/sci/ - Science & Math

Continuing this brainlet-tier bullshit from the previous thread:
Someone, please explain intuitively (with formulas or something) why [math] \text{Arg}(1+e^{it})=\frac{t}{2} [/math] for [math]|t|<\pi[/math].

Also, I wanna know
-if the /sqt/ is automatically created by a robot OP
-when a new /sqt/ gets created, or what the conditions are for a new one

>>9503625
hello newfag, enjoying your stay?

>>9503664
I'm not so new as you think, retard.
My father is a lawyer who will sue the shit out of your attempt to slander me + I have watched every episode of Richard and Mortimer.

Now answer my question if you think you's so smart, motherfucker.

>>9503678
Brainlet.

>>9503623
Anyway, I already found it on some obscure French site, so for who wants to know:
[math] \text{Arg}(1+e^{it})=\arctan{\frac{\sin(t)}{1+\cos(t)}=\arctan{\frac{2\sin(t/2)cos(t/2)}{2\cos^2(t/2)}=\arctan(arctan(t/2))=\frac{t}{2} [/math]

>>9503703
What? You dickhead! Is that all you can give me? Look at your nose. Bitch ass white boi

>>9503718
Goddamn. Corrected:
[math] \text{Arg}(1+e^{it})=\arctan\frac{\sin(t)}{1+\cos(t)}=\arctan\frac{2\sin(t/2)\cos(t/2)}{2\cos^2(t/2)}=\arctan(\tan(t/2))=\frac{t}{2} [/math]

Could we disprove time travel by agreeing to send something back in time to a specific time and place immediately it's invented? If something appears, we'll keep trying to figure out time travel, if it doesn't, never study time travel since it won't ever become attainable?

>>9503798
This can only rule out specific forms of time travel. For instance, it may be that going back in time creates a new universe, and though you travel back to what is apparently an identical time, it's not actually the same timeline from where you came, and therefore can never send messages back to yourself.

>>9503612
Is this monkey the average sci poster?

>>9503916
>calling blacks monkeys
That's pretty intolerant of you.

>>9503623
see >>9503895

>>9503942
>Divide by G*4*m_a^2
why

>>9503979
Because F = G*4m_a*m_a \hat(r) / |r|^2
You want to isolate \hat(r) / |r|^2
Then you can isolated the unit vector \hat(r) to find direction and |r|^2 to get magnitude

>>9503955
Even though I suck at geometric proofs since I forgot everything, I am able to follow this one without drawing it. Zanks for the geometric proof.

[math]\displaystyle{x}^{4}+{32}{x}^{3}+{256}{x}^{2}-{289}={0}[/math]
Not math homework, how do I do this?
I got this quadratic from set
[math]\displaystyle{F}={\left\lbrace{x}{|}{\left({x}^{2}+{16}{x}\right)}^{2}={17}^{2}\right\rbrace}[/math]
Thanks

>>9503625
Anyone knows the answer to my μετά-post?

>>9503994
Oops
[math]\displaystyle{F}={\left\lbrace{x}{|}{\left({x}^{2}+{16}{x}\right)}^{2}={17}^{2}\right\rbrace}[/math]

>>9503994
>>9504002

My brother
Now you only need to take square roots, so get the solutions from
[math] {x}^{2}+{16}{x}={17} [/math] and [math] {x}^{2}+{16}{x}=-{17} [/math]

>>9504010
Holy cow, thanks! I am a moron.

>>9503994

[math] x^4 + 2^5 x^3 + 2^8 x^2 - 2^8 - 2^5 - 1 [/math]
x=1 is a solution by inspection

(x-1)(x^3 + 33 x^2 + 289 x + 289)
Try the factors of 289 = 17*17
x=-17 is a solution

(x-1)(x+17)(x^2+16x+17)
Solve the quadratic.

Can someone help me with gearing on my lathe?
I need as much gear reduction as possible from A to B.
The direction B turns in the end doesnt matter (You can reverse A direction accordingly) hard RPM numbers dont matter

>A is power from spindle with a non changing Duplex gear
>the "front" gear is 16 teeth and the "back" gear is 32
>S is a stud and bushing that stacks any 2 gears
>There are two studs and bushing sets even though only one in picture
>B is the screw that needs reduced, any gear goes on it. It has a spacer to choose "front" or "back" depending on how other gears end up
>the banjo the gear studs attach to moved up and down to accommodate different gear sizes.

Gears I have
20t
36t
40t (x3)
44t
46t (x2)
48t
52t (2)
54t (2)
56t (2)
64t (2)

There are supposed to be 3 studs, and im missing several small gears, and Im not supposed to have any duplicate gears. So im trying to make due with what I do have

The system is made to cut threads. It moves the cutting tool a certain amount per rotation to cut accurate threads.
When you slow it down enough it doesnt cut threads, it just becomes a feeding system to cut off the diameter which is what im looking for. Im missing gears for the stated feed in the manual, hoping to find something close enough

>>9504047
>Try the factors of 289 = 17*17
Why?
I know that x|289 is a necessary condition for rational solutions, but he didn't say that he was looking for rational solutions.

how does the Fiber Bragg Gradient system measure temperature? i understand how it produces strain measurements but research yields no results on temp.

How to actually take good notes when/after reading the textbook without spending much time?

I feel like I'm losing a pretty good amount of time when I write down notes

>>9504095
Just don't take notes.
Mark the important stuff on the textbook and comment when needed.

Could someone explain what exactly question 1 is asking. Is it about the intersection/unions of all the sets in the class or something else?

>>9504132
You are asked to show that the union of all the A's is contained in the union of all the B's when every A is also a B.

>>9504095
Just fill in missing steps in derivations and do the exercises.

>>9504132
{Ai} and {Bj} are collections of sets and {Ai} is a sub-collection of {Bj} therefore for a given Ax there exist a y such that By = Ax.

a∈∪Ai ⇔ ∃x a∈Ax ⇒ ∃y ∃x a∈Ax = By ⇒ ∃y a∈ By ⇔ a∈∪Bj
a∈∩Bj ⇔ ∀y a∈By ⇔ (∀x a∈Ax) AND (∀y st ∄x Ax = By AND a∈By) ⇒ ∀x a∈Ax ⇔ a∈∩Ai

Can someone help
Me understand this. I'm having trouble understanding the derivation of this parametric derivative. The F(x) represents the function of x, but how can the chain rule be applied to this. Can't some functions have multiple chain rules that need to be taken. For example, a function like x^2+2x, wouldn't you have to apply the chain rule twice for x^2 and also 2x which will have two dx/dt?

>>9504247
rotate your image mobilefag

>>9504247
>x^2 and also 2x which will have two dx/dt
Then you factor them out x^2 dx/dt + 2x dx/dt = (x^2+2x)dx/dt

>>9504268
I'm not sure I understand that. Wouldn't you have to use a chain rule on x^2 and also a different chain rule for 2x? >>9504258

Any recommendations for a babbies first dynamic programming tutorial?

>>9504305
https://www.amazon.com/Dynamic-Programming-Dover-Computer-Science/dp/0486428095

>>9504291
You get 2x dx/dt+ 2dx/dt = (2x+2)dx/dt

>>9504315
Thanks I'm starting to get it a bit.

>>9503612
I'm dusty on my control theory and I want to revise some of the basics before next semester.

I'm looking for some slow KA/3B1B-type playlist that goes IN DETAIL over basics of control theory. More specifically, I want to gain a better intuition about the different meanings of the location of poles and zeros in the complex plane.

