.

0 is a limit point, so [math]f[/math] is continuous at 0 if [math]\displaystyle \lim_{x\to 0} f(x) = f(0) [/math]

(I have worked this out to be true, thus [math]f[/math] is continuous at 0)

>[math]f[/math] is differentiable

differentiable if [math]f^{\prime}(0)[/math] exists, i.e.: [math]\displaystyle \lim_{x\to 0} \frac{ x^{2}\sin(\frac{1}{x}) - f(0)}{x-0} [/math] exists (and it does, therefore differentiable)

>>9344529
>>9344712
there are no girls on the internet anon

>>9344529
do you mean chicks (f) or chicks (m)?

what chemical reaction could form from lubricant and the alcohol found within a medical swab, if any?

>>9344800
CS majors are retarded so you're going to be btfo in a real math course. Bit LA is still brainlet tier tho

Can anyone help me identify this fossil? I am not sure this is the right place to ask.

Could someone help with this? I've tried several different ways but I keep getting wrong answers.

>>9345309
coral? it doesn't even really look like a fossil

>>9345327
The options are Ammonites, Brachiopods, Crinoids, Ferns, Graptolites and Trilobites.

>>9345339
like maybe crinoid but actually no
looks like vein of quartzite or something, but why is it so round?

>>9345346
another image of it. I am sure its a fossil, I am leaning more towards a crinoid as it has the circle with a hole in the center shape.

>>9345356
If it's crinoid you'd be looking at a piece of a stem and it doesn't look like that
it looks metamorphic, is there foliation?

>>9345375
I dont know, its fossils in limestone

Why do antibiotics have little to no effect on non-multiplying bacteria as opposed to multiplying bacteria?

>>9345325
[math] 2 \cdot (t + e^t) + (t +e^{2t}) - 10 = 0[/math]

The rest should be quite easy

>>9345325
>>9345468
Oh, and wolframalpha says t ~= 0.6878, but I guess you already knew that

>>9345468
>>9345501
Thanks man, I was looking at the wrong variables.

>>9344057
Anyone?

>>9340584
I've noticed a trend with my math/science career. Where I'll get caught up forever on some small dumb detail and once I stop misunderstanding it becomes clear as day. Does this mean I'm a brainlet or is there something I need to do differently?

>>9345564
You're doing it right

>>9344242
Groebner basis.

>>9345564

Based on how you write, you're a brainlet. Otherwise that's completely normal.

>>9345648
Based on how you write, you're a plebbitor.

>>9345392
Does it have layers?

>>9345200
yes, correct

>>9343750
Every time you learn a new programming thing, think of an idea for a program that exploits it that will be useful to you.

When I learned structs I made a "database" with friends' names, addresses, etc on it.

how do you construct the density matrix of a coherent state?

>>9346011
Very carefully

>>9346011
Literally just matrix of column vectors.
[math]\rho = \bigoplus_n |\psi_n\rangle[/math]

Why do things appear smaller the further away they get?

>>9346044
because jews lmao

finished high school years ago and focused on my career now wanting to pursue computer science
shit at math realizing my teachers were also bad in their methods
need to learn from HS to up can someone make a timelined list of maths to learn. although i want to specialize in either firmware or networking i feel maths aren't that big there but still it will help especially trying to get into comp sci. learning on my own for now

What is a tensor and how is it different from a matrix?

>>9346214
A matrix is "syntax" for a linear map in the same way that (x ↦ x + x) and (x ↦ 3 * x - x) are both syntax for the same function on integers. A linear map is a function f from a vector space V to another vector space W such that f(u + v) = f(u) + f(v) and f(sv) = s f(v) for any vectors u and v and any scalar s.

In contrast, a tensor is syntax for a multilinear map.

>>9346235
So... a tensor is a matrix of matrices?

If a problem can be reduced to a NP-hard problem in polynomial time does this imply the original problem is NP-hard? I figured yes because the original problem would have the same upper bound as the reduced NP-hard problem which would imply a worst case of non-deterministic polynomial time

>>9346316
No.

Take the set A = {w | w is a binary number which contains at least one '1'}

Of course, A can be solved in polynomial time, so it can also be reduced to SAT in poly time. Take f the function that maps a binary number w and outputs the boolean expression '(x1 OR x2)' if w has at least one '1' and '(x1 AND x2)' otherwise. Of course, w is in A iff f(w) is in SAT, and SAT is NP-hard.

>>9346332
Fuck I meant '(x1 OR -x1)' if w contains at least one '1' and '(x1 AND -x1)' otherwise of course.

Write a function, third_at_least(a), that returns a value in a that occurs at least
len(a)//3 + 1 times. If no such element exists in a, then this function returns None. If more than
one such element exists, you should return the smaller one. For simplicity, you may assume that the
list a has at least 4 elements.


