ITT: QTDDTOT

Dunno if I can really help you here, guy

>>8319889
>Are the molecules of an ideal gas not assumed to have negligible volume? I thought the individual molecules were assumed to occupy no space as mere points of masses.
that's just a piece of voodoo magic for simplification of solution
basically, they imply that each molecule resides inside this cubical volume, and on average, it's located in the middle of a cube.
this way, the average closest distance is equal to length of a cube
>Likewise, does the length shown in the solution actually represent the average distance between molecules--or the length across each molecule?
average distance between molecules, given their volume is null

May I ask my own uber-stupid question here?

Why is it that in every textbooks and online equation solvers do
[eqn]\int tanx dx = -ln |cosx| + C[/eqn]
instead of
[eqn]\int tanx dx = sec^2x + C[/eqn]
?

>>8320003
[eqn]\frac{d}{dx} \sec^{2} x \neq \tan{x}[/eqn]

>>8320003
Because it is wrong?

>>8320003
Check your latter equation. It's because [math]\frac{d}{dx}sec^2(x)[/math] won't result in [math]tan(x)[/math].

>>8320003
>>8320020
>>8320021

Looks like someone just realized that they failed their Calc 2 test by mis-memorizing an identity.

>>8320026
Th-that's exactly what happened. ;~;

is there a field whose additive group is isomorphic to its multiplicative group?

are there any pairs of (infinite) fields where the additive group of one is isomorphic to the multiplicative of the other?

>>8320032
Well, that's what happens when you rely too much on memorization.

Be glad that you learned the lesson you were bound to learn somewhere down the road in one of the easiest calc-track courses that you can easily pass regardless of one bad grade.

Is it me or is a pain in the ass to actually, completely, know the mechanism of a reaction? for example I am looking at the Heck reaction and the explanation of the reduction done by the phosphine is in 2 papers I can't access, there is no simple drawing of what to me should be the basis.

I admit I hate and I don't know well organic chemistry, but to me it seems like there should some place where every single mechanism is available.

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Alright you fucks I'm currently looking at braid groups and links and how they relate to the quantum Hall effect and fractional statistics. I have currently a cylinder for the base manifold [math]M = \mathbb{R} \times S^1[/math] and in general [math]\langle \bar{\Psi}\Psi \rangle = N[/math] particles where [math]\Psi[/math] is the 8-component spinor of the Hartree-Fock Hamiltonian [math]H = \int_{M}\bar{\Psi}\left(i\gamma_0\gamma_i\partial_i + g_a A^a\right)\Psi[/math], where [math]A \in \Lambda^1(M) \otimes \operatorname{Lie}(U(4) \times SU(2) \times U(1))[/math]. This means that I have to find the configuration space [math]F_N(\mathbb{R} \times S^1) = \left((\mathbb{R} \times S^1)^N \setminus \Delta\right)/S_N[/math], where [math]\Delta[/math] is the set of diagonals and [math]S_N[/math] is the symmetry group on [math]N[/math] elements, and its braid group [math]B_N = \pi_q\left(F_N(\mathbb{R}\times S^1)\right)[/math].
I can probably find the generators of the braid group [math] B_N[/math] myself but I'm wondering how the gauge group [math]U(4) \times SU(2) \times U(1)[/math] affects the fractional statistics? In general the braid group [math]B_N[/math], and therefore the fractional statistics, can be found completely independent of the symmetries of the Hamiltonian but I'm thinking that maybe the symmetries might change how the generators of [math]B_N[/math] are defined so that the relevant braid group is some subgroup [math]\Omega_N \subset B_N[/math]? If this is the case then by Abelianizing [math]\Omega_N[/math] we can probably find a subset of [math]\left[-\pi,\pi\right)[/math] for the anyon statistical parameter that's relevant to the model at hand, and maybe the same formalization can explain the [math]\nu = \frac{5}{2}[/math] fractional QHE.

Let X be smooth,separated over R.


Let R[I] denote the ring of dual numbers associated to an R-Module I.


Show [math]{\operatorname{Def} _X}\left( {R\left[ I \right]} \right){ \cong _{{{\operatorname{Mod} }_R}}}{H^1}\left( {X,{\mathcal{T}_X} \otimes I} \right)[/math].

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Starting an undergrad physics course, just starting non-bullshit error analysis, specifically error propagation and calculating error by quadrature.

I'm trying to find the error in acceleration calculated from pic related. I have the partial derivatives and the final equation for the error:
[eqn]
\sigma_{a} = \sqrt{( \frac{1 * \sigma_t}{t} ) ^{2} + ( \frac{-v \sigma_{v}}{t^{2}} ) ^{2}}
[/eqn]

But what confuses me is that, if I plug in the time of the measurement (t=1, 2, 3, etc.) into t when calculating the error, what that's going to do is make the error decrease as time goes on, which doesn't make any sense. So what do I use for t?

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Im transferring next semester for engineering.
I've taken all my prereqs ( calculus, physics, diff eq) but I still don't know which discipline to major in. Any advice?
>Do you like machines? Pick mechanical.
Im interested equally in mechanical, electrical, civil, and computer science.
All I can say is I'd actually want to use most of what I learn after I graduate.

>>8322430
What do you want to do? So much of /sci/ is so focused on what they're learning rather on what they're going to do, it's ridiculous.

Excelfag here again. I don't use the program much so I'm back with another stupid question. I'll post the problem and perhaps someone can provide guidance on where to start. I really don't need it done for me but I need to learn how to do this myself.