F.e. if I look at a root locus plot or at the location of the poles and zeros of a filter, I would like to have a better immediate understanding of the characteristics of the transfertfunction and/or which "device" (or model thereof) I'm looking at.

Anyone have a suggestion? All suggestions are welcome even if they don't fit the criteria exactly.

>>9504047
How did you get two [math]2^8[/math]?
How did you get a 5th term? Sorry, brainlet here..

>>9504358
what does [math]2^8[/math] equal?

So theoretically if I punch myself in the jaw it will get stronger?

>>9504514
*groans internally*

>>9504514
That's pretty easy and you didn't try any work yourself. Show work and I'll help you.

>>9504514
A^6=(A^2)^2*A^2=A^2*A=A*A=A
AB(A^tB)^t=ABB^tA=A*A=A
A-A=0

>>9504524
Please don't respond to homework posts unless Anon puts work in.

Why don't we just increase the capability of the inferior parietal region of the brain to be better at math? Einstein's was 15% bigger than the average person.

How do I use "wrapfig" with the "enumerate" functionality of LaTeX?
It seems like if I just keep typing stuff, it just moves the picture down, as opposed to keeping it in place and placing the text around the image. And the whole "picture below the text" is weird because I'm technically creating the image before I type the "a's" (see pic related)

Is science/math worth studying on your own if you never actually plan to get a degree or anything like that? I have an interest in studying but I want to do it on my own terms really.

pic not related

>>9504643
yes I wish I could do this myself
it's a good hobby like playing an instrument

>>9504643
You say you have an interest in it, so do it. What fields are you most interested in? Read some seminal textbooks, watch some OCW lectures, search libgen for articles.

>>9504637
LaTeX thinks it knows better than you on where to place the image and will do whatever the fuck it wants, bitch.

/g/ autism strikes again.

How are u supposed to evaluate the limit 3a

How do you figure out the radius from this, when you don't even know the angle?

>>9504900
l'hopital's rule, it's a doozy but doable with calc I techniques

>>9504900
It looks too much for series expansion and "normal" problem solving, so I guess you need to use l'Hôpital.
Good luck differentiating that shit.

>>9504900
Taylor series: sin(x) ~= x, tan(x) ~= x
x3x/(4x)^2 = 3/16

QED.

>>9504941
>How do you figure out the radius from this, when you don't even know the angle?

r*sin(x/2) = 4
r*x = 8.5

r~=7.08981...

Can anyone recommend me a Stochastic Processes book?
One with an intuitive approach and with applications?

>>9504955
You do not need to differentiate the whole fraction, but the numerator and denominator separately, so it shouldn't be too hard. Unless you need to apply l'hospital multiple times

>>9504990
http://4chan-science.wikia.com/wiki/Mathematics#Stochastic_Processes

>>9504993
I hate wasting brain cells over applying the quotient rule and I see tan^2, so it looks shit to me.

>>9505000
As I said, you do not need to differentiate the fraction, only both parts of it, so no quotient rule, only chain rule

>>9503612
Sorry if the question is too stupid.
Is it true that for any matrix norm [math] ||I|| = 1 [/math] , where I is the identity matrix?
And if not, what about multiplicative norms i.e. such that [math] ||AB|| \leq ||A|| \cdot ||B|| [/math] ?

Please tell me where to start.

>>9505095
Seems to me like all p-norm's values, of the unit matrix E, monotonously grows with the dimension d.
||E|| = d^(1/p)
I.e. no.

Did you make a list of possibly norms and plug in E before asking?

>>9505122
That's horrible notation and nomenclature - who wrote that?

In any case, you start by plugging in, into J, the formulas for the expressions given right before it. The only nasty part is taking the square of the square root etc.

If you feel uncomfortable, test all formulas with two concrete vectors of dimension 2. Then, after you understand how the expressions look for those two vectors, solve it abstractly.

>>9505095
>Is it true that for any matrix norm ||I||=1 , where I is the identity matrix?
No.
Let [math] \lVert \rVert_1 [/math] be a norm where [math] \lVert I \rVert_1 =1 [/math] (e.g. the supremum norm [math] \lVert \rVert _{\infty} [/math] ).
Define a new norm [math] \lVert \rVert_2 [/math] such that for any matrix A we have that [math] \lVert A \rVert_2 = c \lVert A \rVert_1 [/math] where c>0.
You can easily check that [math] \lVert \rVert_2 [/math] is indeed a norm and that [math] \lVert I \rVert_2 = c [/math] .

>And if not, what about multiplicative norms
No. Do the same as above but with c>1.
But, it is true that [math] \lVert I \rVert \geq 1 [/math] since [math] \lVert I \rVert = \lVert II \rVert \leq \lVert I \rVert \lVert I \rVert = \lVert I \rVert ^2 \implies \lVert I \rVert=0 \lor \lVert I \rVert \geq 1 [/math] and since the 0 operator is the only one with norm 0 we have that [math] \lVert I \rVert \geq 1 [/math]

>>9505131
So I'm just plugging in c_1 and c_2 into the first J so that I get the J at the bottom right?
I've been trying that and can't seem to get anything to make sense

>>9505139
Oh, and if the matrix norm is an induced norm (these are always submultiplicative), i.e. the infimum of the m's where m is such that ||Ax||<= m||x|| (||A|| is a measure how much A scales the vectors), then I has norm 1 (it's obvious).

So I'm taking linear algebra at my community college, and the professor keeps doing this thing where she'll give us a problem, tell us to try and solve it, then after like 10 minutes back to lecture and explains why nothing we tried worked and that "this" is how it's done.
If I've already read the chapter, that time is just a waste, but if I don't, then I haven't been able to figure out the answer myself.
I guess I'm just wondering if this seems normal for math classes? Like, it doesn't necessarily seem too impossible yet, but once it's explained I feel like "well yeah no shit, of course that's how it works why did I try anything else"?

>>9505154
You need the right tools in your toolbox to accomplish a given task.
Sure, you could spend 10 minutes trying to drill a hole into a plank with the back of a hammer, but it's probably not going to work out too well.

>>9504643
Yes.
Especially at a bare minimum everyone should understand mathematical logic and the scientific method.

Also, number theory is always fun, but you should probably understand higher level courses first if you want to really grasp it.

If I sleep for four hours one night, will I need to sleep for 12 the next to make up the difference?

>>9505887
No. And sleeping more than 8-10 hours might make you more tired than just sleeping your normal 8

Brainlet here. I'm struggling with some basic math problem I was thinking about. Suppose you have a 50% chance (of winning the lottery or whatever) and you double that chance, what is the new probably?

a) 100% (0.5*2)
b) 75% (0.5+0.5*0.5)
c) 66.6% (going from a 1:1 ratio to a 2:1 ratio)

Feels like it should be b, but c seems to be true as well.

why cant we explore the deepest ocean floors for minerals n shit? its 2018 why do subs still suck

>>9505887
https://en.wikipedia.org/wiki/Sleep_debt

>>9505953
>double that chance
What do you mean by that?
Do you literally mean "double that chance"? If yes, then it's 2*50%=100%

>>9505953
>a) 100% (0.5*2)
double your chances
>b) 75% (0.5+0.5*0.5)
double your trials
>c) 66.6% (going from a 1:1 ratio to a 2:1 ratio)
double your odds

>>9505995
After thinking about it, you seem to be correct. My problem was what I answered 3 different questions:

a) doubling the chance of winning (1)
b) halving the chance of losing (0.75)
c) creating a scenario where I have twice as many wins as loses (2/3)

are there any non-flammable liquids/gasses one could practically use to create a continuously running cloud chamber? i had the idea that it would be neat to try to make a cloud chamber as a decoration piece but you obviously don't want to leave flammable gas/vapor in the chamber and have it be a fire hazard and it wouldn't defeat the purpose if you had to fill it when you wanted it to do anything

>>9506026
what's a cloud chamber?

