/sqt/ Stupid Questions Thread: Oxford Capacity Analysis Edition

[Anonymous No.9475021]

This thread is for questions that don't deserve their own thread.

Tips!
>give context
>describe your thought process if you're stuck
>try wolframalpha.com and stackexchange.com
>How To Ask Questions The Smart Way http://www.catb.org/~esr/faqs/smart-questions.html

Previous thread >>9466071

[Anonymous No.9475124]

>>9475021
what the fuck is the answer to:
sin(x) + cos(x) = a
you are supposed to solve for x.
got it from my teacher as a brainteaser that she says can be beautifully solved geomatrically, but i just don't see how to solve it other than "all x are correct as long as a is an arbitrary constant".'
i feel like a brainlet right now

[Anonymous No.9475136]

>>9475124
I also tried constructing a right triangle where the hypotenuse is equal to one so that i could simplify the length of the other sides as equal to the cosine and sine respectively. then i tried substituting with the pythagoras formula (Hypotenuse^2 = A^2 + B^2 where A and B are the cathetus (if that is even the right word, not native speaker)) but it just gave me cos(x) = cos(x)

[Anonymous No.9475170]

>>9475124
Draw the graphs and use superposition

[Anonymous No.9475246]

Hi /sci/. Is there an n-dimensional equivalent of the linear fractional transformation
[eqn]f(x) = \frac{ax+b}{cx+d}[/eqn]

I have some novel numerical jiggery pokery that is too cool to not understand deeper which operates under the assumption that just such a thing exists, but I'll be damned (as an hobbyist) if I can find anything about this.

[Anonymous No.9475257]

>>9475246
https://en.wikipedia.org/wiki/M%C3%B6bius_transformation#Higher_dimensions

[Anonymous No.9475264]

What's the difference between an integral and an antiderivative?

[Anonymous No.9475265]

How can I graph the Forward 2D DCT?

[Anonymous No.9475270]

>>9475264
>What's the difference between an integral and an antiderivative?
An integral is a number, an antiderivative is a function.

[Anonymous No.9475272]

>>9475257
jesus fucking christ am I retarded

[Anonymous No.9475285]

>>9475124
sin(x) + cos(x) = root2 sin(pi/4 + x)

[Anonymous No.9475293]

>>9475257
>>9475272
that absolute value in the denominator is absolute bullshit

[Anonymous No.9475422]

when I get take the function f(x)=1/x and rotate it about the x axis from 1 to infinity I get a solid of revolution with finite volume. My question is can I take the function f(x)=1/x^2 and also rotate it about the x axis on a interval from 1 to infinity to get a solid of revolution with finite volume and why?

[Anonymous No.9475425]

>>9475422
>My question is can I take the function f(x)=1/x^2 and also rotate it about the x axis on a interval from 1 to infinity to get a solid of revolution with finite volume and why?
Have you tried applying the same reasoning you used to conclude that you get a solid with finite volume by rotating 1/x?

[Anonymous No.9475444]

>>9475425
Well something tells me the volume is going to be finite too, but truth be told I am not capable of checking myself, so I figured I'd ask here because I am very curious

[Anonymous No.9475471]

>>9475444
should be [math]\frac{\pi}{3}[/math]

[Anonymous No.9475551]

>>9475444
A more complete answer. What we're looking for is the value of [eqn]\pi \cdot \int_0^{\infty} x^{-2n}dx[/eqn] for [math]n>0[/math]. Skipping a bunch of limit bullshit this is just [math]\frac{\pi}{2n-1}[/math].

[Anonymous No.9475554]

>>9475551
should be [eqn]\pi \cdot \int_1^{\infty} x^{-2n}dx[/eqn] sorry about that.

[Anonymous No.9475595]

stupid fucking question
why is this 2+4/5 and not 2(4/5)?

[Anonymous No.9475611]

>>9475595
because you're in pre-algebra where people still write mixed fractions instead of improper fractions WHICH TOTALLY IRONICALLY are the preferred form to write rational numbers.

[Anonymous No.9475712]

how do i express [math]\mathbb{R}\setminus\mathbb{Z}[/math] as a union of several open intervals in the same way that [math]\mathbb{R}\setminus\mathbb{N}=\bigcup_{n=1}^{\infty} (n,n+1)[/math]

[Anonymous No.9475717]

>>9475712
take the union over all integers instead of positive ones

[Anonymous No.9475823]

How to compute the coefficient [math][A_1^{p_1}..A_q^{p_q}][/math] of [math](A_1 + ... + A_q)^2 (A_i^2 + ... + A_q^2)^{14}[/math] ?


Example: for [math]q = 2[/math] and coefficient [math][A_1^2A^{28}][/math] the answer would is [math]15[/math]

[Anonymous No.9475825]

>>9475471
>>9475551
>>9475554
thanks I think I figured it out

[Anonymous No.9475878]

>>9475124
cos(x)=e^ix+e^-ix / 2
sin(x)=e^ix-e^-ix / 2i

cos(x)+sin(x) = e^ix(1-i) + e^-ix (1+i) / 2
= e^ix(√2 e^-iπ/4) + e^-ix (√2 e^+iπ/4) / 2
= √2[ e^(i(x-π/4)) + e^(-i(x-π/4)) ]/ 2
= √2cos(x-π/4)

[Anonymous No.9475898]

>>9475717
how?

[Anonymous No.9475919]

>>9475270
So does derivative have a special "number" counterpart too?

[Anonymous No.9475936]

>>9475270
*equivalence class of functions

[Anonymous No.9475942]

>>9475898
Just do it™

[Anonymous No.9475969]

>>9475124
You have a unit vector at angle x <cos(x), sin(x)> and another offset by -90° <sin(x),-cos(x)>.
Algebraically, the vector addition is <cos(x)+sin(x), sin(x)-cos(x)>.
Visually, you know that the unit vectors are at right angles so the resulting one is √2 long and splits the angle in half so it is √2 <cos(x-45°), sin(x-45°)>

cos(x)+sin(x) = √2 cos(x-45°)

[Anonymous No.9475972]

>>9475264
>>9475919
antiderivative is self-explanatory. integral is a number, the signed area under a graph of function. the relation between antiderivative and integral is that the integral can be computed by taking the antiderivative and plugging in the endpoints. this is the fundamental theorem of calculus. for this reason, the antiderivative is usually also called "integral", but it's kind of misleading.

[Anonymous No.9475978]

>>9475919
No because the derivative f'(x) only depends on the local nature of f at x.
The integral depends on a domain, the antiderivative is what you get when you allow that domain to vary.

[Anonymous No.9476000]

What is the point of fourier series if they're used to describe functions you already know? We're doing it in my calculus class and I don't see the application

[Anonymous No.9476005]

>>9476000
Fourier series arise naturally by solving certain PDEs.

[Anonymous No.9476013]

>>9476000
Easier to take derivatives

[Anonymous No.9476014]

>>9476013
but in the creation of the series you have to integrate the original function to get An and Bn terms correct? So I don't see how it fixes anything

[Anonymous No.9476033]

>>9475825
Can someone explain the difference between countably/uncountably infinite to me? Not sure I understand

[Anonymous No.9476039]

>>9476033
countably as the name implies refers to a count (of objects or subjects for examples) that goes potentially to infinity.
uncountable infinity is just the domain of r

[Anonymous No.9476075]

>>9475898
[math] \bigcup\limits_{n \in \mathbb{Z}} (n,n+1) [/math]

[Anonymous No.9476087]

>>9476033
If you can list all elements of an infinite set in this way: [math] \{a_1 , a_2 , a_3 , \ldots \} [/math] , then the set is countably infinite; if you can't then, it's uncountably infinite.

[Anonymous No.9476116]

>>9475021
In an infinite series, can grouping successive terms affect the convergence? I know that if I group terms by changing the order in some way that can affect convergence. But what about just putting parenthesis all over the infinite series?

[Anonymous No.9476120]

>>9476033
countable <-> same size as N
uncountable literally everything else that's not finite or countable

[Anonymous No.9476122]

>>9476116
What do you exactly mean by "grouping successive terms"?
Can you give a concrete example?

[Anonymous No.9476131]

>>9476116
Like grouping by pairs or n-tuples?
No, they're equal at infinite many points so you can rerun the same convergence argument.

[Anonymous No.9476143]

>>9476120
>The set [math]\{1,2,3\}[/math] is not countable because it's not the same size as [math]\mathbb{N}[/math]

[Anonymous No.9476145]

>>9476116
This is one of the things that distinguishes conditionally convergent series from unconditionally convergent series, whether grouping or reordering the terms affects the limit. Conditionally convergent series can be manipulated to sum to any number at all.

[Anonymous No.9476148]

>>9476131
>No, they're equal at infinite many points so you can rerun the same convergence argument.
[math] \sum (-1)^n [/math] doesn't converge.
Grouping by pairs:
[math] \sum ((-1)^n + (-1)^{n+1}) [/math] converges to 0.