>Create a line graph comparing small companies (with employees < 50) and big companies (with employees > 50) on their average morning, afternoon, and evening profits. This will be Figure 4. It should have 6 data points on it, and each data point should have error bars using the standard error

I'm assuming I would create the line graph using the "companies" and "# of employees" columns but 1) I'm not sure how to distinguish them by small and large companies (<50 and >50 employees), and 2) I have no idea where to even begin applying the three profit columns to the overall line graph. I know how to do error bars so I'm good there.

>>8322430
Elec and Civil are bread and butter of Engineering. Elec covers so much shit, power, electronics, radio, and not LEDs and solar panels and shit. Mechanical is making shit and calculating it's properties. Aerospace usually shares a lot with Mechanical. Honestly I like how easy Electrical has been for me, minus the shit teachers. Nothing like seeing the mechbros working til 5AM for like two weeks straight, while I wasn't doing much of anything.

Civil if you're into the outdoors or buildings I guess, architectural if your parents force you into it but you still want to be a faggot.

Computer Engineer is good, you can do a lot of programming with that.

If you're a girl you can go into Chemical or Biomedical Technology or whatever. There's also Environmental.

>>8322517
I guess I'm not sure career wise. I've shadowed in manufacturing with mechanical and industrial engineers and to me their office jobs look boring. I want to do technical work. That's very broad but I'm not picky. I guess a lab or shop would be cool.

>>8322547
Elec and Mech are the bread and butter REEEEEEEEEEEEEEEEE

One of the things I like to point out in terms of job prospects: EE covers like, so much shit, including, you know, ELECTRONICS, THE BASIS OF OUR FUCKING MODERN LIFE, while MechE is a lot more specialized (relatively speaking). Despite there being an estimate 0 job growth according to the Department of Labor, even after a decade of MechEs estimated growth, EE still will be ahead by like 10k+ jobs. It actually is really strange, that if you look it up, EEs are now being produced less than MechEs for like the first time ever.

Checking a quick article, seems a lot of MechEs can get into maintenance jobs, so like a solar installation would have a bunch of MEs as well as EEs, because infrastructure is just as important as the electrical system.

>>8322547
I know the descriptions for the disciplines, hence why Im equally attracted to them all. Thank you, but I need more info on what the day to day stuff is.
>Mechbros working till 5am
I've heard electrical was the hardest discipline.
.
>>8322559
Ive checked the BLS for every interesting job. 0% job growth isnt bad for 300,000 jobs.

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I need to get up to speed in math for pic related in the next 1-2 months. I've pretty much forgotten everything from high school.

Am I totally fucked?

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>(1R,4S)-2,3-bis(phenylsulfonyl)bicyclo[2.2.1]hepta-2,5-diene

How would you synthesise this? I can see it's a 4+2 dienophile + alkyne, but how do you get the bis phenylsulfonyl alkyne?
I know the phenylsulfonyl comes from its halide form, what I would assume is a 1,2 bis-ketone system that gets attacked by the phenylsulfoniyl, forming a vicinal diol that we can turn into an alkyne through dehydration..

>>8324557
Nevermind, I am looking around and sulfone synthesis seem a lot more complex than I expected.

>>8324492
Yeah, probably. If you just want to survive, review basic calc + trig and you'll make it.

Can someone give me a layman explanation of zero point energy?

>>8325633
Do you mean in general, or in cosmology, or string memery?
I'll assume in general: Every system as a ground state: this is the lowest energy state this system can have. If you consider an harmonic oscillator, you notice that the energy value of this ground state isn't 0, but some value higher than that. Which means it can't ever an energy lower than this value, the zero point energy.
Now sci-fi writers try to use it to mean "since such a system will always have energy so infinite energy yay". The reality is, since your system can't be in a lower energy state, it's impossible to extract this energy. And if you think "I'll just make an harmonic oscillator and have energy from nothing then!", you can't either because you would have to put this energy inside it yourself when building the oscillator.

>>8325661
Yeah, I've been watching videos about the possibility of harnessing vacuum energy in order to have "free energy." I just wanted to have a basic understanding of it.

Thank you, anon.

dumbfag here. how do you find
[math]\lim_{x\rightarrow0} \frac{(1-\cos x)^2}{x}[/math]
without using lhopitals rule?

>>8325850
nevermind, its simple figured it out

>>8325850
Use Kramers-Kronig

Lagrange multipliers

Find the least and greatest distances from the origin to a point on the ellipsoid [math]9x^2+4y^2+z^2=36[/math].

System of equations I get:

[math]F=x^2+y^2+z^2+\lambda(9x^2+4y^2+z^2=36)[/math]
[math]F_x=2x+18\lambda x[/math]
[math]F_y=2y+8\lambda x[/math]
[math]F_z=2z+2\lambda x[/math]
[math]F_\lambda = 9x^2+4y^2+z^2=36[/math]

Each of the first equations cancel the variables and leave different values for lambda.

>>8325858

How'd you do it?

If we're taking Similarity Transformation of a plane, is it gonna be it's own invariant regardless of the similarity coefficient?

>>8326046
separate to lim (1-cosx)/x and lim 1-cosx
(1-cosx)/x tends to 0 (easy to prove) and 1-cosx is just 0 when plugged in so its 0 * 0

Anyone with access to this paper? Care to share it?

Green Chlorination of Organic Compounds Using Trichloroisocyanuric Acid (TCCA)
Gabriela F. Mendonca and Marcio C.S. de Mattos
Current Organic Synthesis vol. 10, iss. 6 (2013) pp. 820-836

http://dx.doi.org/10.2174/157017941006140206102255

>>8320033
>is there a field whose additive group is isomorphic to its multiplicative group?
No. Let [math]F[/math] be a field and suppose for a contradiction there exists an isomorphism of groups [math]\phi:F^+\mathrel{\tilde\longrightarrow}F^*[/math].