>>9505953
There are multiple ways to interpret what you’re saying.
If you’re saying you play the same lottery twice, then your chance of winning once is still 50%.
This is called the Bernoulli trial, with p=0.5

>>9506030
lets you "see" the paths of ionizing radiation particles as they travel through it, due to the effect the particles have on the vapor inside the chamber

>>9506026
>but you obviously don't want to leave flammable gas/vapor in the chamber and have it be a fire hazard and it wouldn't defeat the purpose if you had to fill it when you wanted it to do anything

meant to say

>but you obviously don't want to leave flammable gas/vapor in the chamber and have it be a fire hazard and it _would_ defeat the purpose if you had to fill it when you wanted it to do anything

>>9506018
Oh shit, didn't see your post. Thanks for clearing it up while wording it more precisely then I did.

>>9506037
I just derped hard.
If you play the same lottery twice with p=0.5 your odds of winning once (and losing once) are 0.75.

>>9506062
nah you were right the first time, your chances of winning only once is 50%, but your chances of winning at least once is 75%

>>9505154
She's probably hoping for creative geniuses to come up with something clever so she can separate the wheat from the brainlets.

As long as you don't get punished with low marks, it's just an inefficient but fun way to find out who may be genius.

>>9505154
she wants you to try to think through different approaches to the problem so that when you learn the correct approach you'll have a better understanding of WHY it works and why other approaches don't

>>9506166
>inefficient

there's nothing inefficient about trying to work out a problem beforehand to gain a better understanding of it before learning the correct way to do it. you'll probably learn more/remember more through the process than just glossing over the correct approaches to problems as quickly as you can

*Warning* This thread might break.... First of all i am NOT a flatearther <--- correct term? nor am i part of any religion, i base my knowledge in : science, humans, feelings and facts, you can say whay you want about that statement. So here we go, i as many of you i was watching the spaceX launch a few days ago, and boy oh boy what a rocket huh? i also saw the cargo storage release of the tesla, (which some folks claim to be a studio) but forget all about the "it's real or it's fake" discussion i personally believe it was a good test of the rocket and it seemed to do it's job, but one is alowed to speculate right? so my question is dragging on and for that i'm sorry, i am also sorry for the spelling and grammer mistakes.. but surely you understand what i'm writing in some context.. so here we go, my question is not about the media faking it, it's not about if the whole thing is cgi, it's not about why we as a semi intelligent race launced a car in to space.. my question is quite simple, have anyone ever put a balloon into a vacuum chamber? i'm sure most have tried iif not, then maybe seen it. So could some explain how a 45-51 psi pressured tire on a tesla roadstar survives the vacuum of space :\? and shot me down all you want i don't care, i came to the science section on here for a reson, there is a lot of extremely intelligent peeps in here, and i guess my question will answer if i'm one of you.

The line integral [math] \displaystyle\int_C f\, \mathrm{d}S [/math] over the scalar field [math] f(\mathbf{r})=1 [/math] will give the length of the curve C.
Is there something equivalent for the line integral over a vector field?

>>9506244
they probably either drilled holes in the tires or made solid tires to put on the wheels

>>9506244
they could just underinflate the tires
since it doesn't have to drive anywhere or even support any weight they could just inflate them enough to give them some shape

>>9506244
>lol muh quirky intro!1!~
Get on with it

Actual brainlet question.
Where do i start with mathematics/physics and how do i progress from the simplistic things to quantum physics.
Never wanted to learn, grown up and realised my lack of knowledge is unacceptable as a human being. What books should i get etcetera

>>9505154
It's not easy to appreciate solutions to problems. A lot of mathematics appears to the modern student to have fallen out of the sky from nowhere and doesn't give them an opportunity to explore the space and see what kinds of problems stand in the way. I think she's doing a great service to her students.

I was testing how i could hold myself up with friction with a rope on a door and want to know about how much of my full weight was on my waist? I weigh 200 lbs and I was pulling the tip but just enough to hold me up.

I figured that only real weight that wasnt pulling against the loop on my waist was my arm and it weighs about 12 lbs so is it safe to say that about 190lbs was on my waist?

I know this may be a stupid question but i was just curious how this works, thanks

>>9503612
>>9503612
I took a class that touched on vector calculus about a year ago, and I still have some questions

If I'm given a surface,
[math] x(\alpha, \beta)[/math]
And I know that the unit normal is given by
[math]
\frac{d^2x}{ds^2} = k\cdot \vec{n}
[/math]
How do I actually calculate the unit normal? What does it mean to differentiate with respect to the arc length?

And what do the "First/Second Fundamental Forms" even mean? I'm given this equation for one of my classes:
[math]
|\frac{d^2x}{ds^2} |= 1 = Ep^2 + 2Fpq + Gq^2
[/math]
Where
[math]
E = x_\alpha \cdot x_\alpha\\
F = x_\alpha \cdot x_\beta\\
G = x_\beta \cdot x_\beta\\
[/math]
But I have no idea where to even begin for how to parse this expression or understand it. Like, why does the unit normal have anything to do with taking the derivative in a direction of the curve?
Please help a moron out.

>>9506594
The first fundamental form is the riemannian metric.

>>9504055
So ive been playing around with the gears in a calculator with known gear configurations.
I know I said I didnt want hard numbers but

>gear ratio of 51.77 : 1 gives you tool speed of .0024 per inch
>35.84 : 1 = .0035
>24.96 : 1 = .005
>17.6 : 1 = .0071

Is there a formula here or does there need to be more information?
Say I have a ratio of 19.91 : 1, what would the tool speed be and how would I figure it out for other gear ratios I make up?

>be me
>4 week winter break
>fap.webm playlist
>French narrator "4 weeks layter
>now be me 4 weeks into semester
>motivation&concentration.exe not found

Wut do lads how do reboot or am I perma tarded now?
Inb4 degenerate

what the fuck does a "confidence interval" actually mean?

Say if we have a 99% interval of [5,10], would it be fair to say "we predict with 99% confidence that our population parameter lies in between these numbers?"

>>9507071
https://en.wikipedia.org/wiki/Confidence_interval#Meaning_and_interpretation

>>9507071
https://en.wikipedia.org/wiki/Confidence_interval#Misunderstandings

>>9505183
>and the scientific method

But that's a meaningless buzzword

How much progress should I be making per day self studying mathematics? I read about 20 pages of my linear algebra textbook a day and feel like I’m progressing to slowly. Any for tips making my self study more efficient?

>>9507428
>using pages in a book as an indicator of progress

You are doomed anon

> in a static (memoryless) system, the output at any time depends only on the input at the same time, but not on the past time history of input
>in a time invariant system, an arbitrary time shift of the input produces exactly the same time shift of the output
are "time invariant" and "static" systems the same thing?

>>9507450
It was really supposed to be a sort of benchmark, most people here have probably studied linear algebra so they know how much material + exercises are contained within 20 pages of a typical textbook. I know it isn’t a good indicator of progress but it’s better than nothing.

Help me with this equilibrium question

Why the torque equation for this problem is [math]mgdcos\theta-Fn_{2}Lsin\theta=0[/math]?

I understand the torque equation for [math]Fn_{2}[/math] but why the weight equation have [math]cos\theta[/math] on it?