[Anonymous No.9476166]

>>9476148
>>9476145
>>9476131
>>9476122

Okay, I am sorry guys. I had a severe brain fart. It is true that grouping terms can change convergence and I knew this but I started freaking out because I thought this would fuck up an argument I used.

But nevermind, my brain has calmed down and I have proven that the specific grouping I used is perfectly Kosher. Sorry guys.

[Anonymous No.9476423]

How do I calculate the net electric field at point p in unit vector notation?
I solved each vector for it’s magnitude and have the unit vector notation for each of them.
Do I just add them up?
For example, q1 q2 and q3 is(1.2 x 10^3)i , (1.4x10^2)j , (7.2x10^2)i respectively.
Add i together and leave j alone?

[Anonymous No.9476477]

Can someone please help with this?

[Anonymous No.9476480]

>>9476423
>Do I just add them up?
yes
>Add i together and leave j alone?
bingo

[Anonymous No.9476490]

>>9476039
>uncountable infinity is just the domain of r
Wrong.

[Anonymous No.9476509]

>>9476477
wtf are bloch equations

[Anonymous No.9476521]

Does anyone have any good study guides for doing well on the GRE math subject test?

[Anonymous No.9476574]

How the fuck do people isomorphism fast? It took me like a whole fucking hour to do this one, but I definitely need to be able to do these in a few minutes max.

[Anonymous No.9476575]

>Prove that the product of two orthogonal matrices is orthogonal.

Is this correct? I'm not sure if I can assume that A inverse * B inverse = (AB) inverse.

[Anonymous No.9476579]

>>9476575
>Is this correct?
Have you tried to prove it?

[Anonymous No.9476586]

AHHHH I'M A FUCKING BRAINLET

SOMEONE FUCKING HELP ME PLEASEEE

I think i have to use P=IV, V=IR, and inductance for henry but I'm a fucking brainlet so idk

[Anonymous No.9476590]

>>9476579
>Have you tried to prove it?
Yes, that's what's written in the picture. I'm just not sure if my proof is valid.

[Anonymous No.9476594]

>>9476590
>Yes, that's what's written in the picture. I'm just not sure if my proof is valid.
I meant prove that "A inverse * B inverse = (AB) inverse."

[Anonymous No.9476597]

>>9476594
It doesn't seem like it would be true (at least for most matrices), but since A^T * B^T = (AB)^T for symmetrical matrices, I feel like the same could maybe be true for inverses of original matrices.

[Anonymous No.9476598]

>>9476575
(AB)^T = B^T A^T
(AB)^-1 = B^-1 A^-1

[Anonymous No.9476601]

>>9476586
P=IV, V=IR
P=I^2R
400^2 amps * 1 Ohm = 160,000Watts

[Anonymous No.9476621]

>>9476601
how long have you been waiting to use that photo anon?

[Anonymous No.9476622]

>>9476601
do the rest of the problem you fucking faggot brainlet

[Anonymous No.9476634]

>>9476586
>>9476601
b) be all damn hot damn fast yo nigga
dat 1 Ohm better be like all over that wire a long way or it be all meltin and shieet
c) 3T^2 * 1m^3 / 2/1.26*10^6 H/m = 3.57 Mega Joules!
d) 3.57MJ / 2.5kJ/L = 1.43kL of liquid He -> 1.43kL liquid *700 gas/liquid = 1,000,000 liters of gas!
dat shieet is gonna go boom nigga, run!

>and inductance for henry but I'm a fucking brainlet so idk
>https://en.wikipedia.org/wiki/Henry_(unit)
H=J/A^2
>https://en.wikipedia.org/wiki/Tesla_(unit)
T=J/m^2/A
T^2 m^3 /(H/m) = (J/m^2/A)^2 m^3 /(J/A^2) * m = J

[> No.9476671]

>>9476621
How new are you?

[Anonymous No.9476737]

>>9476477
Someone pls

[Anonymous No.9476754]

>>9475021
where can I compute initial value difference equations online?

The examples I want to compute have subscripted elements, like such:

[math]x_n = x_{n-1} + 2n + 1 [/math]

[math] x_0 = 7 [/math]

I've tried to use wolfram alpha:

https://www.wolframalpha.com/input/?i=x(0)%3D1,+x(n)%3D(5x(n-1))-4n+%2B+1


but when I input my problem, I don't know how to input the subscriped elements. I've tried inputing them as functions like:

x(0)=1, x(n)=(5x(n-1))-4n + 1

but im afraid its not recognizing the subscriped elements correctly,

[Anonymous No.9476772]

>>9476754
But anon the solution is on the page you linked

[Anonymous No.9476782]

>>9476772
i was just a little confused when it displays my input in the link i posted, it displays my difference equation as:


x(0) = 7
x(n) = 1 x(n - 1) + 2 n + 1

is my notation >>9476754

with subscripted (n-1) the same as treating it as a function of x?

[Anonymous No.9476788]

>>9476782
I'm not sure what exactly your question is

[Anonymous No.9476801]

>>9476782
It's treating it as a function of n, which is why the solution x(n) is in terms of n and not x.

[Anonymous No.9476803]

>>9476754
[eqn]x_n = x_0 + \sum_{i=1}^{n} 2i + 1[/eqn]
[math] x_n = x_0 + n(n+1) + n = x_0 + n^2 + 2n [/math]

protip: if [math]x_n = a x_{n-1} + f(n)[/math]
[eqn]x_n = a^n x_0 + \sum_{i=1}^{n} a^{n-i}f(n)[/eqn]

[Anonymous No.9476809]

>>9476754
[eqn]x_n = x_0 + \sum_{i=1}^{n} 2i + 1[/eqn]
[math] x_n = x_0 + n(n+1) + n = x_0 + n^2 + 2n [/math]

protip: if [math]x_n = a x_{n-1} + f(n)[/math]
[eqn]x_n = a^n x_0 + \sum_{i=1}^{n} a^{n-i}f(i)[/eqn]

[Anonymous No.9476814]

>>9476782
>with subscripted (n-1) the same as treating it as a function of x?

It's a function of n and yes, "sequence x_n" is a fancy pants way of saying the function x:N->R.

[Anonymous No.9477008]

I am stuck. How do I prove this?:

If
[math] a \in \mathbb{N} [/math] and [math] \lambda \in \mathbb{C}: \lvert \lambda \rvert <1 [/math] ,
then
[math] \lim\limits_{n \to \infty} n^a λ^n = 0 [/math]

[Anonymous No.9477045]

>>9477008
exponentials grow faster than polynomials

for some n big enough
[math] |\lambda| ^{-n/a} > n \\ e^{-n \ln(|\lambda|)/a} > n \\ 1 > ne^{n \ln(|\lambda|)/a} \\ -\ln(|\lambda|)/a > -n\ln(|\lambda|)e^{n \ln(|\lambda|)/a}/a \\
n > a W(-ln(|\lambda|)/a) / -ln(|\lambda|)
[/math]

[Anonymous No.9477049]

>>9477008
https://math.stackexchange.com/questions/55468/how-to-prove-that-exponential-grows-faster-than-polynomial

[Anonymous No.9477111]

>>9477049
Thank you!

[Anonymous No.9477126]

>>9475021
How is anything that isn't in anyone's mind real?

[Anonymous No.9477133]

Ahoy /sci/ anons. Could anyone please explain to me why do we use Newton Cotes formulas?

I think I understand that why we use quadratic interpolation. We can solve integrals easier using approximation => integral of the Lagrange polynomial can be calculated fast. We just need an n number of fix points. This should deal with straight and curved functions.

So Newton Cotes formulas use fixpoints which are all in equal distances from each other. Why?

[Anonymous No.9477135]

>>9477133
>So Newton Cotes formulas use fixpoints which are all in equal distances from each other. Why?

Because symmetry makes things better. That's way mid point rectangle rule can do linear functions perfectly and Simpson's rule (2nd degrre) can do cubics perfectly or Boole's rule (4th degree) can do quintics perfectly.

[Anonymous No.9477275]

>>9475285
>>9475878
>>9475969
thats nice, but the problem asks me to find x, not a. but it is a step forward
(i am aware of the possibility of x being any degree possible)

[Anonymous No.9477281]

>>9475978
>>9475919
can't you just say that the slope of the function at a certain point is the "number counterpart" of the derivative

[Anonymous No.9477287]

>>9477275
are you a brainlet?
x = arccos(a/√2) + π/4

[Anonymous No.9477328]

How would an dfa that accepts the L = {0^k | k <= 0 where k is a multtiple of 5} look ?

[Anonymous No.9477357]

Can someone explain to me the difference between a scalar and a vector field? Both mathematically and physically.

[Anonymous No.9477358]

So, pic related. I have to find the eigenvalues and eigenfunctions of the differential equations with the given boundary conditions. I got to the point where I have the null points of the equations, which are -5 +- sqrt(25-λ). Now I think I have to look at three cases, namely:
1)sqrt(25-λ)>0
2)sqrt(25-λ)=0
3)sqrt(25-λ)<0

I examined the second case and I got y=c*e^(-5x), where c is a constant and is free to choose, however I'm not sure how to proceed in cases 1) and 2).