Then the equation [math]2x=0[/math] must have as many solutions as [math]y^2=1[/math]. If the characteristic is not two, [math]2x=0[/math] has one solution, but [math]y^2=1[/math] has two. If the characteristic is two, then everything in [math]F[/math] is a solution to [math]2x=0[/math], while [math]y^2=1[/math] has only one solution.

These numbers do not agree for any field, so no such isomorphism can exist.

>are there any pairs of (infinite) fields where the additive group of one is isomorphic to the multiplicative of the other?
I don't know, but we can shed some light on where to look by examining what we did above.

Suppose [math]E[/math] and [math]F[/math] are fields, and we have [math]\phi:E^+\mathrel{\tilde\longrightarrow}F^*[/math]. Again, count the solutions to [math]2x=0[/math], [math]x\in E[/math] and [math]y^2=1[/math], [math]y\in F[/math].

If [math]E[/math] has characteristic two, then [math]|E|=2[/math], so [math]E=\mathbb F_2[/math] and [math]F=\mathbb F_3[/math], which work, but aren't infinite.

The other case is that [math]F[/math] has characteristic two but [math]E[/math] doesn't. If [math]\mathrm{char}\,E=c\ne0[/math], then every element of [math]E[/math] is sent to a [math]c[/math]-th root of unity. We know that there are at most [math]c[/math] such roots in [math]F[/math], so [math]|E|\le c < \infty[/math].

So suppose [math]E[/math] has characteristic 0, WLOG an extension of [math]\mathbb Q[/math]. At this point I'm stuck. However, observe that no nonzero element of [math]E^+[/math] has finite order, so everything not equal to 1 in [math]F[/math] has infinite multiplicative order---there are no roots of unity besides 1 itself. That's gotta be pretty weird if it exists.

Why does 16^1/2 equal 4? I mean, I get it, if you do the reciprocal of 1/2 its 2/1 which is 16^2, but *why*?

>>8327363
[eqn] \sqrt [n] { a } := a^{ \frac { 1 } { n } } [/eqn]

>>8327368

Yeah I get it but why the one half? Like I get its just a square root and that you can think of as:

16*1/2 = 8
16* 2 = 32
16^1/2 = 4
16^2/1 = 4

That makes sense. I just don't get it. What's special about the exponant? If you have 16*1/2 you're asking "what multiplied by 2 is 16". If you do 16^1/2 you're asking "what squared equals 16?"

I just want to see it in mechanics, like 8*2 = 16. I can get that.

But 4*4*4*4 = 16^1/2? Where does the "2" come in?

I think I'm thinking too deeply into this.

>>8327392

Never mind I get it now after lloking at what I wrote (which was wrong btw). When you ask "16^1/2", the denominator is representing the the number that it is being raised to 2. The 1 = what that number is multiplied by one.

>>8326104
H E L P
E
L
P

This shit aint googlable

Sorry if this isnt the right place to post this but having problem with a homework question in Discrete structures.

Represent the following quote using propositional logic. "Do or do not, there is no try."

Appreciate it if anyone could help. Thanks

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Can somebody tell me why v ( -dx) and u (dy) represent a ''volumetric flow rate'' ?

I know we are talking about flow and all here, but all I get from those expressions is:

v = velocity component in y
dx = changes in x
v ( - dx) = changes of v in the x axis? I dont get the significance of the '' - '' either.

In other words, why does this mean ''volumetric flow rate per unit depth''?

>>8327707
post more context

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>>8327771

Shit man I dont even know myself, all I know is that this is the Stream function and that its basically derived from the continuity equation.

According to what I found, continuity equation, when satisfied, also means that the volumetric dilatation rate is equal to 0.

Here again they relate it to volume, when all they have in the equation are the velocity components of x, y, z. I dont understand.

how to prove that the weierstrass function is differentiable nowhere?

>>8326351
http://sci-hub.cc/

is tan y/x or sin(y)/cos(x)?

Because wolfram says the latter but mathematica exchange says the former.

http://mathworld.wolfram.com/Tangent.html
http://math.stackexchange.com/questions/434795/finding-functions-for-an-angle-whose-terminal-side-passes-through-x-y

>>8327990
one is linear and one is polar, it depends in which system you're working on

>>8327813
For any x, you construct a certain sequence of [math]h_{n}[/math] such that
[math]\lim_{n \to +\infty} \left|\frac{f(x+h_n) - f(x)}{h_n}\right| = + \infty[/math]

I have a babby question about rule of natural logs.

I got marked down for [eqn]log(x)-log(y)-log(z) = log(\frac{\frac{x}{y}}{z})=log(\frac{x}{yz}) [/eqn]. Why is it incorrect? Doesn't [math]log(x)-log(y)=log(\frac{x}{y})[/math] which would mean that any subsequent subtractions would basically stack under the preceding fraction?

>>8328438
Fucking christ, I meant [math]ln[/math] instead of logs.

>>8328438
Log(X/yz) = log(X) - log(yz) = log(X) - (logy - logx)= logx - logy + logz

>>8328454
This is infuriating me. Am I supposed to combine all natural logs at the same time or something, then? How am I supposed to handle multiple chains of these guys?

>>8328454
Distribute your negatives properly, nigga.
[eqn]ln(\frac{x}{yz}) = ln(x)-ln(yz) = ln(x)-(ln(y)+ln(z))=ln(x)-ln(y)-ln(z) [/eqn]

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What method does one use to solve for y (or x) in these types of equations?

