/sci/ - Science & Math

>>9357587
S T O P
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H I D D E N
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>>9357599
Are you okay?

>>9357619
Literally sick (physically, into a bucket, with rage) of people shitting up /sci/ with these terribad threads.

>>9357587
>>spontaneously realize that a line is the locus of points which are pairwise equidistant from two points whose connecting segment is perpendicular to and bisected by that line in two-dimensional space

Nice

>>9357587
You should look up what a parabola is.

How do I solve this?
moles for silver is .115
I multiplied this by 11.3k, the moles for heat, but I got 11.3kJ. Answer should be 2.44k What do I do with the heat its being heated at?

someone help me with >>9357812
should be pretty simple

>>9357815
[eqn] x^2+y^2-2y=0 \\\
x^2 + y^2 -2y+1=0+1 \\\
x^2 + (y-1)^2=1^2 \\\
x= 1 \cdot \cos(t) \\\
y-1 = 1 \cdot \sin(t) [/eqn]

Does every set of ordinals have a least element?

>>9357921
Yes. If it didn't you would get an infinite decreasing sequence of ordinals which is impossible.

>>9357921
Assuming the axiom of choice, yes, since the ordinals then form a set.

how

Having trouble with basic abstract algebra here.

I'm trying to find the number of elements in {[math]S_5 : \sigma(2)=5[/math]} where [math]S_5[/math] is the symmetric group on 5 elements. I know that [math]|S_5|=5!=120[/math], but I really don't know where to go from there.

>>9357587
What’s the shape of a wormhole called?

>>9358081
It's the number of bijections from {1,3,4,5} to {1,2,3,4} which is 4! .

I want to calculate the vector potential A at a point P located a distance s from an inifinite wire when a current is turned on at t = 0 (this is example 10.2 of Griffiths' electrodynamics book). I'm having troubles understanding how to get the integration limits.

what are some good books on Statics, my school is letting me take dynamics before taking statics and I don't want to come into that class unprepared and get shit on.

How do you convert the 2nd order DE to a system of 2 first order DEs?

>>9358092
Okay cool, thanks, I'm guessing the general pattern holds too?

>Getting high before bed
>Sketching diagrams of Peirce's theory of signs
>Trying to diagram sign structure and catagory
>Finally feel like I got it right
>Accidentally triforce
Pretty amazing, not that significant. Makes me wish I played Zelda as a kid

>>9358116
my bet is eliminate y from each equation, integrate, and then apply the transform

>>9358143
When I wake up tomorrow I'm gonna put a curve on it

>>9358143
damn, you didn't even play Zelda

>>9357587
I have a probability question. I've got an exam in 6 hours so I'm trying to figure out what I can beforehand.

"In average, 120 people enter a mall per hour. There was a 90 minute long worker strike. What is the probability that the mall will lose more than 150 buyers, if the standard deviation of arrival is 30 (on an hour)?"

I've worked through all the theory and all that jazz but I can't figure out how to start with this one. My textbook barely mentions standard deviation at all, let alone how to use it.

>>9358143
what's that?

>>9358087
one-sheet hyperboloid

>>9358213
It's the process of meaning making. I like to use diagrams instead of symbolic logic to think about such abstract things.

Can someone please explain p-value significance to me? The notes I have from class give the different cases of when to reject H0 based on u and z values, but not sure how to apply it.

Example problem that led me to realize my confusion:
>H0: u = 8
>H1: u > 8
>compute z value based on n, o, and x, get z = 3.33
>p-value is P(z > 3.33) = 0.0004 (or z at -3.33)

What do I do with this p-value to determine which hypothesis to choose? What is z-alpha in this case?

>>9358206
>mfw I also have a probability exam in 6 hours

Do you happen to go to the university of indians and chinese?

Me thinks the answer is 0.7486. Assuming a normal distribution and converting the given values for a 90 min. interval:

z = (x - u)/o = (150 - 180)/45 = -0.67.
Az = 0.2514.

Since we are looking for values greater than 150, we look to the area to the left of the z value, so 1 - 0.2514 = 0.7486.

>>9357599
>implying /sqt/ isn't one of the few decent threads in this shit board

>>9357853
thank you

new question, how do I go about solving this one? again I think it's because I don't understand how to parameterize it

>>9358555
forgot to add, I'm supposed to either solve it as a surface or volume integral

>>9357587
can someone help with what witchcraft he derived that first line? or just point me out to a book about series
title is find the sum

>>9358116
Add a variable for each derivative.

So e.g. u=dy/dt =>
du/dt+3u+2y=0 => du/dt = -3u-2y
dy/dt = u

>>9358079
Just figure out how fast the block will be going after it travels the initial 50 cm after it gets slowed down by gravity and friction on the way there. Once you get to that point you just have to figure out when it's velocity reaches 0m/s^2 and to do that you just have to factor in the loss in speed it will suffer from the force applied by the spring on top of the forces of gravity and friction that are already slowing it down.

It's just a bunch of really simple problems that I'm betting you know how to do put together. Don't stress it and just start crunching numbers lad.

>>9358742
Here's a hint to start you out at the very least. The limit is infinity, right? So what's the difference between (n+1)/(2^n) and 1/(2^n) when n is infinty?

>>9357681
Set of points that are equidistant to a line and a point.

>>9358742
He Did use witchcraft. You are not really supposed to think of that step.
Read it from right to left and it will make sense.

>>9358925
Also, the best way to do it is using derivatives.

[math] \text{If } |x|<1 \text{, then } \sum\limits_{n=0}^{\infty} (n+1) x^n = \sum\limits_{n=0}^{\infty} ( x^{n+1} )' = (1- \frac{1}{1-x})' = \frac{1}{(1-x)^2} \\
\text{For } x=\frac{1}{2}: \sum\limits_{n=0}^{\infty} (n+1) (\frac{1}{2}) ^n = \frac{1}{(1-\frac{1}{2})^2} = 4 [/math]

>>9358950
Also, the best way to do it is using derivatives.

> [math] (1- \frac{1}{1-x})' [/math]
[math] (\frac{1}{1-x} -1)' [/math]

>>9358519
>>9358206
it's not normal it's a Poisson distribution

>>9358968
It's not Poisson. It's normal.

What is "Manhattan Distance"?

>>9359034
What is wikipedia?

>>9359034
Sum of the absolute values of the differences between components. E.g. in 3D:
|x1-x2|+|y1-y2|+|z1-z2|
It's the distance between points if you're constrained to travelling along cardinal directions.

>>9358079

There are two possible approaches. You can either do it with energy or forces. I'd suggest the energy approach:

Basically, the block has initial KE. As it slides up, it gains GPE and does work against friction. Then it starts to compress the spring too, storing energy there so:

KE = GPE + Friction + Spring

The only slighly sting in the tail is that it is still working against friction and gaining GPE as it compresses the spring, which makes it slightly more awkward.

Split it up into two parts.

First work out the remaining energy at the instant it impacts the spring, then repeat with the spring compressing as well.

Give it a go yourself and I'll try to hash out a solution here.

(The approach using forces just works out the resultant force due to gravity and friction and the spring, then sets up an equation for the deceleration of the block. It's the same physics).

>>9359260
Thanks.
So it's basically the distance formula without the squaring and square rooting?