P.S. Sorry for not using LATEX, I don't know how.

[Anonymous No.9477515]

>>9477281
I guess, but not in the same sense as the integral.

[Anonymous No.9477522]

>>9477328
I'm guessing you meant >=

Just have five states that represent the number mod 5 - you increment when you hit a 0, and fail on any other character.

[Anonymous No.9477526]

>>9477357
Mathematically a scalar field assigns a number to each point in space, a vector field assigns a vector.
An example would be e.g. mass distribution for a scalar field and gravitational force for a vector field.

[Anonymous No.9477570]

>>9475021
Why are some units wrote with a subtraction? Such as m^3 being m^-3.
I've done maths up to calc 2 and still don't know this.

[Anonymous No.9477571]

>>9477570
>Such as m^3 being m^-3.
As in cubic meters, not an algebraic unknown.

[Anonymous No.9477574]

>>9477570
1 m^-3 is the same as 1/m^3 and means "1 per meter cubed"

It could mean, say, you have 1 atom of uranium in every cubic meter of space.

[Anonymous No.9477585]

>>9477574
Okay so, 2.5 x 10^25 molecules m^-3 is equivalent to saying 2.5 x 10^25 per m^3.

[Anonymous No.9477587]

>>9477585
yes

[Anonymous No.9477596]

>>9476477
REEEEE SOMEONE PLS

[Anonymous No.9477598]

>>9477596
>REEEEE SOMEONE PLS
What have you tried?

[Anonymous No.9477699]

I'm a CS student, I've done some linear algebra, vector calculus, discrete math and probability at uni. I'm interested in more math disciplines, outside of CS focused of course, where should I look in terms of material/textbooks?

[Anonymous No.9477807]

What is the common ratio for 1/n^2?
I can't understand how you can get a common ratio from when the n is squared.

1+1/2^2+1/3^2 etc
because it changes at all times.

[Anonymous No.9477834]

>>9475021
>Oxford Capacity Analysis
I'm a Scientologist since 1994. Ask me.

[Anonymous No.9477848]

How to get good at integral applications? Specifically pic related

[Anonymous No.9477865]

can momentum move an object?

like if im standing still and you run into me at constant speed without directional change, i will move.

so, something other than forces can move an object since momentum is not a force?

[Anonymous No.9477889]

>>9477865
when I run into you it is actually my atoms which will electrodynamically react with with your atoms to push you away, the smaller the distance the greater the force, only forces can cause acceleration

[Anonymous No.9477939]

what is the definition of a linear ODE? the one in my notes says an ODE is linear if each term is linear, though I don't understand what is meant by "term".
Suppose T is a linear transformation so [math]T(y_1'+y_2')=T(y_1')+T(y_2')[/math] and [math]T(\alpha y')=\alpha T(y')[/math], with alpha constant. Then would [math]T(y')=x[/math] for example be linear?

Also, is [math](y')^2=x[/math] linear? Since [math](y'(x_1+x_2))^2\neq(y(x_1))^2+(y(x_2))^2[/math]?? and the squared term present intuitively it seems non-linear, but [math]y'=\pm\sqrt{x}[/math], which is linear

[Anonymous No.9477969]

>>9477939
linear combination of the derivatives of the function(s).

[Anonymous No.9477989]

>>9477807
There isn't one. The term "common ratio" is only applicable to a geometric series.

[Anonymous No.9477995]

>>9477865
A collision will result in a force. Actually, it will result in equal and opposite forces. The momentum of the colliding object will determine the magnitude and duration of the force, after which the objects will be moving apart and no longer exerting forces on each other.

[Anonymous No.9478015]

>>9477969
with the field of scalars being the set of functions of the variable x?
what about(y')^2=x?

[Anonymous No.9478027]

>>9477358
> Now I think I have to look at three cases, namely:
> 1)sqrt(25-λ)>0
> 2)sqrt(25-λ)=0
> 3)sqrt(25-λ)<0
No. The 3 cases are
25-λ>0 => sqrt(25-λ) is real
25-λ=0 => sqrt(25-λ) = 0
25-λ<0 => sqrt(25-λ) is imaginary

The thing is, x^2=k has two solutions: x=sqrt(k) and x=-sqrt(k).

By linearity, if f(x) and g(x) are solutions to a homogeneous ODE, then so is c1*f(x)+c2*g(x).

For a linear second-order ODE, you end up with c1*e^ax+c2*e^bx where a,b are the roots of a quadratic. If the discriminant is positive, a and b are real, and you have the sum (or more often the difference) of exponentials with different time constants, which is basically a hump followed by exponential decay. If the discriminant is negative, a and b are a complex conjugate pair which leads to a sinusoid by Euler's formula e^ix=cos(x)+i*sin(x).

[Anonymous No.9478035]

wannabe biohacker here, I've been tracking brain metrics and I seem to be performing better on less sleep (at 5 hours I performed almost twice as good as I did with 10 hours sleep) and to top it off I've been awake for 12 hours on the ten hour day I tested 5 hours after waking up so I was more energized - can anyone explain this or tell me what it is?

[Anonymous No.9478045]

>>9478035
>biohacker
cringe

[Anonymous No.9478073]

>>9478045
>>biohacker
>cringe
cringe

[Anonymous No.9478097]

>>9478045
sorry new to the terminology, what would you prefer I said?

[Anonymous No.9478101]

>>9478035
The fuck is a biohacker
Also oversleeping is a thing, if you only need 5 hours then good for you but I will but you if I get any less than 8

[Anonymous No.9478106]

>>9478101
*cut you

[Anonymous No.9478366]

I keep seeing space missions extending their lifetime. Why is that a thing?

[Anonymous No.9478500]

>>9477598
I think I found the correct equations and I think you need to differentiate but I don't know how to differential equations??

Can some please help me? Or at least help me differentiate this?

Mega brainlet sorry

[Anonymous No.9478516]

>>9477848
it's basically just plugging into formulas anon

[Anonymous No.9478531]

>>9478366
>Why is that a thing?

Because NASA no longer has the funds to start new missions. Continuing old ones is cheaper and easier.

[Anonymous No.9478615]

>>9475021
I need help please. If i'm trying to find the exact value of Cos(-7pi/3), how would I go about that? The textbook just says Cos(-7p/3) = Cos(pi/3), but i have no fucking clue how they made that connection and it doesn't explain that step at all. What am I missing?

[Anonymous No.9478624]

>>9478500
REEEEE SOMEONE PLS

[Anonymous No.9478649]

>>9477699
http://4chan-science.wikia.com/wiki/Mathematics

Read through Smith's or Ash's proof book first and get a good foundation.

[Anonymous No.9478652]

>>9477357
f: R^3 -> R scalar field (has a value at each point like voltage)
g: R^3 -> R^3 vector field (has a vector at each point like flow velocity, electric field, gravity)

[Anonymous No.9478660]

>>9478500
>>9476477

[Anonymous No.9478663]

>>9478660

[Anonymous No.9478666]

>>9477570
It means per m^3. Milk is 1000$ per 1 m^3 of volume aka Milk is 1000 $/m^3 = 1000 $*m^-3 .

My car goes 100 miles per the gallon aka 100 mpg = 100 mile/gallon = 100 mile*gallon^-1

[Anonymous No.9478684]

>>9477807
https://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers

[Anonymous No.9478690]

>>9478015
What happens to alpha retard?

[Anonymous No.9478760]

On a graph of time and altitude is there a specific point where an airplane can be said to be off the ground?

Having an argument here and I need to win. If the front wheels are up the back wheels are still on the tarmac, and then it bounces during take off. So it would be a changing area across the plane depending on it's ascension?

So it's essentially on the ground until it starts to take off, where only part of the plane is on and part is off the ground, until it gains the speed to get off the ground right?

[Anonymous No.9478767]

What I have so far:
The moment about point O:
(1) [math]M_O = I_P \alpha = \frac{1}{3}mL^2 [/math]
(2) [math]M_O = hF[/math]
(3) [math]F = ma [/math]
I wanted to equate (1) and (2), then use [math] \alpha = a/r [/math] and substitute that into the equation to cancel the accelerations. The only issue is I don't know if i should take r=h or r=C.

tl;dr Is the angular acceleration of a rod its linear acceleration divided by the distance to its center of mass, or the distance to the applied force, or something else?

[Anonymous No.9478772]

>>9478760
>is there a specific point where airplane is said to be off the ground?
I assume the point in time when none of the airplane is touching the ground...

[Anonymous No.9478778]

>>9478772
I guess it would be better to ask if there's a 'last moment' when it's on the ground or not rather than when it's can be said to be off the ground.

[Anonymous No.9478786]

>>9478778
I don't understand. I imagine the plane is said to be on the ground when some part of it is touching the ground, and off the ground when it is not touching the ground at all. But who the fuck cares?