Plugged it in wolfram but the solution didnt make much sense to me.

>>8328468
What are you 12?

>>8328524
Complete the square. You're not finding a single solution, but a family of solutions. It's a hyperbola.

>>8328557

>complete the square

Thats what I was looking for. I completely forgot about that, thank you for reminding me anon.

>>8327825
Rest assured I tried. Several times.
>! Oшибкa: нe yдaлocь oткpыть cтpaницy
>! Error: unable to access the page

I got a tonne of various math textbooks across lots of different topics especially lots on stochastic processes and probability type stuff.
How should I organize my folders?

>>8328571
No problem friend

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I've got problems with Thevenin' theorem, how do i calculate the equivalent voltage? R2 boggles me because it's outside the mesh

>>8328678
R2 doesn't have any effect upon the Thevenin-equivalent voltage.

So the voltage is just f*R1/(R1+r) (i.e. r and R1 form a voltage divider).

The point about Thevenin's theorem is that for any linear network (resistors, voltage sources, current sources), the relationship between output voltage and current drawn is linear. And any linear voltage-current relationship can be obtained with a voltage source in series with a resistor, or a current source in parallel with a resistor.

So you can always derive a solution from first principles using the fact that the voltage-current relationships for the original and simplified networks are equivalent.

If black holes can bend the path of light a la gravitational lensing, can it ever trap light in an orbit?

And, since I have a feeling that the answer is no, and the reason is probably interesting: why not?

anyone remember the name of that site where you could find a ton of books? it was library of somethng i think, dont remember

Should I go into ECE or Double Degree of Math and Business Management at Waterloo?

>>8328770
>can it ever trap light in an orbit?
Yes. Look up photon spheres.

If we're taking Similarity Transformation of a plane, is it gonna be it's own invariant regardless of the similarity coefficient?

>>8330219
Libgen.io

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What am I doing wrong here guys. The website says that answer C. is the correct answer.

>>8330510
Mistake on their part. Unless you're a primary school student you should be confident enough to conclude that.

>>8319889
If we define [math] d(A,B)=inf \{ |a-b| : a \in A, b \in B \} [/math] how can we prove that if A and B are nonempty disjoint sets with b>a for all b and a [math] d (A,B)=|inf (B)-sup (A)| [/math]
I'm trying to prove this lemma to help solve another problem and I'm so shit at this real analysis stuff it hurts.

>>8330521
Thanks buddy.

>>8330547
I'll try and push you in the right direction.

First, your result can be strengthened a bit. [math]|\inf(B) - \sup(A)| = \inf(B) - \sup(A)[/math] under your assumptions. To show this, fix b in B. Then b is an upper bound of A, so [math]\sup A \leq b[/math]. Then because every b in B satisfies this inequality, [math]\sup A[/math] is a lower bound for B, so [math]\sup A \leq inf B[/math].

Now on to the main problem. Here's an outline:
1) Set [math]\alpha = \sup A[/math], [math]\beta = \inf B[/math]. Show that for every a in A, b in B, [math]b - a < \beta - \alpha[/math]. Use this to conclude [math]d(A,B) \geq \beta - \alpha[/math].
2) Suppose for contradiction [math]d(A,B) > \beta - \alpha[/math]. Then [math]\beta < d(A,B) + \alpha[/math], so there is a [math]b \in B[/math] such that [math]\beta \leq b < d(A,B) + \alpha[/math]. Use a similar trick to find an element of [math]A[/math], and use this to contradict the definition of [math]d(A,B)[/math].

>>8330604
Dang anon big thanks man. I did like 8 hours of hw yesterday and at the end I was just fried. I'm gonna try to fix my schedule and hopefully that doesn't happen again.

>>8331006

Lads I've been stuck on a question for quite some time now, and I'm hoping one of you can figure it out. It's my first time posting here and the question is simple to formulate, so I won't type it in latex (I'd just mess it up).
Here goes: Given a bounded hyperplane, how to determine if it contains any points where all of the coordinates are integer.
So basically, the plane is given by an equation a_1x_1 + a_2x_2 + ... + a_nx_n = g, and it is bounded by several equations b_1x_1 + .. + b_nx_n <= b*, c_1x_1 + ... + c_nx_n <= c* et cetera and I'm looking for a way to determine
A) if there exists a vector x of integers that satisfies all the constraints
B) if so, what are the values
C) if not, what is the smallest change in the value g that would guarantee an integer point.

If it's unclear I can try my best to get it in latex, just let me know.

Thanks in advance

>>8331208
shit nigger that actually sounds pretty hard

>>8331208
for A) and B) what you're looking for is called solving diophantine equations. You can probably find some material in your language on it.

C) looks tricky, try to read up about diophantine geometry to see if there's a general solution to that

>>8331208
Are the a_i integers, rational or arbitrary reals?

If the a_i are integers or rationals, then it's basically about modular arithmetic. If there's a single integer solution to the plane equation, there are infinitely many, forming an (n-1)-dimensional grid.

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I'm trying to pay for a parking permit at my college and they are asking for plate type. It's just a regular car.

I believe i asked this in the past but I dont recall getting an answer.

Light can bend around the gravity well of a large star or black hole correct? Which is why we can see objects that are directly behind a large mass that really should be obfuscated from our view.

Does this not occur on both sides of the gravity well? Are many of the stars and galaxies in the sky duplicated?

>>8331285
All coefficients are arbitrary real numbers
>>8331235
Thanks! I'll look into that

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>>8331356
Forgot pic

>>8331179
Maybe i dont understand but I feel like that just doesnt make sense. log8 and log5 are really just arbitrary decimals. The simplest form would be log5*a/a which I mean if you needlessly expanded out you could write as log13/a.