What would be the most time efficient solution. My current number of operations is n^2, im trying to go lower

>>9346067
Functions and Graphs
Trigonometry
Calculus 1
Linear Algebra
Discrete Mathematics for Computing
Calculus 2

>>9346266
A tensor is a multilinear map who eats vector fields and dual vector fields, giving you back a real number, this number is independet from he choise of basis, so, this is the most important property of a tensor, it preserves something. A tensor can be represented as a matrix, but not always.

>>9346350
in this order, would you recommend?
thanks dude or gril

>>9346416
Yup, these are sort of the basics, so you can invest in some other areas

http://4chan-science.wikia.com/wiki/Computer_Science_and_Engineering

>>9346067
Book of Proof by Hammack ( http://www.people.vcu.edu/~rhammack/BookOfProof/ )
Mathematics of Choice: Or, How to Count Without Counting by Ivan Niven
Introduction to Graph Theory (Dover Books) by Trudeau
Basic Mathematics by Serge Lang
Methods of Mathematics Applied to Calculus, Probability, and Statistics (Dover Books) by Richard W. Hamming
Numerical Methods for Scientists and Engineers (Dover Books) by R. W. Hamming
The Art Of Probability by R. W. Hamming
All of Statistics: A Concise Course in Statistical Inference by Wasserman

>>9346469
thanks i'll follow in that order as well
>>9346461
not sure if same but i'm going to use this guide too thank you people

what does d stand for when saying dx/dy

>>9346486
i mean dy/dx but both works i guess
also in integral too, what is d

>>9346486
Differential.

>>9345709
Can't tell, just need to know the fossil.

>>9346214
a tensor is a "coordinate-free" matrix. if you take a square matrix A, you can look at it either as a linear map (you take a vector x and it spits out a new vector A*x), or as a bilinear form (you take two vectors x,y and it spits out a real number xT*A*y). if you change coordinates, A changes differently as a linear map and as a bilinear form: that's because a linear map is a tensor of type (1,1) and bilinear form is a tensor of type (0,2).

I need some kind of anthropology (?) atlas of human morphological diversity, focused mainly on craniofacial characteristics. Something that associates facial features with places, ethnicities, cultures etc. I want to be able to draw nationalities accurately, so when I depict Zambians meeting Finns in my space opera the Finns and Zambians watching will be shocked at how accurate I am. Hate feeling like a hack, pretending like there's 5-7 types of human face in the world.

>>9346486
It is a number so small it's smaller than all other numbers except zero, or a number so big it's bigger than all other numbers except infinity

Describe this structure to me. It's melanin.

Anything interesting about the structure? I'll give you a meme or something if you reply.

just had my analysis final

we're all gonna make it lads.

>>9346235
>In contrast, a tensor is syntax for a multilinear map.
Really? That's it? Then why is the wikipedia article so confusing?

does nofap actually have any benefits?

>>9346486
It does not have a rigorous meaning. It's just an intuitive notation.
It comes from this:
If you have a set of values [math] x_0, \ldots , x_n [/math] then you define [math] \Delta x_i [/math] as [math] x_{i+1} - x_i [/math] .
If you map the values to [math] y_0=f(x_0) , \ldots , y_n=f(x_n) [/math] then you have [math] \Delta y_i = y_{i+1} - y_i = f(x_{i+1}) - f(x_i) [/math] .
Rename [math] \frac{\Delta y_i }{\Delta x_i } = \frac{f(x_{i+1}) - f(x_i)}{x_{i+1} - x_i} [/math] to [math] \frac{\Delta y }{\Delta x} |_{x_i} [/math] .
Now, remember the definition of the derivative:
[math] \lim\limits_{h \to 0} \frac{f(x_0+h)-f(x_0)}{h} = \lim\limits_{h \to 0} \frac{f(x_0+h)-f(x_0)}{(x_0+h)-h} [/math]
If you think that [math] x_0 , x_1 \ldots , x_n = x_0 , x_0 +h , \ldots x_0+nh [/math] , then the derivative becomes
[math] \lim\limits_{h \to 0} \frac{\Delta y }{\Delta x} |_{x_0} [/math]
And you rename this into [math] \frac{dy}{dx} |_{x_0} [/math]

>>9346912
>It does not have a rigorous meaning. It's just an intuitive notation.
wrong. it's an artifact from the days when calculus was dealt with in infinitesimal quantities. it's literally an "infinitesimal change in y divided by an infinitesimal change in x"

>>9346813

It has a higly polar structure and i’d imagine that it acts as a base. Now fork over my memes.