I've missed many Matrices classes so I don't understand what is a matrix. Like why the fuck did you take a bunch of numbers and put it in a bracket. A matrix with 1 column is called a vector? WHAT THE FUCK, MATHEMATICS? please help me i cant live with this brainlet level of understanding i have checked many books but everything just FUCKING SKIPS IT AND STARTS TEACHING ME HOW TO FUCKING DO ALGEBRA WITH FUCKING MATRICES BECAUSE THEY ARE SOOOOOOOOOO SPECIAL.

>>9359448
they're linear equations

>>9359454
But how? Most of what I learned was solely for solving problems related to Matrices and I could clearly make out that you can't do shit with a matrix. It isn't like a determinant which actually gives a value by solving it. The matrix is just there. How do you even represent a matrix in any other fucking way? help me b0ss

>>9357648
/sqt/ is infinitely better than all those other threads, since it aggregates questions which would otherwise be posted in their own threads

>>9359481
with linear equations

>>9359415
There's no "the distance formula". There's Euclidean distance though, which is defined as the square root of the sum of squares of differences, which is probably what you're referring to

>>9359448
A scalar is a single value (a single number)
A vector is an ordered set of scalars
A matrix is an ordered set of vectors

There are plenty of problems which can be solved elegantly using matrices, but since you are just getting introduced to them, you obviously wouldn't know many

>>9359325
>>9358079

Here's a rough solution. I plugged in my formula and got about 13.2cm. There's always a chance that I tried to simplify with too many steps and missed a factor. Bear in mind that this is a quadratic that will offer two solutions, but one is negative so clearly nonsensical.

Regardless, the method is good. If you have questions, or if there are mistakes, then ask.

The approach with forces is much messier. I might persevere to check my answer, but this energy approach is much nicer for typing out a solution.

>>9359499
I kind of get it now after doing some reading. (you know i only read mathsisfun.com best site xdddd)

I don't get the vectors part though. Each element represents a component. Does three components mean a vector in a 3D coordinate system/space? why duh colum be duh vectur and what duh tensur mean mang halp moar

>>9358087
Looks like a tube

>>9359516
Could you give me a few examples? Perhaps I would know of them because even though I don't understand matrices completely I have unfortunately written many tests and was taught a lot of shit related to it.

>>9358087
a double funnel?

>>9359519
Hey I'm the anon who posted the problem. Should've mentioned that I copy pasted the problem into google and there was a video that explained it pretty well. Thnaks for your input anyway. You did get the right answer by the way. Now I'm off to do the exam.

>>9359536
Examples for what? Vectors?

A vector could for example be v = (0, 0.5, 3)
You can multiply it with a scalar, which is just an element-wise multiplication, e.g. v * 2 = (0, 1, 6). Same goes for matrix * scalar.
There is also matrix multiplication (matrix times matrix), you should look that up, it's not intuitive when you see it for the first time. Since vectors are special cases of matrices, matrix multiplication also applies when you multiply two vectors together or a matrix and a vector. Matrix multiplication is not commutative, which means for matrices A1 and A2, A1*A2 is in general not equal to A2*A1

>>9359556
Thanks for your responses

>There are plenty of problems which can be solved elegantly using matrices

I wanted examples for the above. Yeah I do know the struggles of first learning matrix multiplication. My problem is, I know a lot of things related to matrices ie. transposing, inverse, skew-symmetric matrices, solutions of linear equations using matrices just to name a few. But I don't understand the reason for why we use matrices. I know how to use the hammer pretty well but I have no idea why and for what I am using it for. I don't get the vector part and I also don't understand tensors.

whats a factor set

>>9358087
A pen going through a folded piece of paper

>>9358988
It's not normal.

It's Poisson.

>>9359669
If it was Poisson, the variance and the expected value wouldn't be mentioned separately, since the variance is equal to the expected value there (which isn't the case here, since E(X)=120, but Var(X) = SD(X)^2 = 90)

>>9357648

Calm yourself, my foolish little piggot. Both samples given in >>9357599 are equally full of shitposting. The irony is that you really seem to believe that things were so much better a mere two years ago-an opinion that you could only hold if you had not actually been browsing the board regularly at that time.

>>9358560
Well the divergence of your field is 1 so you probably need the divergence theorem or related

Can you listen to music when you're doing math? If so, which music? I like stuff like this: https://www.youtube.com/watch?v=7zvyIv7uwyE , I find it helps me focus.

>>9357710
First of all it's kJ, not just k. That's very important.
Second, I'm pretty sure that there's an identical problem with a different element on your textbook, maybe at page 37.
Third, if you do 0.115 * 11.3, you just can't get 11.3, you obviously did something wrong.

Now, the problem ask you for the heat of just the phase transition (solid -> liquid and gas -> liquid), not the heat to increase the temperature. Basically the latent heat of evaporation and fusion.

12.5 g of silver are 0.116 mol (0.1159, you can't ignore that 9), while 4.59 g are 0.043 mol.
Therefore, the first answer should be
0.116 mol * 11.3 kJ/mol = 1.31kJ
while the second is
0.043 mol * 250 kJ/mol = 10.75 kJ.

I don't know where your 2.44 comes from.

wat do when I can't find a doi number to an article? It's not even on the journal's page for it. Are some just arbitrarily not included or tougher to find?

Is the moment of inertia of a disk shaped object (full disk) equal to I=Io+m×r^2 where
Io=(m*r^2)/2 or is it just I=(m*r^2)/2 without the adding?

>>9360014
you might have to dig and you might not access

>>9358555
this is going to be very easy if you use the divergence theorem

My professor says this heat equation is a diffusion equation. Shouldn't it be Nabla squared T though and not delta T.

Side note I also thought in heat equations dT/dt was proportional to T not delta T. I'm dying guys help me

shouldn't pic related be [math]\cdot[/math] distributes over [math]+_{\mathbb{F}}[/math]
it's one of the vector space axioms if that helps

>>9360093
it's like taking a slice of the diffusion aspect and it's the delta T that matters, the bigger the delta T the stronger the forcing

>>9360093
in physics it is sometimes custom to write nabla squared as a delta, idk why

>>9357587
just realized your pic looks kinda like Brazil's flag...

My book as the solution of the differential equation on top gives the equation on the bottom.
I tried to find the solution using the
[math] y(t)=ce^{-A(t)}+e^{-A(t)}\int{f(t)e^{A(t)}}[/math]
which is used to solve a differential equation of this kind:
[math]y'(t)+a(t)y(t)=f(t)[/math] and where A(t) is an antiderivative of a(t)
i got:
[math]v_c(t)=v_c(0)e^{\frac{-t}{\tau}}+V_s[/math]
and wolfram gives me the same solution.
So, is it that an equation of this kind can have multiple solution, or have I made some mistakes?

>>9359448
Watch this:
https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
all of it

>>9358742
Au druze..

Could anyonw help me with part c and d? Disregard the assignment comment, this is from a past paper

>>9358157
>just put a curve on that bitch

>>9360181
Yes, there are multiple solutions (infinitely many actually), because
[math]-V_se^{\frac{-t}{\tau}}[/math]
is part of the homogeneous solution, which can be multiplied with any scalar.

>>9360498
Read [math] -V_s e^{\frac{-t}{\tau}} [/math]

>>9360466
Part c is asking what the value of m would have to be in order for the system to be stable if [math] \mu = 0[/math]
In part d, there's a possibility that the author made an error and actually meant [math] m_{max} > m_0 > m_{min} [/math]
To check, set [math] \theta = 90^{\circ} [/math] and see if the inequality truly holds or if the author made a typo.
The reason why [math] \alpha [/math] is not 0 is because at alpha, if you set little-m to 0, the block still wouldn't accelerate, which might make your formulas exhibit strange, non-physical behavior if you apply them in the theta < alpha regime.