[Anonymous No.9478804]

>>9478786
Yes. But is there an actual, definitive first point when it's in the air or a last point that's on the ground? Or is it both? Is it neither?

That's what our topic is about and I'm thinking it's a changing point across the plane as it takes off where it can be said to be both until it is definitely off the ground. Would it be, for instance the open interval (Tg, Ta) (Time Ground, Time Altitude) where it's on the ground until it starts to take off, that point being Tg, and the area between Tg and Ta would be as it's starting to ascend until it's actually in the air, Ta?

[Anonymous No.9478836]

>>9478767
(1) is the second moment of inertia around the center of mass, right? I think you have to use the Parallel Axis Theorem for "h"

Are you really sure that the bar will move? If not there's no reaction around the X-axis

[Anonymous No.9478885]

Can anyone tell me if race is just "skin deep," or if there are actual genes to make up an African, German, Japanese, etc.?

[Anonymous No.9478897]

>>9478885
race is genetic yes, even if the only physical differences were skin color (they are not) this would be genetic. These physical differences are well understood and not controversial, unlike the discussion about potential differences in mental capacity.

[Anonymous No.9478966]

>>9478897

That is what I thought, but when I try to do Google searches on this, I only ever find the contrary. I figured that since there were skeletal differences, that it was just more than "skin deep." With that being said, do you know if there's been any discussion on which genes specifically make one "German" or "Japanese," etc.?

I've been seeing a lot of research into CRISPR advancements and would like to know if one could actually edit their hereditary germ-line to have a child of another race.

Example:

> If I'm Anglo and I want to have a Japanese child, I could use CRISPR to modify my heredity germ-line and "copy & past" German genes where the Japanese genes would be, per say.

Almost like a "replacement gene modification" or spermatogonium germ-line modification.

[Anonymous No.9479011]

>>9478966
I'm certainly not an expert on the subject but just from my own knowledge and some brief reading ( https://en.wikipedia.org/wiki/Race_and_genetics ) it seems like there is no 'race gene' than controls race. Rather there will be genes that control for skin color, genes that control for skeletal structure etc, and the various alleles that these sets of genes can manifest as have clustered together over time to form the groups we classify as races. This makes sense as it is exactly how speciation happens, but on a smaller scale.

Scientists apparently have identified sets of genes which they use to accurately differentiate between the races. From the wikipedia article:

A 2005 study by Tang and colleagues used 326 genetic markers to determine genetic clusters. The 3,636 subjects, from the United States and Taiwan, self-identified as belonging to white, African American, East Asian or Hispanic ethnic groups. The study found "nearly perfect correspondence between genetic cluster and SIRE for major ethnic groups living in the United States, with a discrepancy rate of only 0.14 percent".[17]
Paschou et al. (2010) found "essentially perfect" agreement between 51 self-identified populations of origin and the population's genetic structure, using 650,000 genetic markers. Selecting for informative genetic markers allowed a reduction to less than 650, while retaining near-total accuracy.[47]

Of course just because you can effectively identify race using only a few hundred markers, that is almost certainly not enough to encode the genetics for a specific race using CRISPR or whatever, you would probably need a much more complete list, perhaps the 650,000 would do it. It's definitely possible, but I think more research is necessary to do it with any sort of confidence.

[Anonymous No.9479052]

>>9479011
>It's definitely possible, but I think more research is necessary to do it with any sort of confidence.

This is exactly what I was looking for. I'm a 2nd year Biology major and I'm trying to get a focus towards CRISPR hereditary germ-line modification if I can. We can already make certain phenotypical changes, but actual genetic racial changes now, that would be nothing short of amazing.

CRISPR is such a new thing and there's been a lot of innovation and research into it and the new "gene drive" method.

If we could advance this science far enough, we could even hypothetically use it to attempt to bring back endangered/extinct species if we were able to map out their genetic composition enough.

> Modify a handful of elephants to give birth to mammoths using DNA from the frozen mammoth that was found a few years ago.

[Anonymous No.9479058]

>>9479052
sounds like really cool stuff, did they actually recover a complete mammoth genome or just bits and pieces? I know that DNA degrades over time but mammoths were pretty recent

[Anonymous No.9479093]

>>9479058
Literally the entire thing. It still even had the fur on it. It was preserved in the ice within Serbia I believe, so a lot of it's DNA composition might still be in tact.

There's a huge potential for this kind of scientific advancement. With that being said, I'd by lying if I said I didn't want to advance it to the point of enabling people to have children of different races though. For me, that would be the primary reason for getting into this sort of research. Even though that's how I feel, being able to use it to help bring back an extinct species would be entirely worth it too.

Check out the article below.

>http://www.dailymail.co.uk/sciencetech/article-2358695/Woolly-mammoth-frozen-Siberia-39-000-YEARS-goes-display-Tokyo-woolly.html

[Anonymous No.9479124]

>>9479093
damn this is an awesome time to be alive

[Anonymous No.9479130]

>>9478767
F=m∆v
τ=I∆ω= I∆v/(L/2)=Fr
∆v = 0 at O so F/m +(L/2)rF/I = 0
mLr/2 = I
l=1/12 m L^2 [https://en.wikipedia.org/wiki/List_of_moments_of_inertia]

1/6L = r
r = h - L/2

h = 2L/3

[Anonymous No.9479148]

>>9479124
>damn this is an awesome time to be alive

I agree, it truly is the best time to be alive because most of the streamlined advancements are being made right now.

> Cloning
> CRISPR
> Science
> Physics
> Tech
>etc.

> https://www.forbes.com/sites/startswithabang/2017/07/12/first-particle-successfully-quantum-teleported-into-space-are-transporters-next/

Check this out, soon we'll be saying, "Beam me up Scottie!"

[Anonymous No.9479191]

an axially symmetric space station is floating in space with rockets applying a constant torque T around the principle axis (e_3). Solve eulers equations to find the equations of motion, at t=0 take w=(w_10, 0, w_30)

how the fuck do i uncouple them the other 2 equations? Obviously i can get the motion around the principle axis easily but its too late for me to figure out how to decouple the other 2. Please respond im so tired.

[Anonymous No.9479225]

Anyone know the proof to why primes of the form 6n+1 are not prime in [math]\mathbb{Z}[\frac{-1+\sqrt{-3}}{2}] [/math] (Eisenstein integers)
I think you can prove it if you prove that
[math]\exists m\in\mathbb{Z}_p^\times \rightarrow m^3\equiv -1 \mod p[/math].

[Anonymous No.9479255]

something recently has inspired me to attempt grad school but I am a junior with no research at all (EE). I guess I will try applications in the fall, but should I try my best to get into undergrad research at my uni even though we are 2/5 of the way through the semester? I was thinking of asking but not sure if it is strange to do so this far in.

Also is experience even necessary for MS applications?

[Anonymous No.9479424]

How do I break down Special Relativity to an entry-level college speaking class without saying 'it's a lot of math bro' too many times? I'm mostly concerned with intuitively simplifying time dilation and length contraction

I wanted to use the light clock thought experiment as an example, but if light shoots out in every direction from a source couldn't the light 'stretching' along the source of motion just be explained as an angular photon intercepting the mirror along the motion, thus the original beam never really stretches and time doesn't really slow for the moving observer? I mean, why does the hypothetical light beam inherit the mirrors' velocity along the direction of motion anyways? Seems kind of half-baked to me

[Anonymous No.9479458]

>>9479424
https://www.youtube.com/watch?v=IL4vWJbwmqM

[Anonymous No.9479633]

What's an example of a series [math](a_{n})[/math] such that [math]0\leq a_{n} \leq \frac{1}{n} [/math] but [math]\displaystyle \sum (-1)^{n+1} a_{n}[/math] diverges.

[Anonymous No.9479639]

>>9478615
> I need help please. If i'm trying to find the exact value of Cos(-7pi/3), how would I go about that? The textbook just says Cos(-7p/3) = Cos(pi/3), but i have no fucking clue how they made that connection and it doesn't explain that step at all. What am I missing?
By their nature, trigonometric functions are periodic with period 2pi (well, tan/cot have period pi). -7pi/3 = -pi/3-2pi so cos(-7pi/3)=cos(-pi/3). Also, cos is symmetric: cos(-x)=cos(x), so cos(-pi/3)=cos(pi/3).

You can find a list of trigonometric identities on e.g. wikipedia, but these ones are obvious if you know what sin/cos actually mean and you can draw a triangle.

[Anonymous No.9479640]

>>9479633
The fucking obvious one: an=-1^n/n

[Anonymous No.9479641]

>>9479633
>What's an example of a series (an) such that 0≤an≤1n but ∑(−1)n+1an diverges.
(a_n) is a sequence, not a series, and why do you think there exists such a sequence?

[Anonymous No.9479645]

>>9479640
>The fucking obvious one: an=-1^n/n
Do you need to swear? Also that's wrong, please don't post again if you don't even recognize such an elementary Taylor series expansion.