>>9507428
Depends how dense it is. You could spend 1 hour working out one page.

>>9507509
[eqn] \sin(90°-\theta) = \cos(\theta) [/eqn]

>>9507469

No.

Static/memoryless: F(a(t),t) = a(t)/2
T.i.: F(a(t), t) = a(t)/2 + a(t-1)/4 + a(t-2)/8 [e.g. rolling window average]

>>9507531
But why I should use this? Its to make the weight vertical to the L line?

>>9507535
to calculate torque, we need to find the component of force that is perpendicular to the axis of rotation, this is easily done with trig functions and can be found with [math] \sin\phi [/math], the only issue is that we do not know what [math] \phi [/math] is, but we can infer it from [math] \theta [/math] by assuming a right triangle

Whats the name of this type of diagram
>example pic shows how voters changed their party after 4 years

I want to show how a sample of people change their group after x years

Anyone know of a website that would show me what the sky looked like in 4000bc? I've found a website that shows current star maps, but only as far back as 2012.

>>Are there any algorithms for accurately calculating rates with data bins? For example say I want to measure heart rate and get a number every 2 seconds, what's a good way to get an accurate result?
>What is the number you get every 2 seconds when measuring heart rate?
Well that depends on whether heart rate is increasing or decreasing, which is the thing you'd like to know as quickly as possible but not with too much noise.

>"no three of the four points are colinear"
This means if I pick 3 of the 4 points together, they wont be colinear, right?

>>9503612
>questions that don't deserve their own thread.

>>9507910
yes, and this will be so for any three you pick

is there some mathematical correct name for square that is rotated 45° and rests on one of its points?

Do I just say square?

>"Prove: Four points in a projective plane in general position implies no three of them are collinear"
Proof: [math][v_{1}],[v_{2}],[v_{3}],[v_{4}]\in P(V)[/math] are in general position therefore of the representative vectors, [math]K =\{ v_{1}, v_{2}, v_{3}, v_{4}\} , S=\{v_{1},v_{2},v_{3} \}\subset K [/math] are linearly independent. I'm stuck here. I know that they'll correspond to distinct points in the projective plane. Any two projective points can have a line formed between them, thus collinear. So simultaneously, [math]v_{1},v_{2},v_{3}[/math] cannot be collinear. Is this the correct reasoning for stating that any combination of three of the four cannot be collinear?

>>9508017
my problem is that [math][v_{1}]=[v_{4}][/math] breaks this reasoning. I feel like there's a slight nuance I'm missing.

>>9507982
Diamond

Is my proof of [math] \Re\lim_{z\to z_0}f(z)=\lim_{z\to z_0}\Re f(z) [/math] correct? i cant find anything online apart from a proofwiki page with a different proof/theorem, which requires continuity

Let [math] \lim_{z\to z_0}f(z)=\ell [/math]. Then [math] |f(z)-\ell|<\epsilon [/math] whenever [math] 0<|z-z_0|<\delta [/math]. But if [math] |f(z)-\ell|<\epsilon [/math], then

[math] \begin{align}\epsilon &>
\frac{1}{2}|f(z)-\ell| + \frac{1}{2}|\overline{f(z)}-\overline{\ell}|\\&\geq |\frac{f(z)-\ell}{2} + \frac{\overline{f(z)}-\overline{\ell}}{2}|\\&=|\frac{f(z)+\overline{f(z)}}{2} - \frac{\ell+\overline{\ell}}{2}|\\&=|\Re f(z)-\Re(\ell)|
\end{align} [/math].

So for all epsilon whenever delta ...

>>9507037
Well, I feel if you didn't have that French narrator following you and causing you to time-jump, you could take it a bit slower.

In all honesty, just try finding something you're looking forward too every day. Pick up a hobby (besides watching anime, like reading or exercise) and try to make a schedule (and remember to stick to it! A schedule you don't follow is as useless as you can get!)

>>9507037
stop masturbating and lift weights

Is neoteny a good indicator of human evolution, and if so why has Europe not been eclipsed by Asia?

What are the best ways of showing convergence/divergence [math]sum \ln(a_{n}) [/math] ? Suppose I wanted to use direct comparision or limit comparison, what are the best choices to compare with in general?

Prove that [math]f(x) = \displaystyle \sum_{n=1}^{\infty} \frac{1}{x^{2}+n^{2}}[/math] defines a continuous function on [math]\mathbb{R}[/math].

First I note that [math]f_{n}(x) = \frac{1}{x^{2}+n^{2}}[/math] is continuous for all [math]x\in\mathbb{R}[/math] and [math]n\in\mathbb{N}[/math]. So it suffices to show that [math]f_{n}(x)[/math] converges uniformly, correct? That is:
[math]\forall \epsilon >0\hspace{0.1cm} , \hspace{0.1cm}\exists N\in\mathbb{N}, \hspace{0.1cm}\text{such that},\hspace{0.1cm} \forall n\geq N \hspace{0.1cm}\text{and}\hspace{0.1cm} \forall x\in \mathbb{R} ,\hspace{0.1cm} |f_{n}(x) - f(x)| < \epsilon [/math]

[math]\displaystyle\lim_{n\to \infty}f_{n}(x) = 0[/math]

So [math] \left| \frac{1}{x^{2}+n^{2}} - 0 \right| = \frac{1}{x^{2}+n^{2}} \leq \frac{1}{n^{2}} \leq \frac{1}{n} < \epsilon [/math]

I don't think I'm right? Assuming so, let [math]N = \text{ceil}(\frac{1}{\epsilon}) + 1[/math]. So letting [math]\epsilon = 1[/math], [math]N = \text{ceil}(\frac{1}{1}) + 1 = 2[/math], so [math]|f_{2}(x) - 0| < \epsilon \implies \frac{1}{x^{2}+4} < 1 \implies 1 < x^{2}+4 \implies x^{2} > 3 [/math], which isn't true for all [math]x\in \mathbb{R}[/math].

What should I have done? I think my problem is in the uniform convergence proof, probably with the steps: [math] \frac{1}{x^{2}+n^{2}} \leq \frac{1}{n^{2}} \leq \frac{1}{n}[/math], but I'm pretty new at this and can't tell.

>>9508684
>[math] \frac{1}{x^{2}+4} < 1 \implies 1 < x^{2}+4 \implies x^{2} > 3 [/math]
oh dear...this is a pretty big blunder.
[math]x^{2} > -3[/math] is what is should be. Is the argument sound then?

>>9508684
Nibba |1/(x^2+n^2)-1/(y^2+n^2)|=|x-y||x+y|/((x^2+n^2)(y^2+n^2))

|x+y|/((x^2+n^2)(y^2+n^2))<|x+y|/n^4

the series 1/1^4+1/2^4+....+1N^4+.... converges to some C, so

|f(x)-f(y)|<|x-y||x+y|C, from this you get continuity

>>9508684
You're looking at [math] f_n(x) [/math] when you should be looking at [math] \sum_n f_n(x) [/math] m8. Try using the Weierstrass M-test or w/e it's called in english

>>9508816
>>9508828
shit, I realized this soon after. Thanks, will go back at it

I'm currently working through Apostol's Calculus vol 1 as my first time learning calculus, I find the problems hard, especially the ones involving proofs, how can I get better/learn how to write them? Or am I working through the wrong book?

Is there any point in getting a PhD in mathematics if you have mediocre grades? Conversely, does getting good grades mean you will be a successful PhD student?