>>9360114
You're very right.

https://en.wikipedia.org/wiki/Distributive_property
>2 ⋅ (1 + 3) = (2 ⋅ 1) + (2 ⋅ 3)
>it is said that multiplication by 2 distributes over addition of 1 and 3

>>9360114
>shouldn't pic related be ⋅ distributes over +F
You need both, that (a+b)v=av+bv and that a(v+w)=av+aw

can someone explain to a simple man what the differences between free energy, "free enthalpy", and regular energy are? what does free energy/enthalpy represent? the text describes free energy as the total energy required to create/destroy the system minus the energy you get "for free" as TS, where S is the entropy of the system's final state. but I still don't really get it in a practical way

>>9360667
Try this:

http://www.peelified.com/index.php?topic=23582.msg1469911#msg1469911

It's a bit long, but really simple.

>>9360672
stop posting this

>>9360674
Okay.

>>9360667
If someone with more experience notices flaws please correct them.


Energy is stuff like moving up or down in a gravitational field, breaking or forming chemical bonds, motion against a force field. The super standard easy to grasp normal energy stuff.
In very simple setups, the states when the energy is lower are favored. So the ball rolls down the hill, and hydrogen reacts with oxygen and makes water.
Enthalpy takes into account that some states have higher volume than others, so transitioning between them requires a change in volume. This means doing work (positive or negative) on the surrounding medium, which is a type of energy. So when you react chemicals, the free enthalpy of reaction takes into account that you're doing this at a standard temp and pressure.

Free energy (some people use Gibbs' free energy, some people use helmholtz. I'm just gonna use Energy - T*S) also takes into account Entropy. We want to be able to say, for a two state system, "State A has a lower free energy than State B, so the system will be in State A more often than state B"
Consider the system of 10 buckets in a line. There is 1 ball that randomly moves between buckets. Set the energy of the ball being in any bucket as 0. The ball is never not in a bucket. Define state A as "the ball is in the bucket on the far left" and State B as "the ball is in one of the other buckets" The multiplicity of State A is [math] {1 \choose 1} = 1 [/math] and the multiplicity of state B is [math] {9 \choose 1} = 9 [/math]. If we only use Energy, then it seems that both states are equally probably, since they have the same energy. Of course, that's obviously not the case if the ball moves randomly. If we include the -T*S term, we discover that State B has a lower free energy than State A, so it is favored.

>>9357587
>spontaneously realize that a line is the locus of points which are pairwise equidistant from two points whose connecting segment is perpendicular to and bisected by that line in two-dimensional space

Sooo a cylinder?

Find the euler characteristic of the nth Menger Sponge

yo push your bottom jaw as far out as you can, like creating a massive under bite. Do you guys hear like a hissing sound in your ear?? It almost sounds like air escaping

Does anyone know of any sources that explain perturbation theory really well?

What's the method called to solve this differential equation?
x(x-1)y'' + xy' + (x^2-1)y = 0

>>9361318
implicit differentiation
>anon guessed

>>9361186
I've had what you just described a long time ago. I had an ear infection at that time and when I popped my ears by holding my nose, I felt air escape.
My ears are already fucked, I hear ringing most prominent at night with some pain. Also, my jaw is fucked on the left; when I open it all the way it clicks. Been like this for a year now.
What I learned from these experiences is that the throat, ear, and jaws are connected. So like go to an ear doctor or something. Not like they're going to help, though. Look at me. I've read that ear doctors really just don't give a fuck about you.

>>9361318
Try reduction of order. If that's not it, try a series solution.

>>9361318
Sorry, senpai. You're fucked.

Could someone please direct me to some resources for me to learn how to evaluate this.
I think my weakness is in handling infinity.

Or is it really as simple as the top is 2*inf and the bottom is 2*inf, and 2*inf/(2*inf)=1 ?

>>9361379
>infinity
No such thing.

>>9361379
|cis((8x+π)/4)|=cos^2((8x+π)/4) + sin^2((8x+π)/4) = 1
1^2 = 1
Int(1)dx = x + c
So it's inf on top and bottom ezpz

>>9361379
L'hopital's rule. Derivative of the top over derivative of the bottom with respect to T. Let me know if you know that rule.

Don't ever tell me infinity over infinity is 1 without doing at least one l'hopital to try to show it.

>>9358480
>locus of points
it's the chance of the result of your hypothesis being made by confounding variables/chance. it's basically the chance of you being accidentally right. you don't want to be accidentally right. you want to be right. so if you only have 0.05 p value then you only have a 5% chance of the results of your data proving you right on accident.

>>9361396
true >>9361392 is wrong af but it's the right direction
I must've got the trig wrong or smthng bc it would be 1/2 with hopital's rule

>>9359624
Multiplication of matrices is a convenient way to represent linear systems, hence matrices can, to some extent, help you reduce an n-dimensional linear problem to a 1-dimensional problem.
Example: Say you have this complicated recurrence equation between to sequences [math]u_{n+1} = 2u_n + v_n[/math], [math]v_{n+1} = u_n + v_n[/math]
Then, setting [math]\vec{x}_n = \begin{pmatrix} u_n \\ v_n \end{pmatrix}[/math] and [math]A = \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}[/math], you have the much simpler equation [math]\vec x_{n+1} = A \vec x_n[/math], which tells you that (x_n) is simply a "geometric" sequence.
Hence, to get formulas for (u_n) and (v_n), you need only compute the powers of A. For this, it is very convenient to put A in a form more amenable to computations. In this case, it's probably easy to compute these powers directly, but for a generic matrix, it can be tricky, which is one of the reasons why we are interested in eigenvalues and diagonalization (it is much easier to compute the powers of a diagonal matrix, for obvious reasons)

Well /b/?

>>9361396
Thankyou. I had learned l'hopitals years ago, but I had forgotten.

Though I seem to have run into another issue.
I have no clue how to take the derivative of the numerator.

I'm really starting to feel like I will have to entirely relearn calculus. I know I didn't do that great of a job the first time.

>>9361318
> What's the method called to solve this differential equation?
If x isn't time-varying, then it's just a linear 2nd-order ODE:
y'' + ay' + by = 0
with a=x/x(x-1)=1/(x-1) and b=(x^2-1)/x(x-1)=(x+1)(x-1)/x(x-1)=(x+1)/x

>>9361468
[math] (-2)^2 = 4 \\ \sqrt{4} = 2[/math]
Well /b/?

Let's say my dog took vaccine for rabies, but later got biten by a rabbid dog. If my dog bites me, will I catch rabies if I didn't take the vaccine?

>>9357587
Is/was there any scientific project of which the objective was to numerically relate fundament constants of nature? I'm doing atomic physics and some of the parameters are a mess but they should be able to be reverse engineered without knowing the exact quantum theory.

How do I apply the conclusion of the mean value theorem to this
[math]e^(-6x), [0,7][/math]
When I try to solve for x I fuck up the algebra. I apply natural log to both sides but I might just be retarded

>>9361883
What do you mean by apply the conclusion? Do you mean finding the c?