[Anonymous No.9479696]

>>9479633
No such sequence exist.
https://en.wikipedia.org/wiki/Alternating_series_test

[Anonymous No.9479699]

>>9479696
Oh wait I am wrong, you could find a non decreasing one.

[Anonymous No.9479707]

>>9479633

[n mod 2] / n

[Anonymous No.9479769]

Can someone explain me spherical coordinates in terms of differential geometry? In the sense of thinking like polar coordinates are another atlas of R^3 without the origin or something like that.

[Anonymous No.9479899]

I have a list of 337 items. I have three sets within that list, one of 289 items, one of 22 items, one of 23 items, and three of 1 item.

What the fuck do I have to multiply by in order to make it so I have an equal chance of generating one item from any of these sets? I'm a Literature major and I can't figure this out.

And it can't be a decimal in the end, it has to be whole numbers. Someone help.

[Anonymous No.9479953]

>>9479225
That condition is correct if you require m to be something other than -1 mod p (you can multiply m by -1 and require m^3 = 1 instead). To derive it, you could look at the characterization of Gaussian primes given in Artin's book and apply the same methods here (note that the Eisenstein integers form a PID). If p = 3n + 1, then the multiplicative group mod p (which is abelian) has order 3n, which is divisible by 3 so it has an element of order 3. That concludes the proof.

[Anonymous No.9479957]

>>9479699
No, it's impossible since the limit of a_n <= 1/n is zero, so it either has to be decreasing or constantly zero at some point

[Anonymous No.9479971]

>>9479769
in modern terminology, polar coordinates are a parametrization of a certain region of R^3. their inverse is a coordinate patch for R^3

[Anonymous No.9479972]

>>9479971
spherical coordinates, sorry

[Anonymous No.9480010]

Hi, I am a third-year math major and I just discovered a really interesting class of functions that I think I can write my thesis about.

What I found is that to continue my study I will need to highly increase my knowledge of how to compute infinite series of rational functions. The typical techniques are not cutting it. When I asked Wolfram alpha to compute a certain series it did so by using the digamma function but if I plan to do research on this I am going to need much more than just plugging and chugging.

Is there any textbook that focuses just on advanced techniques to compute infinite series of rational functions? As an example of "advanced technique" one I know is that many infinite series like these can be written as a linear combination of Hurwitz Zeta functions and then I can look up the values of the Hurwitz Zeta functions I use.

So I mean stuff like that. I am not shy about complex analysis. I just want to really focus on this and just this to see how far I can go and start researching as soon as possible.

[Anonymous No.9480019]

>>9479633
if you define even and odd cases, then you just need to ensure the difference of the series diverges, which isnt too hard.
[math]a_n =\begin{cases}\frac{1}{n^2},&2|n\\ \frac{1}{n},& \text{otherwise}\end{cases}[/math]
[math]\displaystyle \sum (-1)^{n+1} a_n =\sum \frac{1}{n} - \sum\frac{1}{n^2} [/math]

[Anonymous No.9480047]

I'm have a problem with a rearrangement of an equation. Given is the equation:
[eqn]\begin{split}
U&=\frac{Nk_BT^2}{q}\cdot\left(\frac{\partial{}q}{\partial{}T}\right)_{V,N} \\
&=Nk_BT^2\cdot\left(\frac{\partial\ln{}q}{\partial{}T}\right)_{V,N} \\
&=-Nk_B\left[\frac{\partial\ln{}q}{\partial{}(1/T)}\right]_{V,N}
\end{split}
[/eqn]
My problem is that I have no idea which rules were used to rearrange this partial differentiation. Can anyone help me out? I'm sure it's something simple but I can't get my head around it.

[Anonymous No.9480053]

>>9478690
what alpha? the constant?
if you had (y')^2=0, then [math](y'(\alpha x))^2\neq \alpha (y'(x))^2[/math] so it's not
but i was asking about my previous post, where if you take the square root of both sides, [math]y'=0[/math], the ode would apparently become linear

[Anonymous No.9480103]

Is the correct parameteriazation of y=x^4-x^2 , r(t) = < t, t^4-t^2> ?

[Anonymous No.9480163]

>>9480047
The step from first to second line is the derivative rule for logarithms, just the other way around than you would usually use it:
[math]\frac {d \ln a}{ dx} = \frac 1 a \cdot \frac {d a}{ dx}[/math]

Second to third line I have no idea

[Anonymous No.9480182]

>>9480010
>Is there any textbook that focuses just on advanced techniques to compute infinite series of rational functions?
Can you give an example of the kind of series you mean? Depending on the rational functions you might have relatively easier ways to compute the sum

[Anonymous No.9480213]

what should I learn first: matlab or c++?

[Anonymous No.9480215]

>>9480163
third line is the same for the power rule

[Anonymous No.9480216]

>>9480213
matlab, then list/scheme/racket, then c

C++ is for video games

[Anonymous No.9480234]

>>9480019
You are right that the difference diverges, but your equation does not hold, it should be

[eqn] \sum\limits_{n=1}^{\infty} (-1)^{n+1} a_n =\sum\limits_{n=1}^{\infty} \frac{1}{2n + 1} - \sum\limits_{n=1}^{\infty}\frac{1}{(2n)^2}[/eqn]

[Anonymous No.9480254]

>>9479458
Is, uh, is this the video you meant to embed

[Anonymous No.9480501]

Can you multiply numbers of different bases and if so what would the answer be?

5base10 * 6base2 for example

[Anonymous No.9480514]

>>9480216
>>>/g/tfo

[Anonymous No.9480523]

>>9480213
Usually Matlab -> C++ but Matlab does a lot under the hood stuff that you won't realize making it hard to get a full grip on. So start with C++.

[Anonymous No.9480525]

>>9480501
5*(2^2+2)=30

[Anonymous No.9480530]

I need to learn enough about laser physics to sound smart on a phone interview Monday. I know the absolute basics of how to make a laser (pumping and stimulated emission and all that) but I want to grab a book to get a bit deeper. Suggestions?

[Anonymous No.9480582]

>>9480501
Not really, no. You can convert them to a common base and then multiply as usual, the multiplication algorithm works in all bases just fine.

[Anonymous No.9480638]

>>9480182
Well, there is no specific type. Just a seires of the form [math] \sum_{k=1}^{\infty} \frac{P(k)}{Q(k)} [/math] where P and Q are polynomials.

It can be pretty general so I want to know all the methods out there.

[Anonymous No.9480641]

How common is it for researchers to use stuff like Matlab illegally (without license)? And has it happened that a researcher published a paper in which he mentioned his use of matlab and then got caught by the company for not having a license?

[Anonymous No.9480688]

>>9480638
Are you sure you don't want [eqn] \lim\limits_{n \to \infty}\frac{\sum_{k=1}^{n} P(k)}{ \sum_{k=1}^{n} Q(k)}[/eqn]?

[Anonymous No.9480696]

>>9480688
Yeah, I'm sure. I mean series like the Basel problem.

[Anonymous No.9480750]

I have a theorem in my lecture notes that says:
Suppose f is holomorphic on an connected open set [math]\Omega\subseteq\mathbb{C}[/math]. If [math]\Re(f)[/math] or [math]\Im(f)[/math] is constant, then f is constant.

However, if [math]f(x+yi)=x[/math], then [math]\Im(f)=0[/math]. But f is not constant...
What am i misunderstanding? i think it's to do with the definition of holomorphic, although i don't get what

>>9480234
forgot about the 2|n thing

[Anonymous No.9480757]

>>9480750
>What am i misunderstanding? i think it's to do with the definition of holomorphic, although i don't get what
Well can you prove that your f is holomorphic?

[Anonymous No.9480782]

>>9480757
fuck. i assumed it would be as i was doing real differentiation in my head. but it's differentiable nowhere, right?

[Anonymous No.9480785]

What do you guys do when you get stuck at a very hard problem? Do you try to think every possibility you can imagine to solve the question?

I'm struggling with Fluid Mechanics course. Some of the applications are really hard to understand.

[Anonymous No.9480840]

>>9480785
>What do you guys do when you get stuck at a very hard problem?
Go for a walk. It really clears the mind.

[Anonymous No.9481199]

>>9480641
Their university buys them a copy.

Students pirate Matlab.

[Anonymous No.9481395]

I want to show that if $V$ is a finite dimensional normed linear space then the closed unit ball $B$ of $V$ is compact.

Pick a basis $b_i$ of $V$, with $||b_i|| =1$. Then the map $T:\mathbb{R}^n \rightarrow T$, $e_i \mapsto b_i$ is an isomorphism. Qn: How do i show that this map is continuous? I know it is enough to show $T$ is bounded.

Take $v\in V$, and write $v=\sum a_ib_i$. Then $||T(v)|| \le \sum |a_i|$ by triangle inequality. How do i bound this value? Or should i consider something else?

[Anonymous No.9481487]

>>9481395
Not all normed vector spaces are Euclidean spaces.