>>9508881
If you're learning calculus to practice it, proofs are of very limited value. If you're learning calculus to flex your e-peen on stackexchange/reddit, then you're probably best off going back to other math you're strong with and practicing proofs there.

>>9508881
learn calculus non-rigorously before you learn it rigorously. it'll be MUCH easier then.

>>9508905
Do you have a good research ethic and fresh ideas to bring to the field of your choice? Can you prove most arbitrary things presented to you, or at the very least understand how you'd go about it? Almost certainty, one with good grades will have an advantage at the aforementioned, but there are always exceptions (albeit, few).

How do I graph a torus in desmos?

>>9508941
Would it be a good idea to focus on improving these skills, rather than trying to maintain a good GPA as an undergrad?
I understand that a better GPA allows me to enter a better graduate school, but if what I want to do is research anyway, will spending too much time on maintaining arbitrary grades help me in this?

How do I prove that:
[math]1 + \frac{1}{2} - \frac{1}{3} -\frac{1}{4} + \frac{1}{5} +\frac{1}{6} - \frac{1}{7} -\frac{1}{8} + \frac{1}{9} + \frac{1}{10} - \frac{1}{11} - \frac{1}{12} + \dots [/math]
converges conditionally? I can tell you that it doesn't converge absolutely, since [math]|a_{n}| = \frac{1}{n} [/math], but I have no idea where to go from here

>>9509049
What have you tried?

>>9509057
First looked to see if I could use the alternating series test, but the terms aren't decreasing. That was my only hunch, and as I said I'm not sure where to go. Could you provide a hint?

>>9509049
Isn't that your proof? Show that that series converges using the alternating series test and that the other version of it doesn't converge with the same test.

>>9509069
>but the terms aren't decreasing
?

>>9509069
Well I guess you'll just have to find the sum.

if this guy was 100 pounds and pulled himself upwards wouldnt he have to pull with 200 punds of force?

And would the weight of his bottom on the seat be 100 lbs at all times even as he was raising himself up?

>>9509069
If you are given a series (-1)^n / n you can show it converges by taking the absolute value and showing that that series has a limit as n --> infinity = 0 and that the terms are decreasing (d/dx) 1/n = -1/n^2 always negative therefore always decreasing. Thus the series (-1)^n / n converges but we know it doesnt converge absolutely because 1/n is a divergent series (harmonic series) therefore the series converges conditionally.

>>9509089
>>9509092
how are they decreasing?

>>9509138
>how are they decreasing?
Please re-read what the alternating series test says.

>>9509147
AST only cares about the non-alternating [math](a_{n})[/math], doesn't it?

>>9508881
work through a proofs book
http://4chan-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning

>>9504955
>>9504952
I think we're supposed to manipulate the expression so that it contains "sinx/x" or "1-cosx/x" since the limits of those are already known.

I've spammed lots of trig identities and multiplying conjugates but nothing as worked yet.

How do you guys manage your time with class work and extracurriculars? I'm having a bad time with both of them and any help would be appreciated.

>some retard asks a question on math stackexchange
>give a complete answer
>he says oh I didn't mean that question I have edited
>get downvoted into oblivion because your answer is now irrelevant
non-anonymous communities are complete fucking cancer

>>9509228
>extracurriculars
i used to have those before grad school ;_;

>>9509228
>extracurriculars
lmao

>>9509228
What are you majoring in? What are your extracurriculars? What interests you and what are your goals?

i just cut my **dick** fapping and its not very painful but very worrying. what should i do to protect myself from any diseases? im lifting weights tommorrow and the day after that ill go running and spear throwing. How can i avoid infection as painlessly as possible?

>>9509527
To be certain of your safety, I'd advise cauterizing the wound at minimum.

My question: where does philosophy dip it's heavenly toes into the cool, analytic waters of science? of course, the scientific method itself, and analytical reasoning, is philosophy in and of itself, but hopefully you uunderstand I'm looking for these gray areas, like empiricism, analyticism, etc etc

who are the original authors of the philosophy of science? Aristotle? plato?

anyone work with cell cultures in a biosafety cabinet?

gibco thermofisher advises to place lids open-side down

but the people in the lab i joined say to place lids open-side up

what do?

>>9509527
Just wash it and wear clean underwear, you'll be fine

If you're really worried put some neosporin on it, but dick-skin heals really fast. The best thing you can do is not manipulate it any more than necessary for a few days

I'm assuming it's a small tear

help me bros i dont understand how to do this line integral in the complex plane and i feel like it should be easy

>>9509637
What have you tried?

>>9509639
i just dont really understand the question desu.

How many people do you personally know who study science for the sake of science or understanding the universe or something similar?

My university only has a handful of US born professors in physics (plenty in chem, engineering and math tho). They had to pull in foreign students and professors to teach.

Why is the state of science so abysmal? Has this problem always existed?

>>9509741
>being this nationalist
science is bigger than all of us

>>9509744
how is making the observation that most of my phys dept is foreign "nationalist?"

im just wondering why theres a lack of us born ones. i guess its kinda always been that way tho, lots of great physicists migrated here

>>9509620
modern philosophy has completely diverged from empiricism and the search for truth and such. its a clusterfuck in a hedonistic playpen where no rules exist. nietzsche cut the achillies tendon of logic and everyone since has been trampling on its dead body

so youll have to go back a bit with a few exceptions like popper and feynman.

even early on in philosophy there was some wankery going on. like plato didnt care for experiments or utilitarianism, he was in some mystical abstract universe a lot.

thats not to say everything plato did was junk, just some of his scientific commentary.

my fav science philosophers are feynman, newton and einstein (actual einstein, not the popsci version of him, ex: einstein himself denied black holes and time travel)

>>9509646
parametrize it

>>9509757
It seemed like you were implying that the state of science is "abysmal" because of the foreigners and that they don't "study science for the sake of science or something similar".

>>9509637
∫zdz = ∫ x+iy ds

a) ∫e^iθ ie^iθ dθ = (i-1)/2
b) ∫ 1+iy dy - ∫ x+i dx = 1+i/2 - (1/2+i) = (1-i)/2

Show that if A is a square invertible matrix and A^3= A then A is its own inverse

I feel like a brainlet. I dont even know where to start.

>>9509770
oh. thats a fair interpretation i suppose. i more meant like what is the us doing wrong such that no one wants to go into academia here. everyone goes into applied fields

>>9509794
>I dont even know where to start.
>A is a square invertible matrix

>>9509797
still stumped.

>>9509794
do something to both sides>>9509838

>>9509840
Multiply by A^-1?

>>9509842
well, what do you get if you do that?

>>9509845
A^3(A^-1) = I

>>9509849
simplify it more

>>9509851
Oh yeah my bad.

A^2*I = I

Right?

>>9509856
yeah except without the *I

>>9509860
I dont really understand how this shows A is its own inverse. This is my second week in Linear, and its been kinda weird to me.

>>9509863
look at the definition of inverse

>>9509870
Ohh shit i get that. AB = I = BA. B=A in this one. Damn i feel dumb.

>>9503612
I have a difficult time working mathematics fast enough for testing...but I have zero issues with the concepts or actually working them given enough time.

Am I wasting my time in an attempt to get a PhD in a field that has a good chunk of Calculus based Physics?

>>9509895
Depends how fast you can type/program

>>9509895
What field?

Theoretical physics is really limited in what you can do. Not only in the sense of employment but in the sense that theres no direction for it because our experimental capabilities have hit a wall.

And what do you mean youre slow at calc based physics? Do you know numerical methods? Even if youre going for a heavily theoretical field, chances are youll have to do applied/computational work where the computer does the calculus for you.