>>9361883
[math] \frac{ f(b) - f(a)}{b - a} = \frac{e^{-42} -1}{7} \\ f'(x) = -6e^{-6x}\\
-6e^{-6x} = \frac{e^{-42} -1}{7} \iff \\ e^{-6x} = \frac{e^{-42} - 1}{-42} \iff \\ -6x = \log \left( \frac{e^{-42} - 1}{-42} \right) \iff \\ x = \frac{\log \left( \frac{e^{-42} - 1}{-42} \right)}{-6} [/math]

>>9361902
I did exactly that but the problem is that
[math]e^-42 - 1 < 1[/math]
and so log is fucked

>>9361911
But then you are dividing by -42 which is also negative and negative over negative = positive.

>>9361911
Also how do you exponent in math tags. This is bothering me

>>9361913
I fucking hate myself. Thanks

>>9361914
When the exponent has more than one character you need to surround it by {} so for example, e^{-6x}

>>9357587
What is the recipe for the wax and the liquid in pic related ?
I'm giving some hand my little sibling to ace their science project.
If it requires flammable liquid, is there any substitute to it ?

>>9361942
Ircc you can use some kind of oil and water (with food coloring) as substitutes
there should be guides online

>>9357587

You've figured out that a hyperplane in any dimensional space defines a unique line perpendicular to it, and vice versa. Nice going, asshole.

>>9361962
Unique? Not unless it goes through the origin.

>>9361967

Obviously it's going through the origin. We're talking vector spaces, not cucky affine spaces.

>>9361977
>lines are all through the origin
>therefore parallel lines don't exist

ok anon

in lecture notes i've often seen the notation [math]E^2, E^3,...[/math] used for the set of vectors in a plane, space, and so on. Is this a common notation? I can't seem to find it used elsewhere online.
and is it essentially the set [math]\mathbf{R}^n[/math] but with where the elements have a displacement associated with them instead of just being points?

>>9362278
E stands for Euclidean space. Technically Euclidean space isn't a vector space (as it has no chosen origin or unit of distance) but here it seems synonymous with R^n.

>>9360538
Both are ⋅ distributes over +F
Probably the right-distribution is called F+

>>9360538
Both are ⋅ distributes over +F
The right-distribution is probably called F+

Just had my circuits exam, how the fuck am I supposed to memorize the formula's for a pi or t transformer?

How do u get from 2nd to last line?

>>9362479
Square root

>>9361756
Nice meme, but you forgot that it's + or - 2.

>>9362479
[math]cos^2\theta+sin^2\theta = 1[/math], and then factorize by [math]mg[/math], take the square root.

By reducing a system to row echelon form, how would you be able to tell if it had a unique, infinite or no solutions?
For instance, given a system of vectors which equals the 0 vector, how would you tell if it had infinite or a unique solution?

Any CompSci students/grads?

I want to study compsci but I want to read a few books on stuff I know I'll be weak in first.

I started Introduction to Algorithms and I can't understand what the loop invariable is supposed to be for my code. The book's psuedocode is different in many ways (obviously) and I can't relate it to python's implementation.

I don't want to continue unless I firmly understand what my loop invariable is.

Apparently the answer is C, but I got E. Where does the second term come from?

>>9362835
Show how you got E so we can at least point out what you did wrong

>>9362847

>>9362818
>I want to study compsci

In undergraduate? Don't do it, just read books.

>>9362866
why would you have your particular solution as that, remember reduction of order, y2=uy1. y2=xy1

>>9362885
Any ideas on my problem?

>>9362818
http://openbookproject.net/thinkcs/python/english3e/index.html

don't worry about sorting that shit is easy as fuck you'll pick it up right when a prof explains it

>>9362835
>A (c1+c2)e^-x ~ only one linearly independent solution
>B c2*e^x -> 4c2*e^x = 0 which isn't a solution
>D it's a solution to y''+y=0 so the 2y' will be left over
>E second order equation need ~2~ linearly independent solution

>C c*x*e^-x -> -2ce^-x + c*x*e^-x + 2ce^-x - 2c*x*e^-x + c*x*e^-x = 0 so it's a solution.

>>9362818
If this is insertion sort (which it looks like), I think that the loop invariant is that for every loop, all elements up to j will be sorted.
Not 100% sure though.

>>9362818
>>9362906

Loop invariants are a meme CS kids talk about to appear smarter than they actual are. It's just literally anything that doesn't and shouldn't change after each loop. It's nothing profound.

len(listy) is an invariant
the elements in listy do not change (but are permuted) aka multiset of the elements doesn't change aka the unique elements and the frequency/multiplicity that they appear doesn't change
1≤j≤len(listy)

>>9362835
>>9362866
I'm not sure why you're bothering with y_p in a homogeneous ode but I hope this helps.

>>9362460
Ri = Rleft*Rright / sum of all
Rside = dual products summed / opposite one

>>9362944
THANK YOU.

You're the closest to being right between you and me since the book kinda hints to this but I couldn't prove it with my own implementation.

I thought I simply had to identify a line as the loop invariable.

>>9362959
You're also a big help, I won't let this bog me down too much in the future.

>>9362885
I live in a developing country and I don't want to work in shitty IT jobs anymore. I want to work for more than $408 US a month and most places won't higher unless you have a bachelors at least in something computer related, in IT, for a manager position.

IT, btw, is the only interesting field available here that I will do. And only managers make a respectable amount of money.

[legit]i-is this Sam?[/legit]

>>9362292
thanks.
> Technically Euclidean space isn't a vector space (as it has no chosen origin or unit of distance)
but if i were to specify the origin as (0,...,0) and the distance as the standard euclidean distance, then it would be, right?

>>9363015
(0,...,0) *is* the origin. In Euclidean space you don't have God-given coordinates at all. You can get rid of the origin using a vector space acting on a set freely transitively but in practice people just go straight to manifolds if they want to remove coordinate arbitrariness.

How do you deal with the fact you understand the concepts, can solve simple exercises but struggle once they get more difficult and make careless error? How do you approach that barrier and are learning to not make them anymore?

>>9358206
Look up the Gaussian distribution (Ga(x)) and see where the standard deviation is and plug it in, together with the average (protip, these are the only two variables of Gaussian distributions). Understand what it means.

Find the x for which Ga(x)=150. Integrate from x to infinity, that is the probability of fucking up.

>>9362835
If [math] e^{rx} [/math] is a solution, then you would have
[math]
r^2 e^{rx} + 2r e^{rx} + e^{rx} = 0 \implies \\
r^2+2r+1=0 \implies \\
r=-1 \text{ (double root) }
[/math]

It is because the root is double.
http://tutorial.math.lamar.edu/Classes/DE/RepeatedRoots.aspx

>>9362967
>your general solution must have as many constants as the order of your differential equation.

holy shit why couldn't my teacher have explained it that simply
thanks anon

>>9362988
IIRC, a loop invariant is something that states that after every loop, it will hold.
A loop can consist of one line or a whole body, as is this case with sorting algorithms after all.

>>9362550


>>9362648
Ok am i missing something? I don't how to get to the final line. There is no g in the second term so how an i supposed to factor mg?

So I was solving this trig function were the unit of time was months
I got t=0,3698 which means it's in January. I multiplied 0,3698 by 31 and got 11.4 does it mean that t corresponds to 11th or 12th of January?