>>8331323

Nevermind, figured it out.

>>8331359

i believe we would see a single star - the light would bend around all 'sides' of the gravity well. showing light as a single thin line like in that pic doesnt help at all m8, its more like a massive broad beam of photons eminating from the source which would envelope the whole sun and we would only see the one star

>>8328638
Use Mendeley

>>8331393
Then how does it choose which side of the star to bend around? If the gravity well is uniformly radial, I feel like there should be a path on all sides of the star, and we should really see a ring around the sun.

>>8326795
>The other case is that F has characteristic two but E doesn't.

Why does F still have to have characteristic two? All we know about it is that there is only one solution to y^2 = 1, namely y = 1.

>>8331285
So let's say the coefficients are integer as well. How does this make things different? Would it be possible to answer A,B and C?

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I was watching a stream of the ISS the other day when I noticed these things on the station at the bottom of the screencap, wondering if there's someone here who can tell me what these things are for.

>>8331484
> So let's say the coefficients are integer as well. How does this make things different?
Bézout's identity.

Let d be the greatest common divisor of the a_i. sum_i(a_i*x_i) must be a multiple of d. So if g is a multiple of d, then the equation sum_i(a_i*x_i)=g has infinitely many solutions, otherwise it has none.

And if solutions exist, they form a regular grid. I.e. there exist n-1 n-dimensional axis vectors (y_1,...y_n) such that if sum_i(a_i*x_i)=g, then sum_i(a_i*(x_i+y_i))=g.

Note that the axis vectors don't depend upon g, only upon the a_i. Also note that these vectors are all perpendicular to the plane normal (a_1,...a_i), i.e. sum_i(a_i*y_i)=0.

>>8325947

How about solve the integer solutions, then for the greatest distance argue that there exists a greater distance, e.g. plot a sphere against it and find out whether there is a solution or not. Same goes for the minimum.

Also as far as I know you got your lambda applied to the wrong function, try again.

>>8325947
That's correct! This tells you that at least two of the x,y and z must be zero.

You know that already. It's a sphere centered on the origin with axis in the coordinate directions.

>>8331927
Alright thats already some really helpful information, thanks, but there's still the problem of the linear inequality constraints. If n is large, the gcd will be 1 and any integer value g will ensure integer solutions to exist, but what guarantees there will/will not be one that satisfies the constraints?

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Why isn't the raddi (3)^(1/2)?

Should it be (3)^(1/2)-1? Because of the lower bound in the inequality statement?

>>8331179
Assuming these logarithms are to base ten,[eqn]\log5=\log\frac{10}2=\log10-\log2=1-\frac{3\log2}3=1-\frac{\log2^3}3=1-\frac{\log8}3=1-\frac a3.[/eqn]

>>8332222
It asks for the radii of two spheres, separated by a comma. You entered one number.

I hope I don't fuck it up too bad.
Let's say I've got a complex function f(x,y)=u(x,y)+iv(x,y), with both u and v differentiable as real-valued functions, and the limit [math] \lim_{\Delta w ->0} \left |\frac{\Delta f}{\Delta w} \right | [/math] exists.

How should I go about proving either f(z) or [eqn] \overline{f(z)} [/eqn] is complex-differentiable?

I tried expanding the module but it becomes a mess quite fast, and I'm not sure how to show that either of the fucntions satisfy the Cauchy-Riemann equations.

I'm revising high school math before uni, and there's this exercise, says "Find a complex number for which [math]w=\sqrt[3]{8i}[/math] is worth." I don't even know what the fuck I'm supposed to do. I hate math exercises like this.

>>8332429
>hasn't understood complexes yet
You're in trouble m8.
Try to make a picture.

>>8332320
cauchy-riemann equations? just take derivatives, show they satisfy.

>>8332429
[math]2 w=2 \sqrt[3]{i}[/math] you only need the cube root of 3 part. you should get 3 values.

>>8332487
this. what z gives you z^3 = i ? use the geometric interpretation of complex multiplication.

>>8332504
>what z gives you z^3 = i

Oh lord. I just noticed what the fuck this is all about. What x gives x^4=x^4? I shouldn't do maths past midnight...

>>8332429
Do you know what [math] i [/math] equals?

>>8332597
>What x gives x^4=x^4?
all of em

So my vector calculus book is probably trash. Has 2 stars on Amazon and it's a shit read. Does anyone have any other suggestions for an intro to multivariable calculus?

I was thinking of just trying to get through as much of Apostol's V.2 book as I could before the quarter started, but I'm not sure if this is a good utilization of my time. Open to suggestions

There's this dude who "degreases" his pizzas before he'll eat them. He doesn't like the pools of oil and moisture (or whatever it all is) on a pizza, so he'll painstakingly soak it up with paper towels as shown in his pizza degreasing tutorial:

https://www.youtube.com/watch?v=UQbI76qFU6g

I'm curious. Is there a way he could evaporate the pizza "grease" faster? What kinds of temperatures would be needed to do this? Pizzas are already cooked in the 400-500 degree Fahrenheit range and that doesn't evaporate pizza grease. How would you dry out a pizza?

>>8332927

I heard Stewards Calculus is good.

I am personally going to use that.

>>8332972
I suspect pizza grease will burn before it volatilize, imparting an acrid taste to the whole dish in the process. Also lengthy/high temp baking will have a definite negative impact on the other ingredients. Not recommended.

Rinsing the pizza with soapy water or dipping it in suitable solvents may work, but I suspect you'd rather keep the pizza edible, right?