If youre just worried that youre a shitty test taker, you can still do a phd in the US. Test scores become less important the higher you go. Put together some quality research, do something related on the side (like a presentation at a physics conference). Thatll go a long way in making up for your test scores.

Is there a /sci/ certified guide on the cleanest/most professional way to write proofs?

>>9510023
>Is there a /sci/ certified guide on the cleanest/most professional way to write proofs?
Yes, you do it in Coq.

>>9503612
How do I go about solving this problem? I don't get how to find t from the point given.

>>9510840
Forgot pic. Here is the problem. I'm not asking for someone to do my homework for me, just explain what I need to know or point me in the right direction please.

Does rain water contain chlorine? Would H2O from the atmosphere deposited in ice in a freezer contain chloride ions?

I'm looking for drinkable (in the ml, won't be drinking more than 1ml a day) water without any chloride ions. Looking to dilute a chemical that's attacked by chloride ions in tap water. As far as I'm aware there's no deionised water sold for drinking purposes, and I've read deionised water on the market for cars and things like that have trace amounts of heavy metals.

>>9510842
I mean, you should be able to tell us a, at least?
For the other two, keep a picture of the unit circle with you.

>>9510856
I'm clearly missing something. The way I understand it is this, t is a real number which when traveling that many units from (1,0) places is at point P. I don't even know how to find t in the first place from the information given. I don't know exactly where (-3/5,4/5) falls on the unit circle. Am I supposed to use the distance formula to find the distance between that point and (1,0)?

What equation am I trying to find?
I rewrote
||a+b||^2
as
||a||^2 + 2a(Transpose)b + ||b||^2

I kind of get what the problem is saying but I don't understand what I'm supposed to write.

>>9509757
thanks anon. I'm just trying to build myself up a solid curriculum in philosophy. Unsubstantiated claims really rustle my jimmies, and a lot of writers (like Nietzsche) are full of that mumbo jumbo (or so it seems, I haven't really read much yet). I guess I'll check out /lit/s guides and keep your thoughts in mind.

>>9510852
>Does rain water contain chlorine?
no
>Would H2O from the atmosphere deposited in ice in a freezer contain chloride ions?
only very small traces e.g. if there were tap water stains on the ice cube tray before filing rain water into it
>I'm looking for drinkable (in the ml, won't be drinking more than 1ml a day) water without any chloride ions.
just buy some that aqua dest or distilled water in the super market, it's clean. it's distilled, how are any heavy metals supposed to go into it

>>9509178
It cares about the absolute values of all a_n
Obviously the a_n are not decreasing if they have alternating signs

>>9506594
THE first fundamentals form Is the line element on your surface or the riemannian metric. It's an inner product so it isn't invariant under change of coordinates (reparametrization invariant).

Help with pic pls?

How does "A is B" translate logically?

I think that "A is B" implies that there can be Bs that are not A, while still being True. That sounds more like an implication than a conjunction, because a conjunction would be False for Bx True but Ax False.

That would mean that a) is correct and b) and c) are wrong

Consider the sequence [math]a_{n}[/math] defined recursively by [math]a_{1} = 1[/math], [math]a_{n+1} = \frac{a_{n}}{\sqrt{n}}[/math], for all [math]n\geq 1[/math]. Does [math]\displaystyle \sum_{n=1}^{\infty} a_{n} [/math] converge? So I just directly apply the root test?
[eqn]\lim_{n\to\infty} \left| \frac{a_{n+1}}{a_{n}} \right| = \lim_{n\to\infty} \left|\frac{1}{\sqrt{n}} \right| = 0 < 1 [/eqn]
so it converges absolutely ? This seems too simple.

>>9511007
>it's distilled, how are any heavy metals supposed to go into it
I don't know the chemistry behind it, but supposedly deionised is more susceptible to peeling off heavy metals from pipes and containers or even during the deionisation process itself. Not sure if it's true though.

Prove that [math]\lim a_{n} =0 [/math], given that [math]\sum a_{n}[/math] converges.

The series converges, so the sequence of partial sums converge. Thus, the sequence of partial sums are Cauchy. For all [math]\epsilon >0[/math] there exists [math]N\in \mathbb{N}[/math] such that for all [math]n\geq m\geq N[/math], [math]|a_{m}+a_{m+1}+\dots a_{n}| < \epsilon[/math]. From this, [math]|a_{m}+a_{m+1}+\dots a_{n}| \leq |a_{m}|+\dots + |a_{n}| \leq |a_{n}| < \epsilon \implies \lim a_{n} = 0[/math]

good, or nah?

If I have a series, [math]\sum (\frac{n^{2}+n^{3}}{n})[/math], is this the same as [math]\sum n + \sum n^{2} [/math] ?

>>9511676
sum a_n + b_n = sum a_n + sum b_n whenever sum a_n and sum b_n are convergent

>>9511701
Alright, thanks.

What's the best way to show
[eqn]\sum \frac{n\sin^{2}(n)-3n^{2}\cos(n)}{2n^{4}-1} [/eqn] converges absolutely? Perhaps direct comparison test with those factors of [math]n[/math] tacked onto the trig functions and the denominator ? At first glance then I'd compare it with the convergent [math]\frac{2}{n^{2}}[/math], but I wouldn't know how to justify this in say a test condition.

>>9511772
so something like, because of the natural bounds on sine and cosine, for large [math]n[/math] we have [math]|\frac{n\sin^{2}(n)-3n^{2}\cos(n)}{2n^{4}-1}| \sim |\frac{n - 3n^{2}}{2n^{4}-1}|[/math]

does [math]\displaystyle \int_{C} B\cdot d\mathbf{s} = \mu_{0} I [/math] make sense if I'm calculating magnetic circulation about a unit circle in the yz plane?

Made a video on a very basic tasked to be solved and discussed without the help of all too strong analysis tools

https://youtu.be/QoJIAzGTLwo

>>9511772
You can find an expression which is strictly larger than the sum (without sine and cosine) and which also converges, then this one will converge.

Doing Linear Algebra and Linear Map Matricies are confusing the fuck out of me. I understand how to do differential equations and manipulate matricies and everything but this is, idk, I'm probably fucking retarded.
[math]$V$ and $W$ and finite-dimensional and $T \in L(V,W)$. Find a basis of $V$ and a basis of $W$ such that with respect to these bases, $M(T)$ entries are 0 except for row $j$ col $j$ equal 1 for $1 \leq j \leq $ dim range $T$[/math]
I've got no idea what to do with this. I even looked up the solution and I still don't know what the fuck is going on.
We have a basis for V of v_1 ... v_n and a basis for W of Tv_1 ... Tv_n. Okay, good so far.
Use fundamental theorem to extend them. Okay, I don't know why but okay.
Then that somehow does the trick? I don't understand

What you guys do when you're supposed to read a lenghty book? After a few pages I get distracted and bored

>>9512073
Set a 5 minute timer and starting reading (really focused reading) until the time is up.

How do I show [math]\displaystyle \sum_{n=2}^{\infty} \frac{1}{n\ln(n)}[/math] diverges WITHOUT using the integral test (i.e. one of the comparison tests)

>>9512125
Can you use Cauchy's condensation criterion? (not sure if it's called that in English)

I'm not in school, haven't been for some time now.
I'm thinking of going back and becoming a nutritionist
how could I contact someone who would be able to answer basic questions about the field of nutrition?