>>9362835
>>9363086
This one is the superior approach which makes everything clearer
http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/diffeqdim.pdf

>>9363145
You still can factor out an mg. It will produce the 1/g factor in the term that doesn't have a g. Factoring out is just another way of saying division.
You have [math] \sqrt{(m\omega r)^2 + (mg)^2} [/math]
Multiply the Right hand side by (mg)/(mg)
[math] \frac{mg}{mg} \sqrt{(m\omega r)^2 + (mg)^2} [/math]
and send the 1/(mg) inside the square root.
[math] mg \sqrt{\frac{1}{(mg)^2} (m\omega r)^2 + \frac{1}{(mg)^2} (mg)^2} [/math]
The simplification is the [math] mg \sqrt{1 + (\frac{\omega^2 r}{g})^2} [/math] that you want

>>9363155
11th if theres a 0th day
>which I imagine there is because trig

>>9363183
hmmm could you explain what you mean by 0th day
I thought it's 12th becuase
0-1: 1st day
1-2: 2nd day
......
10-11:11th day
11-12: 12th day

>>9363199
Oh true nvm

>>9359415
yes, or sqaring and sqarerooting with 1

>>9362702
If the system has any all-zero rows, and for any of those rows the corresponding RHS element is non-zero, it has no solutions (you have an equation of the form 0=k for k=/=0).

Otherwise: remove the all-zero rows (these are equations of the form 0=0, which is redundant). If you're left with a square matrix (which will be upper-triangular), the system has a unique solution. Otherwise (i.e. the matrix has more columns than rows) it has infinitely-many solutions.

Any other case means that the system isn't in row-echelon form.

>>9363155
> So I was solving this trig function were the unit of time was months
"months" isn't a unit of time. A month could be 28, 29, 30 or 31 days.

>>9363232
Excellent, thanks a lot man.

>>9363248

>using the inferior Gregorian calendar that we've all been cuckolded into using

Sometimes, the ancients got it right. For the ancient Egyptians, a month was defined to be exactly thirty days, with the extra five days being "bonus content" at the end of each year (they also correctly understood the earth year to within one day, defining it to be exactly 365 days. You could do a lot worse.) The Egyptian calendar was logical smooth sailing, as far as it went.

>>9363248
ahhh it's approximated t=1 is January and t=12 is December. I guess the counted 1 as 30.5 days

>>9363118
This is only true for the homogeneous case where you have no initial conditions however.

>>9363293
I prefer a 13 month calendar

>>9363161
>(Does anyone read this? The first one in the course to tell me they did, by email, gets a small prize.)
lol

>>9363316
So in this case, do I NOT need the second term, since it's non-homogeneous, and I have initial conditions?

>>9360138
>in physics
Wrong. The Laplacian is denoted by [math]\Delta[/math] in Riemannian geometry based on its definition in the de Rham complex: [math]\Delta = d\delta + \delta d[/math]. It is the unique positive-definite operator [math]\Delta:C^k(M)\rightarrow C^k(M)[/math] that is invariant under the Hodge dual. It gives the Hodge decomposition of [math]k[/math]-forms in de Rham cohomology.
The notation [math]\nabla^2[/math] is a historical artifact. The Laplacian [math]\Delta[/math] becomes what is usually meant by [math]\nabla^2[/math] on [math]\mathbb{R}^n[/math].

>>9358087
its a toroidal field mane

>>9363334
Operator [math] D^2 +2 D + D [/math].
y solution, iff y in the kernel of the operator, iff [math] y=c_1 e^x + c_2 x e^{-x} [/math]

Find function f such that it gets mapped to [math] e^{-t} [/math], i.e. [math] ( D^2 +2 D + D ) (f) = e^{-x} [/math]
That just means find one solution for your differential equation.

If g is another function which also gets mapped to [math] e^{-t} [/math] , then g-f get's mapped to 0 (by using linearity), which means that g-f is in the kernel of the operator.
Therefore, g=f+Ker{D^2 +2 D + D}= f + {solutions of the homogenous system}.

If you are given initial conditions, then you know which element of the set {solutions of the homogenous system} you are going to pick. You are not going to be needing the second term if and only if the initial conditions give you c2=0 .

>>9363383
>y solution, iff y in the kernel of the operator, iff
y solution of the homogenous system*

>>9360138
>idk why

Laziness, there's also the box operator: = ∆ - 1/c^2 ∂^2/∂t^2

Is there an easy criterion for when a truncated Taylor series of a function will be an upper bound or lower bound to the function?

For example, a seemingly really useful inequality is [math] e^x \geq 1+ x [/math] and if we observe the right term we see that it is just the truncated Taylor series for [math] e^x [/math] with two terms. So this got me thinking that a method I can use to guess possible inequalities is by taking a truncated Taylor series of a function and then comparing it to the function but then obviously not always the truncated taylor will be an upper bound or lower bound which means that if I wanted to use this method, I'd always have to prove the inequality via the usual methods and that sounds boring. This sounds like the kind of thing that mathematicians have already thought about. So, is there some general rule that I can apply to immediately tell if a truncated taylor series is a lower or upper bound?

>>9363349
Um exsqueeze me but what is de Rham cohomology?

>>9363426
The de Rham cohomology is the cohomology of the constant sheaf [math]A_\mathbb{R}[/math] of differential forms.

>>9363422
Well,if you have a convergent power series [math] \sum\limits_{i=0}^{\infty} c_i (x-x_0)^i [/math] in some region around [math] x_0 [/math] and [math] c_i (x-x_0) > 0 [/math] for all x in that region then obviously [math] \sum\limits_{i=0}^{\infty} c_i (x-x_0)^i > \sum\limits_{i=0}^{n} c_i (x-x_0) [/math] for any n.

That's what happens with [math] e^x [/math] for example.

>>9363438
Well, I forgot about x being negative for e^x.
That's because x^n/n! given any x goes down to 0 really fast as n increases or something like that.

>>9363446
>That's because x^n/n! given any x goes down to 0 really fast as n increases or something like that.
That doesn't sound like rigorous proof.

How do I begin solving this? wtf is the teacher asking for?

linear algebra 1 final tomorrow, he said its gonna be 20% of these kind of 'proofs' and 80% matrix calculations like 'find eigenvalue etc'

>>9363458
>How do I begin solving this? wtf is the teacher asking for?
What have you tried?

>>9363460
https://www.youtube.com/watch?v=H9BWRYJNIv4&list=PL9E3DXpVMsE5iV-DKYbgZMNlkEKMaTlCS&index=2

entre khan academy playlist

theres something about visualizing this im not too sure about

I know systems of equations come up in every science but wtf is the question asking? isnt the proof proved in the question?

>>9363468
What does Khan have to do with this? Just use the definition of an eigenvalue, it's trivial in the fullest sense.

>>9363456
https://math.stackexchange.com/a/504876

>>9363473
so whats the answer to the true/false ?

>>9363458
Let [math] x [/math] be an eigenvalue and [math] v [/math] one of its eigen vectors:
[math] A = A^2 \implies \\ Av = A^2 v \implies \\ xv = A(xv) \implies \\ xv = xAv \implies \\ xv = x^2v \implies \\ (x^2 - x)v = 0 \implies \\ x^2 - x = 0 [/math]

You should know how to justify what I did in the last line. And then you show the only eigenvalues can be 0 or 1.

>>9363476
and he obviously uses the fact that the convergence is absolute in this case, so that he can rearrange the terms

>>9363476
Nice source but that argument is very [math] e^x [/math] specific. Not quite the general criterion I want.

>>9363481
There is no general criterion.

>>9363483
Then that's the answer I seek. Source?

>>9363477
Well, they are less trivial. I mean 1 is still completely trivial, 2 requires a short argument, 3 is probably just the definition of diagonalization. 4 is again trivial and 5 is probably also just definition.
For 2, take any eigenvector of B and construct an eigenvector of A with the same eigenvalue.