So, best options are: a) don't eat pizza, b) make your own pizza without anything likely to release "pools of oil" on , which means no cheese nor fatty meat, c) tighly roll your pizza, crust out, and eat it in the dark while concentrating on how dry and not-fat it is, or d) stop being such a puss and eat the damn pizza as is.

>>8333054
or using a fuking napkin, friendo

>>8333067
Since s/he/you posted a video describing just that, I thought we had this covered.

>>8331368
>>8332112
Call a topological space "existential" iff limits always exist. When is a space existential? Clearly indiscrete => existential, and also existential => connected:

Assume we have U != V open and disjoint. Then pick x in U and y in V. If the sequence x y x y x ... converges to p, then p is in neither U nor V.
Therefore, any space where limits always exist must be connected.

Are any non-indiscrete spaces existential?

>>8333073
...Actually, any topology where some point p is in every nonempty open set will have this property. So now my question is, are those the only ones?

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This is my homework, and I have no idea how to even start thinking about it.
I'm given a square with a point in each corner. Each side is 1 meter long and each point is moving towards the next point with speed of 1 meter per second. Point 1 is moving towards point 2, 2 to 3, 3 to 4, 4 to 1. What distance will the points have travelled when they meet up?

Obviously they are spiraling into the center. No idea what formulas to apply or what to do.

>>8333101
Plot the updated positions after 0.7s.

>>8333107
How do I even plot that? Can I somehow predict what angle will the points be moving? And I'm pretty sure that those angles are changing all the time.

>>8333101
How is speed relevant?

>>8333113
No idea. It's just given. I'm guessing that this anon >>8333107 has some clue

Does 4chan render \mathrm tag correctly?
[eqn] \mathrm{Does it?}[/eqn]

How do I go from F = BD'+B'D+AC'+A'BC to
F = BD'+B'D+B(AC'+A'C)?
Also F = AB + (AB)'C to F = (AB + (AB)')(AB + C)? ' being the complement.

>>8333117
No, no clue, we understood the problem differently. I didn't get the "1 is moving towards 2" in a dynamic fashion, so I expected the four point to just run along the side of the square, never to meet up.

I'm out, carry on.

>>8319889

If I'm numerically solving a differential equation, I know that grid spacing effects the accuracy of the solution but can it also effect the stability and convergence of the solution? I ask because I'm trying to simulate a certain type of FET and I need to couple together my solutions for the Schrodinger and Poisson equations and I'm having trouble making it converge

How do you know whether you need adderall or ritalin? I have trouble concentrating on anything and crazy sleep-wake cycles.

>>8333329
It's also getting worse I think. When working on math problems my vision becomes blurry. I can never finish a TV show and movies are hard to finish too.

>>8332056
The fact that the solutions form an affine grid mean that the set of solutions can be expressed as an affine transformation of Z^n.

So you can reformulate the constraints accordingly, so that the problem is simplified to whether there are any integer solutions to the new constraints, i.e. you've separated solutions to the plane equation from solutions to the constraints.

>>8333199
> can it also effect the stability and convergence of the solution?
Yes.

E.g. if you try to simulate a classical spring-mass-damper system (or RLC circuit) by numerical integration and the time step is large compared to the period, the amplitude will increase exponentially.

More generally, that tends to happen whenever you overshoot an equilibrium point such that the new position is farther from equilibrium than the original position.

I'm fairly sure that this is related to the stability of a discrete-time IIR filter.

>>8333428
Well I'm feeling like a buffoon compared to how smart you lads are on this board, but I can't figure out what it is you're telling me. Could you perhaps explain an algorithm that would solve this in general?

So assume all parameters are integers and g is a multiple of the lcd of the a_i's.

From what I've read, the so called "Extended Euclidean Algorithm" can give me an integer point on the hyperplane (although I haven't read enough to see if it works beyond 2 dimensions but I assume so). This point in general doesn't satisfy the constraints sum_i(b_ix_i) <= b* , sum_i(c_ix_i) <= c* et cetera.
From this point on, can you explain to me how to either get to an integer solution that satisfies these constraints or to a proof that such a point does not exist?

Thanks in advance, I am really grateful for your help!

I want to make an eternal terrarium using a moderately large mason jar. What are some must have compounds/ingredients that will ensure that my terrarium can sit in isolation more or less forever?

My ideas thus far:
The bottom: Dirt, maybe sand, and small stones.
Life: Hardy plants, so I'm looking at moss, a fungus, and possibly cacti given their low water requirements.

the electric field module is defined as E=k.|Q|/d2
Being E the eletric field, k the eletrostatic constant
Q the particle charge and d the distance between then.

My question is: can be d any lenght possible? e.g a proton in the moon and an eletron here in earth? i know the result would be so little that it could be neglected, but could it?

Do tinfoil hats actually work, or should one go with a Faraday cage? How about a signal blocking device?

>>8334785
> can be d any length possible?
As far we know, yes.

We know that the inverse-square law holds true for gravity over vast distances, so why wouldn't it hold true for charge?

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Where the fuck did the -4xy came from? Was it added from adding -2xy and +2xy to both sides(then turning the left side in 0)?

Also, any good books on inequality? I'm quite bad at it, even when reading proofs about it.

>>8335767
x^2-2xy+y^2+2xy-2xy=x^2+2xy+y^2-4xy

>>8335767
It is called being good at algebra.

Notice that in the line before the -4xy appears, you have a term that is -2xy

Then notice that in the next line it changes to +2xy. Why did the author do that? To simplify the equation.

But you can't just be changing terms so he added a -4xy term to the expression because 2xy - 4xy = -2xy so nothing has changed, except that now he can do a clever simplification that allows him to get an answer.