>>9346912
> [math] \lim\limits_{h \to 0} \frac{f(x_0+h)-f(x_0)}{(x_0+h)-h} [/math]
Meant [math] \lim\limits_{h \to 0} \frac{f(x_0+h)-f(x_0)}{(x_0+h)-x_0} [/math]

>>9346920
here's a meme

>>9346916
That's literally what the things I wrote mean.

>>9340797
>your material has a non-null magnetization
You should really say non-zero, since null in relativistic physics (which EM obviously is) means light-like.

Given any x in [-A,A], how can one show that

[eqn]f_n(x)=\left ( 1-\frac{x^2}{n} \right )^{n}[/eqn]

is an increasing sequence for n>A2?

This result was used in a solution for an exercise, and I have no idea how they got it. Perhaps it would be easier to prove that

[eqn]log(f_n(x))=nlog\left ( 1-\frac{x^2}{n} \right )[/eqn]

increases, but I couldn't manage that either.

>>9346935
For n>A^2, I meant

>>9346935
induction on n in the definition of increasing

Absolute brainlet here.
So lets say :
[math]x(x+1)/(x+1) = x[/math]
Which I think is a fair assumption to make. But in the first equation, x is not defined in -1. So they're supposedly equivalencies, but not equal functions? Can someone explain this to me because It's a concept I'm struggling to understand.

>>9343814
Look on the nLab, for example:
https://ncatlab.org/nlab/show/higher+category+theory+and+physics#Fundamentals
is a huge list of the most abstract, hardcore mathematics applied to physics in lots of different (probably useless from a physicists point of view) ways.

>>9346946
it only makes sense to simplify (x+1)/(x+1) to 1 if x is not allowed to be -1.

>>9346876
I was looking it up and found this:
https://math.stackexchange.com/a/10374

Made everything clear.

what the fuck is an antibonding orbital
this whole molecular orbital concept feels abstract to me, is it a theory or real?
how are these orbitals attached if they are not bonding?

>>9346946
They are two different functions that coincide everywhere except -1. You can say f(x)=x if x=/=-1, otherwise f(x)=/=x

>>9346920
>>9346922

I don't think it's a polar molecule. It's planar with an inversion center, the vectors would probably partially cancel. I'll try to simulate the partial charges.

>>9346946
Alright. First a minor nitpick, the expressions themselves aren't called equations, as an equation has two sides and an equality symbol.

Now, a *function* is actually defined by three things: A domain, a codomain and a rule that assigns each input to its output.

When people write "Let f(x)=x be a function", they implicitly mean that f is a function from R to R (the real numbers)- of course, it can have other domains, but it's usually R in the context of algebra.

The function g(x)=x(x+1)/(x+1), is NOT defined on the number -1 (as you said), so its domain is R\{-1} (all real numbers besides -1).

You can write x(x+1)/(x+1)=x, which means: whenever both functions f and g are defined, their values are equal.

However, f and g are NOT the same function, as they don't have the same domain- g is not defined in x=-1 while 1 is.


As another example, take f(x)=sqrt(x) and g(x)=sqrt(|x|). One can say that f(x)=g(x) on the positive real numbers. However, f and g are NOT the same function, as f is only defined for x>=0 while g is defined for all real numbers.

>>9343915
Yeah, first year courses are pretty easy.

>>9346956
>>9346966
Thanks a lot, this clears things out.

>>9344057
Write the RHS as (ye^y) + y, then hope you can make sense of what's going on

>>9346946
You have to understand that functions aren't formulas. Functions take an element of a certain set and map it to a unique element of another set.
It's just that some functions can be DESCRIBED by simple formulas.

Now that function f is not actually defined, since we don't have a domain given to us (or a codomain).
You just Assume that the domain is composed by all the real numbers x which make sense to send to x(x+1)/(x+1), which is all the real numbers except -1.

It all comes down to what the fuck the one who wrote [math] x \mapsto x \frac{x+1}{x+1} [/math] meant.
It might as well mean [math] x \mapsto x [/math] .

>>9344069
Stop studying STEM, become an artist or bartender.

>>9346979
That doesn't make things any clearer.

>>9346813
>>9346961

I ran a quick calculation, and the low debye units mean that it's basically non-polar. The Mulliken charges confirm that it's non-polar since they cancel out; check out N8 & N19, O14 & O22, O12 & O 24.

Any good set theory resources? I've already passed it but I feel like it's going to kick me in the ass later on if I don't fully understand it. I'm having trouble with the super abstract shit in general.

>>9346941
How exactly?

>>9347077
>set theory
>good

>>9347057

I’d imagine that the partial charges do have an effect however. Eg. the oxygens form hydrogen bonds.

>>9347103
Take your pedophile cartoons back to >>>/a/

Is studying while being tipsy - not drunk - somewhat efficient? What are your experiences with that?