>>9363486
What source? The is no general criterion about what you asked, because what you asked is not well stated.

>>9357587
2 + 2 = 4 ? REALLY?!
OP confirmed VIP at my orgy.

>>9363458
1. T: It is literally in your fucking textbook
2. F: A and B represent the same transformation f under a different basis. The eigenvalues of a transformation and the eigenvalues of the any matrix which represents that transformation are the same. Or you can just use (4). Also, it's in your fucking textbook.
3. T: It is literally in your fucking textbook
4. T: It is literally in your fucking textbook
5. F: because 0 is excluded from the definition, see (1). Literally in your fucking textbook

Quit being a fucking drooling retard and read the theory before you go to excercises.

https://www.real-world-physics-problems.com/ferris-wheel-physics.html

I don't get why they say N2 > N1
Surely if you feel heavier at the bottom it means there's LESS force pushing UPWARDS than there is at the top.

mg is the same at the top and bottom. So you should subtract the normal force from mg to get the total force. N2 being greater than N1 would mean you get a lesser value for mg-N2 than you do for mg-N1

>>9363504
how do spics pronounce meme

>>9363670
actually wait
if there's more force down on you, you feel lighter
if there's a lot of force up on you, you feel heavier

>>9363334
the unknown constants would be solved for with the initial conditions. in that question you would still write c1 and c2 out until you solve for them

>>9363701
Yo soy tú : m3m3 : Tengo que: m3m3

>>9363177
Great thanks for the help

>>9359530
yes a vector is like a coordinate in a cartesian plane. The transpose of the vector (turn it 90deg cc) would look like a list of numbers, just drop commas between them and you have a coordinate. A vector is basically an arrow from the origin (0,0,0...) to that point.

They are really fucking useful when dealing with big sets of data, but I can see how you would think they are pointless when first being introduced.

>>9357587

This was taken as trivial in my complex analysis course, as was a lot of other basic geometry. Really got me desu

>>9363458

>Proofs

Nigga these are trivial definitions you should know before even attempting to do engineer tier plug n chug. What are they teaching you?

>>9363232
What would it mean if the system had more rows than columns?
Would that mean it isn't in row echelon form?

How does one use induction over the reals?

>>9364372
One does not use induction over the reals,

I've got some coding done to simulate diffusion limited aggregation, now I need to use it to do some actual science for my report. But they haven't told us what DLA can be used for so does anyone know any science I can model with DLA? The only inkling I have is to do with dielectric breakdown, but I have no idea why DLA models it or the mechanism for breakdown that makes it happen

If a set if vectors is linearly dependent, does that mean they won't span a space R, and if a set does span a space R, does that mean they are linearly independent?

>>9364394
>If a set if vectors is linearly dependent, does that mean they won't span a space R, and if a set does span a space R, does that mean they are linearly independent?
no and no

>>9357587
I'm doing some spectral analysis and I'm using the PSD to evaluate the noise of a signal. To estimate the PSD I use the Welch method. It seems like high frequencies near the Nyquist frequency are a bit filtered (pic related).
My question is : what is the maximum frequency I can use after which the PSD is no longer accurate ?

>>9364387
Why not?

>>9364399
But if a set of vectors is linearly dependent, that would mean the determinant is 0, which also means the set can't span the space Rn, doesn't it?

[math](A^{-1}(B^{2}-I^{2}))^{T}(AI^{-1})^{T}[/math]
How would you go about simplifying this expression for matrices?
I have on clue where to start.

I think I can do it for n=k, but how do I show that a permutation to nk for every n in Z is the identity too?

>>9364526

[math]I^2 [/math]

>>9364535
How did you get that?
I have no idea how to start simplifying it.

>>9364533
[math]
\pi := (a_1, a_2 , \ldots , a_k) \\
\pi ^n (a_i) = a_{i+n \mod k} \\
\pi ^n (a_i) = a_i \iff i+n =i \mod k \iff n=0 \mod k
[/math]

How exactly does Gravitational time dilation work? Why does time slow down in strong gravitational fields?

>>9358480
p-value is the chance in percent that H0 will be correct and all your work will suck, the lower the better, general is lower or equal to 0.05

>>9364526
(AB)^T=B^T A^T

>>9364523
>But if a set of vectors is linearly dependent, that would mean the determinant is 0, which also means the set can't span the space Rn, doesn't it?
no, consider the linearly dependent set of all vectors in R^n

>>9364393
Lichtenberg figures

What is an example of two positive irrationals that add up to a rational?

>>9364983
pi, 5-pi

>>9364983
Couldn't you just have something like
(10 - pi) + (pi) = 10

Hello, how would you obtain the number 300 using only 1 and 4 once each and no other numbers? All mathematical operations are allowed.
Thanks.

Question about this differential equation problem
I got the equation
5y''+60y = 45sint=10cost
What do I do with the air resistance?

Kinda off topic, but:

Does Europe have private universities like America does? Do students have to pay to go or are they government funded as well?

>>9365037
Looking at Damped Motion Problems, should air resistance be my y'?
So 5y''-35y'+60y = 45sint - 10cost
Then solve by undetermined coefficients?

>>9364983
two of the same irrational number (pi+pi).

If the DE is equal to 2e^-t, what is the form of the particular solution? I figured it would be Ate^-t, but the solution manual says to use At^2e^-t

>>9365050
UK has private universities, typically costs ~£9250 a year and literally everybody gets a student loan from the Govt' and leaves uni with ~£40,000 of debt to the govt that they dont pay back until they earn enough money

For a fractal on a 2D space, does its fractal dimension have to lie between 1 and 2?

Help /sci/, stuck on matlab

Trying to set initial conditions along a length (L) =1

e(x,0) = 0 for 0.00<= x < 0.25
e(x,0) = a for 0.25<= x <= 0.5
e(x,0) = a for 0.5< x <= 1

Pic is where I'm at so far, I can't get the syntax right

What's the point in using Bayes theorem when you could just swap the way the original formula to find A|B?

Like A|B = A^B/B
So why couldn't you just do:
B|A= B^A/A?
Or is it assuming you don't know A?

Please help me understand this problem about vector fields, /homework/

Given a scalar field, I'm supposed to find the x component of the unit vector in which I have to move for the variation of the scalar function to be minimal, given that we're initially in a point P

Do I have to find the gradient, then use it to build a unit vector by substituting the values of point P? Or maybe the opposite of the gradient since the function is supposed to be minimal.

>>9365157
I'm struggling with something really stupid in MatLab.
I basically have a function
f = x;
I want to get all the coeffs for it, so I type
coeffs(f,x,'All')
Yet I get an error about "Too many input arguments."
I just want to get the [1 0] vector out of it, what am I doing wrong?

I need the integral of a continuous function, but it has no closed form. I thought about doing a fourier transform, is that possible? The function is periodical and composed mostly of trigonometric functions, but as I said, there's no closed form integral of it.
Or do I have to use numerical integration?

I'm coding my first neural network. A simple classifier.

I have a training set with 3.000 x,y input points and each has the respective output class index (1, 2 or 3)

I convert the output to vector form, so class 1 is [1, 0, 0], class 2 is [0, 1, 0] and class 3 [0, 0, 3] therefore I have 3 output neurons with range (0,1).

Now, if input coordinates x and y are in range (-1.6, 1.2) then should I normalize them to (0, 1)?