Congratulations, you just learned that algebra is not just about computations.

What's a good book on machine learning?

>>8333101
Assuming that the square rotates about its center, we can effectively plot a circular path around the square (intersecting the 4 corners) which traces the path of the points.

The radius of this circle is

root (0.5^2 + 0.5^2)
=root (0.25+0.25)
=root (1/2)
~0.7

Use 2πr=C

2*π*0.7 = 4.44221201218

A single 360 degree rotation will cover the distance 4.44221201218m.

That should be your answer. Although I doubt that is what the question actually asks for, you explained it very badly.

When self studying math ( say near or at graduate level ) with access to solutions, what is the indicator that you should stop and look at the solution to continue onwards? I find this hard to gauge for myself 8 months out of graduation and I feel like I either rush to it or stay too focused on a problem.

What is a brainlet?

>>8335979
there's always other questions to work on, just come back to it later

>>8335979
I'd say, if you've spent a decent amount of time on a problem and you haven't cracked it, let it go and move on without looking at the answer. When you come back to it, you may have some more familiarity or insight that will make the problem easier.

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what is this fucking sorcery

>>8336255
What are you confused about?

Second line is application of the binomial theorem.

Third line is distributive law.

>>8336267
FUUUUUUUUUUUUUUUUUUCK

just saw that all he did was multiply each by one term in the constant and just labelled one as having k as an iterable and one as having j as an iterable

fuck me I'm retarded

Econ memes incoming

Does the production function Q=f(E,K) always equal the supply function Qs=g(P,Prg)?.

If so, knowing that in a market where there is an equilibrium (ie every market), and the supply function is equal to the demand function Qd=h(P,Prg,Y), can we use this to show the derived demand for factors of production?

>>8331425
It bends around all directions. The intensity from each observed direction depends on the locations of source, gravity well and observer.

If all three are aligned the source becomes a ring around the gravity well, this is called an Einstein Ring.

https://en.wikipedia.org/wiki/Einstein_ring

We don't observe it with our eyes because the gravity well doing the bending is our sun which outshines everything else in the sky.

How can I be responsible for anything if every action is predetermined by the initial state of the universe? You don't treat a person who straight up kills a man vs someone who has a gun pointed to their head and is forced to kill someone the same, but the latter is not even the half of it since in reality the will to kill and live or not kill and die doesn't exist at all. If I kill someone it wasn't my will. The universe is the killer. Plus, we all were made in the universe, in fact we are the universe. I'm not really doing anything because the matter is still there and the universe is the same. So, why am I blamed for killing someone?

>>8336529
I don't know, I think you should try murdering someone and give the judge that argument.

>>8336529
>How can I be responsible for anything
Is an emergent notion. On the same level of granularity of your argument the judge is predetermined to send you to jail.

>>8332320
https://youtu.be/rY9OegpAdyE First bit of this lecture could help you with [math] \overline{f(z)} [/math] being holomorphic or not ( it isn't ).

>>8333329
>>8333332
Bipolar fag here. As with all psychiatric meds you simply just have to give them a try and see if it helps your situation.

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How do I prove that these five points are equivalent?
I think that the first point implies that the points 2 to 5 are true but how to prove that the points 2 to 5 imply that the first point is true?

So over the Summer I took Real Analysis (which went up to Taylor Series). For Fall I'm deciding between doing Complex Analysis or the second part of Real Analysis.

I'll probably end up taking both (I like the topic) at some point, but any recommendations on which I should do first?

I still don't understand, I'm supposed to find a complex number [math]w[/math] for which [math]w=\sqrt[3]{8i}[/math] is valid. I simply don't understand what's going on here. I only learned the calculating part, I don't know how this connects to the imaginary plane.

>>8336773
If x != y then wlog x < y. So since |y - x| = y - x >= 0, statement (2) fails for epsilon = 2(y - x).

The other ones require knowing that the rationals are dense / Archimedeanness.

So this problem gives me four matrices and four vectors and asks me "Define 4 schemes of fixed point iteration. Let p < 0.05 denote a probability of less then 5%".

What the fuck is this talking about? What is a scheme and what does probability have to do with it?

>>8336789
shit, that should just be epsilon = y - x. |x - y| = |y - x| = y - x which is not less than itself.

>>8336787
Ok I get it. No need to respond. I swear to God, I'm practising math exercises from this test, and the exercises' wording is so out of this world, like holy shit. It asks of you one thing, and makes it look like it's asking you to resurrect fucking Adolf Hitler. I swear to God...

>>8319889
>> stupid questions thread
OK, here's one:
I've heard people say increasing entropy means a reduction of the amount of information in the universe.
That the heat death involves a total loss of information in the universe since everything is reduced to a homogeneous cloud.
I've also heard people say the opposite.
I'm inclined to agree with the first camp, but I'm just a code-monkey without a degree.
What does /sci/ think?

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>>8336803
Oops, forgot pic

>>8336803
>I've heard people say increasing entropy means a reduction of the amount of information in the universe.
Yes it's a way to see it in thermodynamics.

>That the heat death involves a total loss of information in the universe since everything is reduced to a homogeneous cloud.
Yes, sort of. However keep in mind this is a simplistic description rooted in late XIXth, early XXth century physics. Engineer science in other words.
And we have learned a lot since then. In particular that information is really never lost.
And also that space expansion is accelerating, which means the entropy/volume of the universe actually won't increase in the long run, because it will expand faster than entropy is created.

Cosmology is hard mayne. I suggest you look at the Cornell lectures of Susskind on the topic. They are for the general public.