>>9512129
So
[math]\displaystyle \sum_{n=2}^{\infty} \frac{1}{n\ln(n)}[/math] diverges if and only if [math]\displaystyle \sum_{n=1}^{\infty} \frac{2^{n}}{2^{n}\ln(2^{n})}[/math] diverges. Ah, it makes sense now, thanks.

>>9512154
You're welcome. Good luck!

>>9512160
Now, in general if I had
[eqn]\sum_{n=2}^{\infty} \frac{1}{n(\ln(n))^{p}}[/eqn]
for some [math]p\in \mathbb{R}[/math], and had to determine the values of [math]p[/math] that make this converge, I could demonstrate that [math]p>1[/math] by the same test, yes?
Since,
[math]\displaystyle\sum_{n=2}^{\infty} \frac{1}{n(\ln(n))^{p}}[/math] converges/diverges if and only if [math]\displaystyle \sum_{n=1}^{\infty} \frac{2^{n}}{2^{n}\ln(2^{n})}[/math] converges/diverges. This simplifies to
[math]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^{p}\cdot (\ln(2))^{p}}[/math], which is just a p-series times some constant, which we know to converge for [math]p>1[/math]. Is this reasoning sound?

>>9512206
there's a math previewer available dude just click the "tex" in the top left of the reply box

>>9512206
It seems sound to me. However it has been a long time since I last manipulated such sums, so maybe someone else can double check. But yeah, seems like your reasoning works.

>>9508017
In general position means not overlapping, senpai

how do i find the interval of convergence for

\sum_{k=0}^\infty \frac{x^k}{k!}

how do i prove

[math]\sum_{k=0}^\infty \frac{x^k}{k!}={e^x}[/math]

is convergent?

>>9512283
Ratio of two consecutive terms of the serie.

>>9511278
my dudes

please

thanks

>>9512253
thank you

>>9512294
holy shit, what is that from? toy story?

>>9512253
so..does this mean I'm right?

>>9505122
I'm still stuck on this problem, please send help.
There's also #4 which stresses me out to even look at.

>>9511493
Wrong, the sequnce of partial sums must exist since the series converges, and [math]a_n=s_n-s_{n-1}[/math]. Let [math]\epsilon>0[/math] be given and suppose [math]\lim s_n=s[/math], find N so that for all [math]n-1\geq N[/math] we have [math]|s_n-s|<\epsilon[/math] then [math]|a_n|=|s_n-s_{n-1}|=|s_n+s-s-s_{n-1}|\leq|s_n-s|+|s-s_{n-1}|<2\epsilon[/math].

>>9508187

I don't know how to write math on here but:

I feel like you could prove this more directly by writing f as g + ih, where g and h are both real, and then you immediately get lim f = lim g + i lim h, where lim g and lim h are also both real. And then you're just done, I think?

Your proof looks correct to me, anyway.

can someone help me with what is meant by "canonical" in this context?

>>9512656
Just come up with the most obvious homomorphism you can find

How does memory loss work?
I get this autistic thought process that if I were to lose my memory I wouldn't remember anything going on right now because this counts as a memory for some reason.
Obviously that's not how it works but for some reason I can't let go of memory in relation to time.
I just can't wrap my head around it though.
I guess it relates to persistent consciousness as well.
I'm stupidly thinking that if something in the future affects my memories of the past then I should be at that point already.
Like if a document were to lose half its pages.
I guess.
Man this is more stupid than I thought.

I am working on an algebra assignment, we need to make a 3D simulation with our own matrices. I think I got everything right, but the axis confuse me during rotation.

I got a vector of (0, 3, 0). When I rotate yaw on 90 degrees (converted to radians), I expect the new position of the vector to be (3, 0, 0), but it's (-3, 0, 0) instead. In order to get the expected result, I have to roll 180 degrees.

Is the z-axis supposed to point downwards when all axis are rotated to zero degrees?

>>9512656
> G/N -> G/M

99.9% sure that's a typo and should be G/N -> H/M

>"canonical" in this context

Obvious redefinition

Is there a maximum AC frequency that a conductor can "support"?

Is there any evidence of phytoestrogens having no effect on men, having an effect or is it inconclusive?
>t. question spurred on by lurking a butthurt "soyboy" argument on /v/ where some e-celeb political rant was cited as "evidence" that it's harmless

>>9513209
http://www.fertstert.org/article/S0015-0282(10)00368-7/fulltext
>Soybean isoflavone exposure does not have feminizing effects on men: a critical examination of the clinical evidence

For a C^2 function, is it immediately clear that
[math] \frac{\partial^2}{\partial z \partial \bar{z}}=\frac{\partial^2}{\partial \bar{z} \partial z }[\math]?

[math] \frac{\partial^2}{\partial z \partial \bar{z}}=\frac{\partial^2}{\partial \bar{z} \partial z }[/math]

Say I have a hot pan. If I want to produce more steam when I add water, would it be better to add hot water than cold water? My assumption is that the hot pan has only a finite amount of kinetic energy before it cools down, so it would be better to add hot water since it will require less energy for it to reach boiling point than cold water. Is that correct?

Given an invertible linear map [math]T:V\to V[/math], I'm trying to show that if [math]v\in V[/math] is an eigenvector then [math][v]\in P(V)[/math] is a fixed point.

T is linear, so there exists a corresponding matrix [math]A[/math] such that [math]T(x) = Ax[/math]. [math]v[/math] is an eigenvector, so [math]Av = \lambda v[/math]. Since T is invertible there is a corresponding projective transformation, [math]\tau : P(V) \to P(v) [/math], such that [math]\tau ([x]) = [T(x)][/math]. It follows that, [math]\tau([v]) = [T(v)] = [\lambda v] = [v][/math], by virtue of homogeneous coordinates. Is this reasoning sound?

I stopped keeping apace with math around the 6th grade. I passed algebra and everything, but it was such a chore.

This isn't a question, I was just trying to place where it all went wrong.

>>9513410
>Is this reasoning sound?
Yes.

>>9513415
Neat. In general for [math]\mathbb{R}P^{2}[/math], given a projective transformation since there's a corresponding nonsingular matrix characterizing the transformation, there will exist at least one eigenvector to this matrix, thus by similar reasoning there will always be a fixed point on a projective transformation [math]\mathbb{R}P^{2}[/math]

>>9513410
>Is this reasoning sound?
No. It implicitly uses the axiom of choice.

>>9513425
hmmmm

>>9513428
What do you mean?

>>9513430
I don't follow. Can you point to the problem explicitly?

>>9513425
>No. It implicitly uses the axiom of choice.
You must be mistaken, it's not used anywhere in that proof.

>any two distinct points in projective n-space lie on a unique line
is the dual of this: any two unique lines in a dual projective n-space intersect at a distinct point? Do I need say "dual projective n-space" here?

I'm sick of being a code monkey, what's a good math field to do that is primarily about maths but also involves IT or economics

>>9513501
numerical analysis / dynamical systems. I.e., any decent applied math program.

>>9513501
graphics and rendering

>>9513505
>>9513415
Something like this?

http://www.simge.edu.sg/gePortalWeb/appmanager/web/default?_nfpb=true&_st=&_pageLabel=pgCourseDetails&contentID=SIM001922

>>9511492
it's crap

>>9512774
it's like you WANT to become pasta

How do you find terminal points etc without having the Unit Circle to look at? For example, if t = -3pi/4, I can look at my drawing of the unit circle and figure out it's -sqrt(2)/2,-sqrt(2)/2.

But what if I didn't have that drawing? How would I mathematically work out the coordinate I end up at? Is there a formula or something?

Which one would be correct here?