>>9365054
2pi isn't rational buddy

>>9365178
difficult to say much unless you describe the function, a lot of such integrals actually can be written in "closed form" in terms of non-elementary functions (which themselves, of course, have no closed form in terms of elementary functions, but which have been well studied and often not too difficult to work with)

>>9362866
You've got cute handwriting faggot.

>>9362866
You don’t need to solve using undetermined coefficients. Literally where are you pulling that Ax^2+bx+c from?
Your answer is 0

>for a tree with v vertices, what is the minimum number of leaves?
for this I thought you could just connect each vertex in a line, then you would have a tree with v vertices and 2 leaves (the only vertices with degree 1 are on the ends). so 2 would be the minimum number of leaves for a tree with v vertices.

>what is the maximum number of leaves?
I thought about just making the tree like a star; have one vertex in the "middle" and have every other vertex connect to it. then you would have v-1 vertices with degree 1, and one vertex of degree v-1. so maximum number of leaves is v-1

is this right? I feel like I'm oversimplifying it

How hard is a multivariable calc class compared to calc 2? I'm sitting at 12 credits right now and this is the only thing I can cram into my schedule to get 16, everything else is time conflicts. Thing is I dont actually have to take it, but it is a prereq for a graph theory class I am interested in. My 12 credits are pretty heavy in the workload dept so I dont want to bite off more than I can chew, but I think I can swing it if it follows the difficulty curve of calc 1 to 2 and isnt a massive leap.

Spend two years trying to get a Finance degree or one year getting a marketing degree? I've already spent four+ years between CC and university.

>>9357587
HOLY SHIT
you just figured out Thiessen polygons!!!!!!
better publish it, and get your Fields metal!

>fell for the comp sci meme

I have done a year and a bit, found out from a professor I graduated in the top 4% of the class of last year, and now it bores me to tears. Considering philosophy at an elite school or mathematics at a second rate one (currently at a plate glass one in the UK, considering red brick ones for philosophy, probably would do plate glass if I chose mathematics)

What do? It's a boring autistic mess which I refuse to study any longer.

>>9365757
> so 2 would be the minimum number of leaves for a tree with v vertices.
Depends upon the definition of "tree" and "leaves". For a directed graph, I'd say 1 on the basis that the root node (in-degree=0, out-degree=1) isn't a leaf (out-degree=0).

Can I always use the limit comparison test in place of the comparison test?

Get a grip science monkeys this garbage doesnt explain shit

If a set of vectors is a basis for R3, does that set need to be 3 vectors big, and do they all need to be in the space R3?
For example could you have a set which spans R3 such as:
{(a,b,c), (d,e,f) (g,h,i), (j,k,l)}
or
{(a,b,c,d), (e,f,g,h)...}
?

>>9366891
>does that set need to be 3 vectors big
Every basis for R3 will have 3 elements.
>do they all need to be in the space R3
Depends on your definition of "basis", there is a general construction of free (real) vector spaces where any 3-element set is a basis for R3.

given a system of equations which has more equations than unknowns, when put into row echelon form, is it guaranteed to either be square or have more unknowns than equations (i.e. is it guaranteed to have a row or rows of all 0s?)

>>9367001
only if it's homogenous

>>9367003
thanks
so if it's a homogeneous system and the system is square when in row echelon, it has a unique solution, otherwise it has infinite?

>>9367009
the free variable theorem says that if there are more unknowns than equations in a homogenous system there are free variables and if there are free variables there are infinite solutions - doesn't say anything about square systems
A square homogenous system may have one or infinite solutions, you might still end up with a row of zeros

>>9367017
okay, thanks.
how can you tell if if a system has a unique solution or not then though?

>>9367028
homogenous systems always have the trivial solution so just convert to row echelon form and solve by inspection
no free variables - trivial solution
free variables - infinite solutions

If you have a vector v that is the result of the cross product of two other independent vectors, can you multiply v by -0.5 to give you a vector v' that is both orthogonal AND is part of a basis for some vector space R?

For instance, given the vectors t = (1, 2, 3) and u = (-1, 2, -1).
The cross product of t and u gives v which is
(-8, -2, 4).
By multiplying v by -0.5, we get v':
(4, 1, -2) which is also independent.

Does this apply to all cross products between two independent vectors?

>>9367168
I don't much about talking about vector spaces, but if
A = BxC
Then
A' = -0.5 * A = 0.5 * (CxB)
and they'd be collinear, so I dont know if you can make a space from that, if thats what you're asking

>>9367168
>If you have a vector v that is the result of the cross product of two other independent vectors, can you multiply v by -0.5 to give you a vector v' that is both orthogonal AND is part of a basis for some vector space R?
The cross product of two linearly independent vectors is always orthogonal to the two vectors you took the cross product of, and {t,u,t x u} always form a basis. Scaling a vector (by any nonzero scalar) doesn't change whether it's orthogonal to another vector or not so {t,u, c(t x u)} is also a basis.

given a vector (2x-1, 1, -3), why is the magnitude of it sqrt((2x-1)^2 +2) ?
Shouldn't it be sqrt((2x-1)^2+ +10)?

>>9367294
>given a vector (2x-1, 1, -3), why is the magnitude of it sqrt((2x-1)^2 +2) ?
It's not.

>>9367305
It is assuming the axiom of choice.

>>9365181
>class 3 [0, 0, 3]
You mean 1 in the last element?

>Now, if input coordinates x and y are in range (-1.6, 1.2) then should I normalize them to (0, 1)?
I don't think it matters for neural networks, since they will just adapt the weights to the inputs

>>9365172
>coeffs(p,var) returns coefficients of the polynomial p with respect to the variable var.
Remove the 'All'

>>9367294
[math] \lVert (a,b,c) \rVert = \sqrt{a^2+b^2+c^2} [/math]

>>9367423
Is this well defined though?

>>9367467
yes

how the fuck does plasma work?

What is the "smallest" algebraic closure of the rational numbers? Obviously the complex number is an algebraic closure but is there anything smaller?

What about Q extended with all the nth roots of every prime number and the square root of -1. Would that be enough?

Can someone explain to me how to derive a Mean Square Error(MSE) using Residual Sum of Squares(RSS) through Ordinary Least Squares(OLS)? I've coded an OLS estimator that outputs my beta. I don't know how to get MSE. Any help would be greatly appreciated, thanks.

I know how to compute and represent convolutions integrals, but I don't get what they suppose to mean, what's their purpose.
Can someone explain that to me?

Is it theoretically possible to charge a Li-SOCl2 battery under the right conditions?

They can rupture from heat right? So what if you kept it cold, like extremely cold? (CO2, Liquid Nitrogen, etc) and charged it?

I notice there are some 3.6v/2200mah batteries with a 560 wh/kg density, but not chargeable.

>>9367493
The complex numbers are the smallest.

>>9367496
What's beta? Are you talking about the MSE of a predictor or of predicted values?

>>9367493
>What is the "smallest" algebraic closure of the rational numbers?
https://en.wikipedia.org/wiki/Algebraic_number#The_field_of_algebraic_numbers

>>9367508
>The complex numbers are the smallest.
Wrong.

>>9367508
The complex numbers can't be the smallest algebraic closure of Q since it's not even an algebraic closure of Q to begin with.

>>9357587
Why isn't the American language a mishmash of English, German, Irish, Italian, Spanish, etc., as English is a mishmash of various languages?

What am I getting into as an EE?
I'm about to transfer to a 4 year from Community in 2 semesters. I thought differentials was easy and that's pretty much the only thing I know about electricity. Other than that, I took a really easy class on basic circuits.