>>9347112
I may be wrong but you might be thinking about solubility instead of polarity.

>>9347121
Redditors are not welcome here.
>>>/r/eddit/

>>9346979
I get [math]y=W(x-y)[/math] then, but that's not solved for y.

is it worth it too learn calculus through Paul's Online Math Notes or it would be better for me to read a calculus textbook? I've never studied calculus 1 and I plan to learn it in a month (or less) dedicating myself like 10 hours a day

>>9347386
>is it worth it too
is it worth it to*

I don't get double dual space pls help

In solidworks went I click the reference triad, it used to snap to the axis. Now when I click it, it irritatingly pivots the sketch by like 10 degrees. I'm a googlet and cant find any way to fix it

>>9342420
L'hopital that shit?

>>9343750
Firstly, focus on one language until the general concepts click. It's better to get a foundation then generalize and abstractify it

Then, start writing down in english what you would do as a human. Step by step. Just like a a set of steps you would tell another human to physically do what you want done, then start making that into pseudocode, and finally convert it into real code. That usually works for me.

Shouldn't the square of any number be positive?
-7^2 should be 49 shouldn't it? (-7 * -7)
Why do calculators produce a negative?

>>9340584
Any chemfags here?
Pic related is what I use to give my surfaces and electronics a quick clean (Clorox for the former, Lysol for the latter). I just did a pretty detailed cleaning using both, and without thinking just threw the used wipes in the trash. I then realized I shouldn't be so careless with house hold cleaners. Will their combined chemicals result in any hazardous reactions?

>>9347707
Yes, the square of any non-zero real number is positive. The calculator you're using is probably parsing things differently than you -7^2 = -(7^2) = -49 instead of (-7)^2 = 49.

Since a neutron star is so dense, is its surface
solid or more of a very slow moving liquid? Or neither?

>>9340625
guys why didn't the e go away on the left side of the equation

also why did the -3 change to a -4 just by being divided by e

>>9347834
>>9347834
remember that for [math]a\geq 0[/math] you have [math]a^n\cdot a^{-m}=a^{n-m}[/math]
and
[eqn]\frac{e^{3x-3}}{e}=e^{3x-3}\cdot e^{-1}[/eqn]

>>9347868
Fug. Alright thanks anon.

What "is" an oil? Is it just any liquid that will not mix with water or is there more to it than that?

If a large asteroid were to hit the moon today (think of the asteroid that made the Copernicus or Tycho crater), would you hear the impact from Earth or would it be silent?

Would you hear any sound from outside Earth if it was loud enough and came from close enough?

>>9340584
I'd like to learn about continued fractions. What concepts should I have under my belt and through which texts should I work?

If I listen to recordings of lectures with only one headphone in one year so audio coming in only one ear so only one side of brain is processing it, is that worse than listening to the audio through headphones in both ears so both sides of the brain get to process the audio?

My algebra is rusty. How do I separate this fraction?
.9s/(s-.1)(s+.2)
I should get .3/(s-.1) + .6/(s+.2)

>>9346813
Symmetry like a Julia fractal.

>>9340584
I have a question that's more about college administration than anything. I want to take classes where the pre-req is pre-algebra. When I asked at least a couple people in charge to define exactly what pre-algebra IS, they would only say I should take the test to figure out what I need.

Is pre-algebra just arithmetic, or what? This is a community college with a math tests that breaks down into arithmetic, "elementary" algebra about which half is beyond me, and "college-level math" which is just baffling. I'm trying to get into these classes and don't want to take a semester of math.

If Law of Non-contradiction provable? I thought it's an axiom but apparently Russell proves it Principia.

>>9347891
>How do I separate this fraction?
Write
.9s/(s-.1)(s+.2) =
a/(s-.1)+b/(s+.2)

multiply both sides by (s-.1)(s+.2) so that
.9s =
a(s+.2)+b(s-.1) =
s(a+b)+(.2a-.1b)

then solve for a and b

>>9347891
Basically, you want an expression of the form [math]s(\frac{A}{s-0.1}+\frac{B}{s+0.2})[/math]
Take the least common denominator, and equate the numerator with 0.9s
Why the s multiplying that sum of fractions? Basically, separating fractions works well when there's a constant above. If there isn't one, just factor the numerator outside and procede normally.

>>9346954
Electron fill the lowest energy states first
2 orbits could be in phase or out of phase

>>9345032
Understand why it was designed that way instead of memorizing that it was designed that way.

>>9346954
>is it a theory or real?
Both, since there is no difference.

>>9341952
Seems like what you currently do is more than a lot of people do while studying full-time. You'll make it! Sorry if not quite a helpful answer.