[Anonymous No.9481589]

What's it called when one guy is bullying another guy, and you stay silent the whole time until the guy getting bullied speaks up for himself you come in and say "hey guys stop" instead of stopping the bully from bullying in the first place?

[Anonymous No.9481764]

Going to have to take a subject about radiation physics, but I've never taken a physics subject. Can anyone recommend a resource to teach myself basic wave physics as preparation? Preferably not a textbook.

>>9481589
Bystander effect?

[Anonymous No.9481876]

anons, what are the pre-requisities to learn Linear Algebra? also, what's a good introductory book about this subject?

[Anonymous No.9481878]

Good morning /sci/
I have a maths/econ question. Can i use the properties of ln if i have ln(a+b) ?
My goal is to simplify the last line written in blue

[Anonymous No.9481879]

>>9481487
I see, what would be a good way to prove then?

[Anonymous No.9481888]

>>9481878
>i

Your goal should be to learn how to use the shift key. Till then, no answer for you.

[Anonymous No.9481889]

>>9481876
Not much.
You'll need to know:
Basic set theory (sets, functions, equivalence relations, etc).
Complex numbers.
Basic high-school-tier stuff about Polynomials.
How to prove mathematical statements / basic logic: https://en.wikipedia.org/wiki/Mathematical_proof#Methods

A truly introductory book will probably cover these stuff on its own. It's really nothing. You can learn all that in like 1 day.

I personally really like Sheldon Axler's book "Linear Algebra Done Right".
The only thing that's "wrong" about it is the fact that it doesn't cover determinants until the very end and briefly so.
Imo his approach on determinants is the correct one.
You can easily pirate that book, but that would be illegal ;)

[Anonymous No.9481893]

>>9481889
thanks for replying, anon, good post

what you say about Shilov's Linear Algebra? is that a good book to learn, I mean can I use it as say a complement to Axler's book?

[Anonymous No.9481896]

>>9481876
For Matrix Algebra aka Intro Linear Algebra aka Elementary Linear Algebra: Algebra 2 or Precalculus. There's going to be one example of solving a system of differential equations by diagonalization but it's not important and you'll see the same example again in Ordinary Differential Equations.
http://4chan-science.wikia.com/wiki/Mathematics#Matrix_Algebra

For Theoretical Linear Algebra aka Finite Dimensional Vector Spaces aka Linear Algebra 2: Proofs, Matrix Algebra, and a maybe tiny bit of calculus in a few of the examples.
http://4chan-science.wikia.com/wiki/Mathematics#Finite_Vector_Spaces

[Anonymous No.9481908]

For my dissertation I'm investigating the effect of a TEG between a CPU heatspreader and a Heatsink.

I specifically want to model this, currently have matlab using finite difference between the different thermal conductivity.

What would be the best simulation software, such as ANSYS? E.g. fluent, CFX, steady state thermal etc?

I'll keep the cpu has a boundary condition (between 40 and 90'C) and create the fins with a constant thermal loss approximating fans

[Anonymous No.9481912]

>>9481893
Haven't read it, but I just checked it a bit.
Its first chapters are of this order:
1) Determinants
2) Vector Spaces
3) Systems of Linear Equations
4) Linear Maps

This ordering is just bad, in my opinion. And this makes me think that the book isn't good. It's also a pretty old book and the formatting looks shitty.
I wouldn't recommend reading it before Axler. You can definitely use it as a complement though.

[Anonymous No.9481919]

>>9481912
Read it a bit more.
The book seems to be trash. Better avoid it.

[Anonymous No.9481924]

>>9481896
>>9481912
great! thanks, anons

[Anonymous No.9481926]

>>9481908
>TEG

You mean TIM or a ThermoElectric Generator?

[Anonymous No.9481927]

>>9481912
>Axler

Top meme.

[Anonymous No.9481936]

>>9481919
>t. brainlet cs major who couldn't understand it

[Anonymous No.9481938]

>>9481926
Thermoelectric generator, generate charge from delta T (seebeck effect)

Similar but opposite of a thermoelectric cooler (peltier effect)


TL;DR is so far it's silly because of the reduction in cooling (components use more energy as they increase in temperature)

Studying this is basically my thesis though

[Anonymous No.9481941]

>>9481938
Undergrad thesis or high school science project?

[Anonymous No.9481955]

>>9481941
former

don't be rude ;-;

[Anonymous No.9481956]

>>9481927
But good meme.

>>9481936
>implying
I'm almost done with my mathematics' degree.
The book literally starts by essentially saying:
>Hey, faggots, let's talk about determinants. A determinant is this thing: *shows the permutation formula*. I am sure you now understand what a determinant is and why I just showed it to you.
How is this not trash? It's pure fucking trash.

[Anonymous No.9481966]

>>9481956
I liked it a lot. You've just been brainwashed by Axler and will never be a good mathematician.

[Anonymous No.9481972]

>>9481966
Nice counterargument

[Anonymous No.9481973]

>>9481956
Where did the determinant touch you anon?

[Anonymous No.9482118]

Wtf are you supposed to do when the textbook only gives answers to half of the problems (only odd numbered)?
There's no solution manual either. I won't know if I got the correct answer.
Do I just skip half of the problems? Wtf.

[Anonymous No.9482284]

can someone translate

[Anonymous No.9482291]

>>9482284
normal

[Anonymous No.9482295]

>>9482284
"I'm as Gaussian as anyone"

[Anonymous No.9482334]

>>9482284
https://en.wikipedia.org/wiki/Normal_distribution

[Anonymous No.9482395]

What does a zero with a line over it mean? I assumed it's just a zero, but my textbook is wording it like it's not the same thing so I'm kind of confused.

[Anonymous No.9482402]

>>9482395
Oh never mind, apparently it's the null vector.

[Anonymous No.9482495]

Brazil has a site where most Brazilian researchers publish their curriculum and research topics (http://buscatextual.cnpq.br/buscatextual/busca.do?metodo=apresentar))

Do other countries have something similar?
If not, where can i find these things?

[Anonymous No.9482589]

>>9477287
that is still fucking choosing a deliberatelly though,
x has a definite answer, of that much im certain, unless my teacher is tickling me in the ass just to make me fail my other subjects

[Anonymous No.9482654]

How do I write "the smaller of two variables"?

In programming you'd call it [math]min(x,y)[/math], but this doesn't seem to be formal in the math world.

[Anonymous No.9482657]

>>9482654
>How do I write "the smaller of two variables"?
min(x,y)

[Anonymous No.9482682]

>>9482654
https://math.stackexchange.com/questions/1437513/use-of-max-and-min-functions

[Anonymous No.9482819]

How do I solve this?

[Anonymous No.9482822]

>>9482819
Start with a rotation counter-clockwise by [math]\frac{\pi}{2}[/math]

[Anonymous No.9482889]

Why does the square of 1/x just disappear at the end there? Where did it go?

[Anonymous No.9482897]

>>9482889
>Why does the square of 1/x just disappear at the end there?
If you mean the third last equality, it's because the limit was evaluated, and 1/x goes to 0 as x goes to infinity.

[Anonymous No.9482903]

>>9482897
That would have been nice to learn in class. Thanks for the help, appreciate it.

[Anonymous No.9482915]

How do I git gud at representing systems as matrices? My understanding is that matrices are a collection of vectors but I think my interpretation infantilizes it.

[Anonymous No.9482974]

>>9482915
>matrices are a collection of vectors
correct.

[Anonymous No.9482986]

>>9482974
Wrong, matrices are much more general than that.

[Anonymous No.9483032]

>>9482915.
Say you have a linear system like in pic related.
You can rewrite this as
x1 * column (ai1) + ... xn * column (ain) = column (bi)
And the left side of it is, By Definition,
[column (ai1) ... column (ain) ] [x1 ... xn]^T

>My understanding is that matrices are a collection of vectors but I think my interpretation infantilizes it.
Matrices are whatever they are.
But, the best way to interpret them is as representations of linear maps.
See here for some intuition:
https://www.youtube.com/watch?v=kYB8IZa5AuE

[Anonymous No.9483070]

I have a question about the memoryless property of the exponential distribution. Let's say I have an exponential RV X with E[X} = 40 mins (let's say X is the time it takes a clerk to help someone). I've already been waiting for the clerk for 20 minutes: is E[X] still 40 mins? I know that memoryless states P(X > 40 | X>20)=P(X>40) but I'm not sure how that affects expectation

[Anonymous No.9483106]

>>9483070
>I know that memoryless states P(X > 40 | X>20)=P(X>40)
You don't know shit.
That's not what memoryless means.
Memoryless means P(X>40 | X>20) = P(X>20).
More generally P(X>t+s | X>s) = P(X>t).

[Anonymous No.9483137]

If you go out for lab dinner, the PI typically covers the whole tab right?

[Anonymous No.9483267]

My backyard was covered in about 6 inches of snow yesterday. Evenly distributed. Loosely packed.