>>9367467
Yes, why wouldn't it be?

>>9367493
>What about Q extended with all the nth roots of every prime number and the square root of -1. Would that be enough?
Nope. The roots of [math] x^5+x^2+1 [/math] are (by definition) algebraic, but you can't get them by using only by adding, multiplying and rooting rationals.

https://math.stackexchange.com/questions/760528/are-rational-numbers-numbers-constructed-with-a-root-algebraic-numbers

halp

Why this fucking nabla isn't in both sides of this equation? This is the last piece to me to really understand the line integral over a conservative field.

>>9367838
Wait, the nabla denotes the partial derivative over all the coordinates of G, that's why G is missing the '

Is that it?!

>>9367848
in components

[math] \dfrac{d}{dt} G(\sum_{i=1}^3 r^i(t) \, e_i) = \sum_{i=1}^3 \left( \dfrac{d}{dx^i}G(\sum_{i=1}^3 x^i \, e_i)\right)_{x^i = r^i(t)} \dfrac{d}{dt} r^i(t) [/math]

where the e_i are the unit vectors along the axes

>>9367848
in components

[math] \dfrac{d}{dt} G(\sum_{i=1}^3 r^i(t) \, e_i) = \sum_{i=1}^3 \left( \dfrac{d}{dx^i}G(\sum_{j=1}^3 x^j \, e_j)\right)_{\sum_{i=1}^3 r^i(t) \, e_i} \dfrac{d}{dt} r^i(t) [/math]

where the e_i are the unit vectors along the axes and after the spatial derivative, you plug the trajectory funciton r(t) back into the argument of G

>>9367883
>>9367866
Shit, I'm enlightened now. Thanks, I can die in peace now, there is nothing left to me in this dirty planet.

>>9367838
Chain rule.
[math] r [/math] is a function from [math] \mathbb{R} [/math] to [math] \mathbb{R}^n [/math]
[math] G [/math] is a function from [math] \mathbb{R}^n [/math] to [math] \mathbb{R} [/math]
[math] f:=G \circ r [/math] is a function from [math] \mathbb{R} [/math] to [math] \mathbb{R} [/math] .

The derivative of a function [math] f: \mathbb{R}^k \to \mathbb{R}^m [/math] at a point [math] x_0 [/math] , is symbolized as [math] D_{x_0} f [/math] and it is a linear map [math] \mathbb{R}^k \to \mathbb{R}^m [/math] .
Given a the usual basis (1,0,0...,0) , (0,1,0,...,0) , ... , (0,0,0,...,1) , you can represent this linear map with a m by k matrix. This matrix is called the Jacobian matrix. Its elements are the partial derivatives at the point [math] x_0 [/math].

In the simple case where [math] f: \mathbb{R} \to \mathbb{R} [/math] , we have [math] (D_{x_0} f) x = f'(x_0) x [/math] and its matrix is [math] (f'(x_0)) [/math] .

The chain rule says this:

[math] D_{t_0} f = D_{t_0} (G \circ r) = D_{r(t_0)} G \circ D_{t_0} r [/math]

You have [math] D_{t_0} r = \begin{pmatrix} \frac{dr_1}{dt}|_{t_0} \\ \vdots \\ \frac{dr_n}{dt}|_{t_0} \end{pmatrix} [/math]

and

[math] D_{r(t_0)} G = \begin{pmatrix} \frac{\partial G }{\partial x_1}|_{r(t_0)} & \cdots & \frac{\partial G }{\partial x_n}|_{r(t_0)} \end{pmatrix} [/math]

Your textbook/proffesor is retarded enough to represent [math] \nabla G [/math] as a vector. Don't do it this way.

Anyone care to help a brainlet out?
So I know almost nothing about math, just some high school shit, but I'm working on a shooter video game and I'm about to program this utility for the game to recommend the player's best mouse sensitivity.
It should work by having the player swipe his mouse across the mousepad to turn sideways, and that should equal one revolution. Of course it's not going to be perfect, so the idea is that after the first swipe, the player is asked to swipe again a few times in the same way. If the player swipes less than 360º then we increase the sensitivity, if the player swipes more than 360º we decrease it.

I think it's a good case for Bayesian statistics, we could consider the sensitivity as a normal distribution, or rather the probability that the best sensitivity is X. After the first swipe we get a general idea, but our confidence is low so the standard deviation sigma is high. Once sigma is small enough we can say that we're confident enough that his sensitivity should be the peak of the normal distribution.

My theory is that we could use all the sweeping tries to move the peak of the normal distribution left and right, and to also increase our confidence and reduce sigma.
Do you think this should work?

Why is sqrt(2)^2 = 2 but sqrt(-2)^2 is not real?

How do I actually solve this? Where can I learn more about these kinds of problems?

>>9368112
>Why is sqrt(2)^2 = 2 but sqrt(-2)^2 is not real?
Why would sqrt(-2)^2 not be real?

>>9368112

sqrt(-2)^2
= (sqrt(2)*i)^2
= sqrt(2)^2 * i^2
= 2 * -1
= -2

it is real.

>>9367976
Cringed.

>>9368134
>>9368136
Doesn't say so on my calculator

>>9368144
What does it say?

>>9368144
>>9368149
You must own a calculator that can't do complex arithmetic.

>>9368149
non-real answer. plugged it in on a TI-83

>>9368153
https://www.wolframalpha.com/input/?i=sqrt(-2)^2

>>9367500
It's a tool to solve integro-differential equations.

>>9368129
Anyone?

>>9368153
in "mode" change "REAL" to "a+bi"

Is there a way for me to write something in summation form based on whether its even or odd?
effectively I want to put this into maths notation
if (n % 2 == 0) n += 1;

Applying for MS programs next year in EE and looking at European universities (US citizen) to have some abroad experience. Any euros here know the best universities for EE in the UK, Germany, and Switzerland? Plan on MS and maybe PhD, but don't plan to go into academia afterwards if that matters.

I have no idea how to approach this question, shouldn't the volumetric flow rate remain constant? I'm able to solve V1=6m/s, and I get that I'm supposed to manipulate Bernoulli's equation to find H2 and V2, but I don't know how to go about doing it.

This is probably a really stupid question but how do you visualize division? I dont think i ever learned how to properly. Multiplication is easy. Multiplying x times y means taking x, making y rows of the quantity, then adding them all up (so of course it is repeated addition). How do you visualize this with division? Since it undoes multiplication it should be repeated subtraction but it isn't as clear when I try to visualize what's going on

>>9367505
>Is it theoretically possible to charge a Li-SOCl2 battery under the right conditions?

I'm quite sure you can't.
I'm not sure about the reaction that takes place, but SOCl2 is not like a metal that can be oxidated/reduced easily. And very low temperatures definitely won't help.

>>9357587
I've got a long flight ahead of me anyone recommend some books or documentaries to pass the time?

>>9368751
The Story of Maths featuring Du Sautoy
https://m.youtube.com/watch?list=PLuAlidJsus0nVYkA3vLKHYhE4VmmASpEY&v=mJbChZrXDJE

I studied 15 hours straight for 2 days in a row to finish one of my finals and now I feel dead inside. How do I make this feeling go away?

>>9368808
Exercise, play vidya, try to get laid, have a few drinks or smoke with friends, practice PDEs...

>>9368335
[eqn]n' = \begin{cases}
n+1,& \text{if } 2\vert n\\
n, & \text{otherwise}
\end{cases}[/eqn]

New thread
>>9368782