How do I prove that that f(x, y) = x^2y + 1 is continuous in (0, 0) using the epsilon delta proof?

>>9513834
The top is the correct choice. I think it's best if you simplify the 75/pi/2 to 75/2pi first so you don't get confused.

>>9513846
Cool, thanks.

if i pull an elastic cord say 1 metre long with a 1kg weight on the end, when is it travelling the fastest? how far does it travel before it reaches its maximum velocity?

so I did a small trial on l theanine, it went well and I've now cycled off it because I want to test another nootropic how's this for doing a trial
>1 participant
>placebo controlled
>20 doses, 10 placebo, 10 nootropic
>over the course of 30 days
>benchmarking brain performance, mood, anxeity and physical metrics at perceived onset, peak and after effects

>>9513850
if we treat the elastic cord as a spring then the net force on the weight is [math] F_{\textrm{spring}} - F_{\textrm{kinetic friction}} [/math]
if the net force is positive then the mass is speeding up, and if the net force is negative the mass is slowing down, so to find the maximum velocity we want to find the point in which the mass is no longer speeding up but is not yet slowing down.
So maximum velocity occurs when [math] F_{\textrm{spring}} - F_{\textrm{kinetic friction}} = 0 [/math]
expanding the equation leads to [math] kx - \mu_kmg = 0 [/math] where k is the spring constant x is the displacement from equilibrium and [math] \mu_k [/math] is the coefficient of kinetic friction.
solving for x the equation becomes [math] x = \frac{\mu_kmg}{k} [/math]
note that the maximum velocity will occur at the same distance from equilibrium regardless of how far the spring was initially stretched assuming that the initial displacement is at least as great as x, if it was equal to or less than then the mass would not move.

in order to find the true answer we need to be more specific than "pulled one meter" if we mean that the initial displacement is one meter away from equilibrium, than we simply subtract x from one meter. If we mean that the total length of the elastic cord is one meter than we need to subtract x and the equilibrium distance from one meter.

also we are assuming that we are not continuing to pull the mass, the solution would be a bit more complicated but can be solved in a similar manner.

I have a relatively simple combinatorics question, I'm mostly just stuck on the semantics of the question more so than the answer itself.

"On a bookshelf there are 7 different red books, 6 different green books and 5 different
blue books.

(A) In how many ways can we choose exactly one book of each color?

This would just be "By the multiplication principle, there are 7 * 6 * 5 = 210 different ways to choose exactly one book of each colour.", right?

(B) In how many ways can we choose at most one book of each color?

How do I distinguish between exactly one and at most one?

>>9513835
>How do I prove that that f(x, y) = x^2y + 1 is continuous in (0, 0) using the epsilon delta proof?
'What have you tried?

>>9513956
Nevermind, figured it out.

At most means you can have either 0 or 1, whilst exactly one is just 1, therefore the answer is 8 * 7 * 6 = 336 different ways to choose at most one book of each colour.

Anyone able to help with specifically the second part of this? I believe I've found the appropriate Green's function from part (i), but I'm at a complete loss for how to continue.
I'm fairly certain it involves the use of Green's second identity somehow

>>9513960
Not much really, I'm pretty new to delta epsilon proofs. I know I have to prove that f(x,y)=f(0,0) as x,y approaches 0 to prove continuity in 0,0. I know I've got to use the inequality of (x^2+y^2)^0.5<delta somehow. So far I've had problems where the function was some fraction and I was able to manipulate it into the delta inquality, but I don't know how to do it with this one

Can someone explain my conceptual error here?
I'm not sure where/how I'm fucking this up.
>R dot dot should be the acceleration tangent to the bar
>Therefore, sum all forces tangent to the bar
>The terms tangent to the bar will be:
>-mgcos(40)*Coefficient of friction
>-mgsin(40) (force gravity)
>(m*v^2)/r Force of centripetal acceleration
>v = 1.2* 5 = 30
>m = .0155 slug
>r = 1.2 ft
Given this is true, force should be .06784 up the bar, divide by the mass of .0155 slug and acceleration will be 4.369 ft/s.

>>9513131
You need to decide which direction is positive. The usual convention is that a positive angle corresponds to a counter-clockwise rotation when the rotation axis is pointing toward the viewer (a clockwise rotation when the rotation axis is pointing away from the viewer).

With a right-handed coordinate system (e.g. X=East, Y=North, Z=up), a positive rotation about the Z axis will map [1 0 0] to [0 1 0] and [0 1 0] to [-1 0 0], i.e. a counter-clockwise rotation when viewed looking downward.

>>9513177
>>9512669
thanks, I figured it out.

Is there a way I can analytically find these values?

I have a question and I need to "show all working", I'm assuming that'll include derivations etc but I don't really want to just use the value if there is a method of finding it (without experiments)

>>9514356
here's the question anyway, it's worth 10% and I have the right answer I just don't want to drop marks because I've just taken the equilibrium constant from a table

How is this allowed?
What the hell is up with the melting point of iodide and bromide?

Is this accurate?

>>9514368
>>9514356
rip

>>9514375
Almost, [math]\in[/math] stands for "is".

question:
would it be possible to gather energy by exciting pressurised gas in space with solar winds? by the way i dont mean in a heat exchange to another medium or something like that. thanks for any reply.

>>9514403
In which country? Here it means "exists in".

>>9514403
that symbol is almost always, in a set theory context, interpreted as "is an element of" or "in", or what >>9514528 said.

Does anybody know where I can find worked examples of the problems in Apostol's Calculus?

>>9514731
In hell.

What are the possible l values associated with transitions in the Balmer series?

I know that n=2, and so l={0,1}, but it’s asking me to be mindful of selection rules where Δl=+/-1
What does that even mean? How does that affect possible l values?

how can i prove that

a ≡ b (mod n) and c≡ d (mod n), then ac ≡ bd (mod n)

where n is a natural number and a, b, c and d are integers

>>9515093
n|(b-a)
n|(d-c)
b-a=nk
d-c=nj
a=b-nk
c=d-nj
ac=bd-bnj-dnk-n(nkj)
ac-bd=-b(nj)-d(nk)-n(nkj)
ac-bd=n(-bj-dk-nkj)
b,d,j,k∈Z
Therefore
ac-bd=ni
acΞbd(mod n)

What's the proof that time is a dimension that can be traveled through and not just the human perception of motion?

Can you separate motion from time?

>>9515139
particle decay

>>9515139
Entropy?

>>9503612
Is it safe to define [math] 0^0 [/math] as [math] 1 [/math] ?

>>9515651
It's complicated
https://math.stackexchange.com/a/11155

analysis midterm in an hour

thanks for your help lads, but it's all ogre now

>>9515852
what are the topics?

>>9515651
[eqn]\lim_{x\to 0} 0^x = 0 \\ \lim_{x \to 0} x^0 = 1[/eqn]

>>9515885
Series

Is it possible to find the square root of -36+36sqrt(3)i with De Moivre's theorem? Tutoring a kid and i had a brainlet moment

>>9515940
Yes, just write it down in goniometric functions and put a half in the angle and square root the modulus. For the other solution just put a minus in front.

Shame on you

>>9513950
thanks for the insight my man

Personal version: Maple or Mathematica?

I have a better impression of Maple for reasons that have nothing to do with mathematics.

can EGR be used to increase compression ratio? it seems like the easiest way to increase compression, but I can't find much info

>>9516176
Mathematica is the better programming language.
Maple is the better mathematics toolbox.

>>9516225
>>9516225
>>9516225
NEW
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