I walked through it in snow using boots which left implants.

It was freezing temperature overnight.

I go out into my backyard today and the snow is the same but my boot implants had froze into ice. Why did my boot implants freeze but the snow remained the same?

[Anonymous No.9483284]

>>9483032
That's what they are in R

In Survo matrices truly are matrices

[Anonymous No.9483656]

Can anyone think of a good, nonstandard motivation for learning matrices? I have a friend whose daughter is interested in math and in pre-algebra. I already taught her about polynomials and polynomial arithmetic/long division, and she snapped it up quickly. Matrices are so powerful but in my opinion they are extremely difficult to motivate.

What did you find most interesting about matrices, /sci/?

[Anonymous No.9483744]

>>9483656
>matrices, polynomials and polynomial arithmetic/long division
>math

[Anonymous No.9483751]

>>9483656
Start by showing her how they can be used to solve systems of linear equations really easily; that's how my linalg prof began and the motivation for inventing matrices in the first place. She'll think that it's the coolest shit ever. Then, launch into the geometrical interpretation of these systems of equations.

[Anonymous No.9483771]

>>9483751
Unfortunately it's not easy to motivate systems of linear equations, either.

[Anonymous No.9483773]

>>9483656
Linear Transformation and Geometry. Show her how rotation matrices are used in computer graphics/games and art software. Show her how she can use projective transformation to fix images taken at a slant to see them head on.

[Anonymous No.9483790]

How do I into discrete maths

[Anonymous No.9483800]

>>9483656
Tell her how the determinant measures the signed volume of the vectors in the matrix

[Anonymous No.9483806]

>>9483790
Look up telescoping series

[Anonymous No.9483809]

>>9483773
This is a pretty interesting idea. I might code up an example application to do this so it's easier to explain. She's interested in programming, too, so this might be a very good fit.

[Anonymous No.9483815]

>>9475021
>Pic related
I might be overthinking the answer to this one. The most I can come up with is that "There is no linear relationship between [math]t and f(t)[/math], so the linear least squares method of minimizing the residual won't work", but I'm not sure if that explanation is right. Is there a more rigorous way of proving LLS won't work in this case?

[Anonymous No.9483822]

>>9483815
Perhaps it would help you to explain to me like I'm an idiot why a quadratic best fit is "linear". Then it might occur to you how to explain in one sentence why this isn't.

[Anonymous No.9483839]

>>9483822
Okay... Here goes.

A quadratic best fit is linear because a system of polynomial equations can be rewritten as a matrix multiplication between the value of x and the coefficients of x (see pic).
The fact that we can write this function application in terms of matrix-vector multiplication means that the value of [math]f[/math] can be written as a linear combination of a matrix and coefficient vector.

Is this the right train of logic? Because I'm having trouble seeing why we couldn't write [math] f(t) [/math] in terms of matrix operations for a given set of c's and t's

[Anonymous No.9483864]

>>9483839
Polynomials in general aren't linear. But, they are linear in their coefficients, with the variable powers as basis vectors. What does it mean to be linear in their coefficients? It means that a linear operator which operates on a sum is the same as that linear operator on each component which is summed after application, namely f(x+y) = f(x)+f(y). Additionally, f(ax) = af(x).

Is this preserved for [math]c_1[/math] in your pic? What about [math]c_2[/math]?

[Anonymous No.9483875]

>>9483864
Okay. that makes sense.
So is this a good explanation?
"
This cannot be solved directly because there is a nonlinear relationship with the coefficient [math]c_2[/math]. In otherwords, for [math]c_2[/math], superposition does not hold:
If [math].c_2 = a + b[/math]., then
[math]e^c_2 = e^{a+b) = e^a \cdot e^b[/math].
"
The only thing I'm worried about is that I'm not sure why the coefficient not being linear means we can't solve it using Least Squares.

[Anonymous No.9483896]

>>9483875
What you've proven is that [math]\exp(x)[/math] is not a linear operator. But that's not a problem. Neither is [math]x^2[/math].

[Anonymous No.9483914]

>>9483790
>P(1):1/(1*2)=1/(1+1)

CS majors are this retarded.

[Anonymous No.9483923]

>>9483875
>>9483896
Actually I apologize I read what you wrote in haste. That seems like a good argument to me.

[Anonymous No.9483925]

https://en.wikipedia.org/wiki/Great_Attractor
can someone explain to me how this thing is pulling things towards the center of the universe, but then everyone says the universe is constantly expanding away?

[Anonymous No.9483927]

>>9483815

ln(f(t)) = ln(c1) + c2*t = k1 + c2*t

You can use linear least squares, no?

[Anonymous No.9483933]

It isn't pulling things into the center of the universe, it is still a local phenomenon compared with our observable universe. As a matter of fact there is no "center of the universe" in the sense you are thinking all points in space used to be much closer together. Spacetime itself has expanded

[Anonymous No.9483938]

>>9483927
This is linear, it is true, but you're minimizing the wrong errors. This procedure can give a good starting point for nonlinear regression, though.

[Anonymous No.9483939]

>>9483927
https://math.stackexchange.com/questions/1488747/least-square-approximation-for-exponential-functions

[Anonymous No.9484009]

http://www.cpp.edu/~cba/technology-and-operations-management/tom-curriculum/career-tracks.shtml

Which track is worth going?

[Anonymous No.9484088]

Hi, can someone please give me a quick rundown on dual spaces and the double dual (linear algebra)? I’m having trouble trying to conceptualize it.

[Anonymous No.9484115]

>>9484088
Let V be a vector space over some field F (that field F can always be regarded as a vector space over itself).
The Dual space of V is the space of all linear maps from V to F.

The double dual is the dual's dual.

[Anonymous No.9484120]

>>9484115
>field F
This need not be well-defined in general.

[Anonymous No.9484129]

>>9482654
inf

[Anonymous No.9484179]

>>9484120
What do you mean?

[Anonymous No.9484182]

Brainlet here.
I don't need you to solve this for me, just explain what maths I should use to solve it. Or direct me to a fucking calculator tool for this kinda shit.

Say I have 20 marbles. I choose 10 of these marbles at random, mark them with an X, and put them back in a box.
If you choose 10 marbles at random what are the chances you happen to pull out all 10 marbles that are marked with an X?

[Anonymous No.9484195]

>>9484182
(20 choose 10)

[Anonymous No.9484208]

>>9484182
N:= total number of marbles
K:= number of marked marbles
n:= number of pulls
The number of ways to select exactly x marked marbles is [math] \binom{K}{x} \binom{N-K}{n-x} [/math] .
The number of all possible pulls is [math] \binom{N}{n} [/math] .
Therefore, assuming all pulls are equally probable, the probability of selecting exactly x marbles is [math] \frac{\binom{K}{x} \binom{N-K}{n-x}}{\binom{N}{n}} [/math]
In your case, n=K and x=K, therefore the probability becomes
[eqn] \frac{\binom{K}{K} \binom{N-K}{K-K}}{\binom{N}{K}} = \frac{1}{\binom{N}{K}} = \frac{1}{\binom{20}{10}} = \frac{1}{184756} [/eqn]

[Anonymous No.9484383]

Hi, where can I download the course materials of the Open Yale Course's Physics II and II?

https://oyc.yale.edu/NODE/206
I can't download from here: "No file available for download."

[Anonymous No.9484385]

>>9482495
>>9482495
>>9482495

[Anonymous No.9484588]

I don't get it, how do I get the differential? I'm just applying what we learned in school but I don't get the same thing as the textbook answer and there is no explanation whatsoever.

[Anonymous No.9484594]

>>9484588
Oh nevemind I saw it when I posted, I feel dumb for thinking so long about this now.
Now I actually understand how this works, but I doubt I will ever think of it myself honestly.

[Anonymous No.9484623]

>>9484588
>>9484594
First of all, this is called "Partial Derivative with respect to x".
To calculate it, you treat the variables y and z as constants and you differentiate with respect to x the way you do single variable functions.

[math] \frac{\partial S}{\partial x} := \lim\limits_{h \to 0} \frac {S(x+h,y,z)-S(x,y,z)}{h} [/math]

[Anonymous No.9484632]

>>9484623
Uh, yeah I know. I was just confused because I didn't have the same result as the one in the textbook, really the problem was me not seeing how to reach the solution but it worked out after all.

[Anonymous No.9484654]

>>9484383
Help pls

[Anonymous No.9484720]

>>9475021
Can someone explain how to do partial fraction decomposition?

[Anonymous No.9484803]

>>9475021
How do i find tangents of 2x^2+ 4y^2=1 that go through A(1,0) using derivatives?

[Anonymous No.9484847]

>>9484803
Implicit differntiate

[Anonymous No.9484889]

>>9484720
https://youtu.be/KJGp0pyPoVo
I'd reccomend watching this guy if u don't have a textbook

[Anonymous No.9484911]

>>9484803
Consider the function [math] g(x,y)=2x^2+4y^2-1[/math] and its contour at 0 which is the ellipse [math] 2x^2+ 4y^2=1 [/math] .
Consider also a point [math] (x_0,y_0) [/math] of the ellipse.
The ellipse's tangent is described by the points (x,y) of the plane that satisfy the following equation:
[math] y-y_0 = \nabla g(x_0,y_0) \dot (x-x0) [/math]
Now you want this to pass through (1,0).
Plug in x=1 and y=0 and find x_0 and y_0.
Write out the equation with the now known x_0 and y_0 and you are done.

[Anonymous No.9484913]

>>9484720
I'll only do it for fractions of the form [math]p(X)=\frac{aX+b}{cX^2+dX+e}[/math]. The other cases are similar.
First, factorise the denominator so you have something of the form [math]p(X)=\frac{aX+b}{(fX+g)(hX+i)}[/math]

The aim of partial fraction decomposition is to basically rewrite p in the form [math]\frac{A}{fX+g}+\frac{B}{hX+i}[/math] where A and B are to be found.
To do this notice that
[eqn]\frac{A}{fX+g}+\frac{B}{hX+i}=\frac{A(hX+i)+B(fX+g)}{(fX+g)(hX+i)}=\frac{(Ah+Bf)X+Ai+Bg}{(fX+g)(hX+i)}[/eqn]
We want this to be equal to p(X). By comparing the coefficients you have two equations to solve to find A and B: [math]Ah+Bf=a[/math] and [math]Ai+Bg=b[/math]

[Anonymous No.9484921]

>>9484911
Ignore what I wrote, I am retarded

[Anonymous No.9484949]

>>9484913
why does latex fuck up like that? i guess it's because, for something like [Math] [/Math][Math] [/Math], it thinks the two inner tags are part of the formula, but how do i stop it? putting spaces in spaces doesn't always work

[Anonymous No.9484994]

>tfw you want to switch majors, but that major has bad growth, and you don't want know if you want to delay your life any further.
I hate being mortal.

[Anonymous No.9485041]

Show that if T is any subspace of V that contains U ∪ W, then T contains U + W. Thus, U + W is the smallest subspace of V containing U ∪ W.

How do I prove it's the SMALLEST? Just take a vector in U+W and show it's in U union W? That shows U+W is a subset of U union W, is that what I want?

[Anonymous No.9485050]

>>9485041
>How do I prove it's the SMALLEST?
If P contains U ∪ W then P also contains U+W, so (U ∪ W) ⊂ U+W ⊂ P.

[Anonymous No.9485054]

>>9485041
You're correct. This is the canonical way of proving two sets are equal; show [math]A \subseteq B[/math] and [math] B \subseteq A[/math], which forces A = B.

[Anonymous No.9485097]

>>9485041
If T is a SUBSPACE and it contains all the elements of U and all the elements of W, then it must contain all linear combination of the form c1 u + c2 w. These linear combinations are exactly the elements of U+W.
So, any subspace containing U and W must also contain U+W.

U+W obviously contains U and V.

So U+W is the smallest subspace of containing U and V.

[Anonymous No.9485096]

>>9485041
>Just take a vector in U+W and show it's in U union W?
You won't be able to show this.

>>9485054
>You're correct.
No he/she is not. U union W is not necessarily equal to U+W, and in particular U union W is not even necessarily a vector space.

[Anonymous No.9485236]

>>9484720
For simple cases: factor the denominator, write as c1/(x-r1)+c2/(x-r2)+... Convert to canonical form (by multiplying each term by the product of the other denominators and expanding the resulting numerator; a/b+c/d=(ad+bc)/bd). Equating coefficients gives you a system of linear equations which you can solve.

E.g. 1/(x^2-3x+2)
= a/(x-1)+b/(x-2)
= (a(x-2)+b(x-1))/(x^2-3x+2)
= ((a+b)x-(2a+b))/(x^2-3x+2)
=> a+b=0, 2a+b=-1
=> b=1,a=-1
=> 1/(x-2)-1/(x-1)

As the degree increases, this starts to get complicated, so you use residues. Consider:
f(x)/g(x) = c1/(x-r1)+c2/(x-r2)+c3/(x-r3)+...
= (c1(x-r2)(x-r3)...+c2(x-r1)(x-r3)...+c3(x-r1)(x-r2)...)/((x-r1)(x-r2)(x-r3)...)
=> f(x)=c1(x-r2)(x-r3)...+c2(x-r1)(x-r3)...+c3(x-r1)(x-r2)...
=> f(r1)=c1(r1-r2)(r1-r3)...
(all of the other terms have x-r1 as a factor and so are zero when x=r1).
=> c1=f(r1)/(r1-r2)(r1-r3)...

Similarly for x=r2, r3, ...

IOW, for each pole (root of the denominator), evaluate the numerator and divide by the remaining (non-zero) factors of the denominator.

Things get a bit more complicated if the denominator has complex or repeated roots.

[Anonymous No.9485289]

why is the line integral/work done of pic related not zero? (intuitively though, i don't really care about the calculation.)
in my mind, if you imagine a particle on the curve, since the vector field is pushing the particle in the same direction, we don't have to do any work to move it around the curve. obviously that's wrong.

[Anonymous No.9485330]

If an asteroid like 2002 AJ129 was on collision course with our planet, how long it will take until NASA can't hide it anymore?

[Anonymous No.9485437]

How I can Prove this?

[math]\mathbf{SO(3) / SO(2) \simeq S^2}[/math]

Help, capeshit ruined my brain

[Anonymous No.9485460]

>>9485437
draw a picture

[Anonymous No.9485591]

>>9485437
With what operation is S^2 equipped?

[Anonymous No.9485642]

Let A, B be formulas and p a variable

Prove by induction that A[p:=B] is a well-formed formula

where the heck do I start with this question

[Anonymous No.9485655]

>>9485642
>where the heck do I start with this question
draw a picture

[Anonymous No.9485708]

what is the difference between the following parameterisations?
[math]r(t)=(t,t),\quad t\in[0,1][/math]
[math]r(t)=(t^2,t^2),\quad t\in[0,1][/math]

[Anonymous No.9485711]

>>9485708
Velocity.

[Anonymous No.9485734]

Whats a comprehensive reference book for trig?

I dont need it to be good to learn from, just a reference

[Anonymous No.9485736]

>>9485655

[Anonymous No.9485824]

>>9485437
Determine the isotropy group, i.e. show that, say, (1,0,0) is isomorphic to SO(2).
Then you automatically get the desired isomorphism by standard arguments (using that S^2 is Hausdorff and SO(3) is compact).

[Anonymous No.9485831]

>>9485824
Sorry, I meant, the subgroup stabilizing (1,0,0) can be identified with SO(2).

[Anonymous No.9485866]

If you have weight on the end of a rope and hold it over a support that is flat, you can hold it without actually having to pull at all.

How does this work?

Is there a name or equation to calculate how many lbs the person holding it in place is holding?

[Anonymous No.9485877]

>>9485289
> why is the line integral/work done of pic related not zero?
Because the field isn't conservative.
> since the vector field is pushing the particle in the same direction, we don't have to do any work to move it around the curve. obviously that's wrong.
The field is doing work to push the particle around the curve. A particle starting from rest and constrained to the curve will constantly accelerate, gaining energy.

If you consider the component of the force in the direction of the tangent at each point, it's always positive. With a conservative field, the positives and negatives always cancel out for any closed loop.

[Anonymous No.9485886]

>>9485866
> If you have weight on the end of a rope and hold it over a support that is flat, you can hold it without actually having to pull at all.
If you didn't need to pull at all, you could let go and the weight would stay there. If letting go causes the weight to fall, then you *were* pulling on it.

In practice, the force you need to exert will be much less than the weight because of friction between the support and the rope. But friction requires a perpendicular force to press the rope against the surface, which requires that the rope is taut. So you won't actually be able to let go unless the rope itself is extremely heavy, or the weight is extremely light, or the coefficient of friction between the rope and surface is extremely high, or some combination of the three.

tl;dr: the higher the friction, the less force you need to exert to keep the weight in place.

[Anonymous No.9485888]

>>9485866
You're just applying a force against the tension of the rope

[Anonymous No.9485914]

Is there any definite, thorough studying guide to math? From basic shit to topology. I've seen PDF's but lost it. What are the best textbooks? In spite of the fact I've been studying math for two years in college, basically as a brainlet I was never able to figure out shit on my own, always cheated on exam.

Should I just kill myself and give up?

[Anonymous No.9485918]

>>9485914
Sorry, missed a post with wiki-article.

[Anonymous No.9485922]

>>9485886
is there a way to calculate how much force youre pulling with? im sure there is but I have no idea where to look for it.

[Anonymous No.9486053]

>>9476574
Determining if graphs are isomorphic is rather hard but that one is rather easy - try exhibit an isomorphism between the complement graphs (which both are 8-cycles).

[Anonymous No.9486680]

>>9485914

[Anonymous No.9487183]

>>9485939
NEW
>>9485939