>>8336702
If g is holomorphic, and [math] f = {\bar g}[/math], then [math]{\bar f}[/math] is holomorphic.

How do I answer this question I'm asking?

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>>8336917
Thanks, have some tits!

In my work I have some awkward-arse double-area-integral which I've been able to reduce to a double contour-integral using Stokes' theorem, of the form:
[math]\int_{A_1} \int_{A_2} f(A_1, A_2) dA_1 dA_2 \Rightarrow \oint_{C_1} \oint_{C_2} F(C_1,C_2) dC_1 dC_2[/math]

However, the [math]f(A_1,A_2)[/math] is only part of the picture. In a simplification of the problem I'm solving, an extra part of the integral can be factored out as a constant. The REAL integral I need to simplify is:
[math]\int_{A_1} \int_{A_2} f(A_1, A_2) g(A_1) dA_1 dA_2 \Rightarrow \mathrm{?}[/math]

Am I able to use Integration by Parts on this, and still get a "relatively" simple expression in terms of the contour integral? I haven't done this for a little while, so whenever I try to work that out on my own I fudge it up, so I'd appreciate it a lot if, if it's possible to do, someone show how it what it does simplify to.

>>8319889
Energy and enthalpy related:

Can someone explain to me why the heat change equals the change in internal energy when the volume is kept constant?

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I am struggling with this definition of simple connectedness from Bak and Newman.

[math] \textbf{Definition 8.1} \\ \text{A region } D \textit{ simply connected } \text{if its complement is "connected within } \epsilon \text{ to } \infty \text{." That is if for any } z_{0} \in \widetilde{D} \text{ and } \epsilon > 0 \text{, there is a continuous curve }\gamma(t), 0 \leq t \leq \infty \text{ such that} \\ \text{ (a) } d(\gamma(t),\widetilde{D}) \lt \epsilon \\ \text{(b) } \gamma(0)=z_{0}, \\ \text{(c) } \lim_{t \to \infty} \gamma(t) = \infty \\ \text{A curve satisfying (b) and (c), is said to "connect } z_{0} \text{ to } \infty." \text{ (See Chapter 1.4.) (here they just talk about Cauchy sequences which makes sense )} \\ [/math]

I mainly have issues with part a, but I think it is saying that any point on the curve is epsilon small from [math]\widetilde{D}\\[/math] which means that it cannot be in [math]D[/math]. But I have a problem with one statement in the proof of the Lemma.

[math] \textbf{Lemma} \\ \textit{If D is a simply connected region, }\Gamma\textit{ is a closed curve contained in D and }z_{0} \in \widetilde{D}, \\ \textit{ then there exists a differentiable curve }\gamma(t) \textit{ which connects } z_{0} \textit { to } \infty \textit { and which does not intersect } \Gamma. \\

\text{Proof: According to Definition 8.1, there exists a continuous curve } \gamma \text{, connecting } z_{0} \text{ to } \infty \\ \text{ with } d(\gamma(t),\widetilde{D}) \lt \epsilon. \text{ If we take } \epsilon = \frac{1}{2}d(\Gamma,\widetilde{D}) \text{, } \gamma \text{ will not intersect }\Gamma. \text{ **Moreoever,since } \gamma \rightarrow \infty \text{ for some } N, t\ge N \implies |\gamma(t)|\ge max{\{|z|:z \in \Gamma}\}.** \\
\text{ We can then redefine } \gamma(t) = \frac{t}{N}\gamma(N) \text{ so that } \gamma \text{ will be differentiable for } t\ge N. \textbf{Why does this(**) matter?, it seems obvious and I don't see how it contributes.} [/math].

>>8336789
>The other ones require knowing that the rationals are dense / Archimedeanness.
Thanks for the answer
>The other ones require knowing that the rationals are dense / Archimedeanness.

How would that help?

>>8338068
Nice math tags, mate.

>>8338072
Figured using \text{} versus wrapping it in math tags would be better. I'm a noob to LaTeX so I'm not entirely sure what best practice is.

>>8338080
\mathrm{} might have been a better idea.

>>8338070
You need to show that for every [math]\varepsilon > 0[/math] there is a natural number N such that [math]\frac{1}{N} < \varepsilon[/math].

When I was a kid I was in a junkyard and found some engineering-looking thing that I bought because it was cheap and looked interesting.
After actually bothering to look it up now, I've learnt that it's a 'Rok-It' gauge (for checking bore sizes of pipes and such), and on the case it comes in it says it's an 's-tube' gauge.
As far as I can find out, S-tubes are a fancy design of impellers that the parent company loves to advertise and brag about the efficiency of and I can't see how a rok-it gauge could be used on one.

Any ideas?

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Could somebody verify that this property relation gives accurate results? I keep getting bogus temperatures when I use it but maybe I'm just doing something wrong.

ty love you forever

Has anyone tried using a FPGA to simulate FEA or CFD?
Also, which book about funadamentals of computing theory do you recommend?

What should I read if I want to learn game theory?

I'm going through Spivak's calculus and didn't expect to get stumped this early, but anyway:

Why is it that the absolute value of 1+sqrt(2)-sqrt(10) comes out to -1-sqrt(2)+sqrt(10)?

There's clearly something I'm missing here

>>8338302
https://en.wikipedia.org/wiki/Absolute_value
You are effectively calculating a distance, so you can take the modulus and you notice that after a calculation
[math] [1+\sqrt(2)-\sqrt(10)]^2 = [-1-\sqrt(2)+\sqrt(10)]^2 [/math]. However, a negative distance does not make sense, also in real numbers you cannot have any imaginary parts, so you take the positive of these two which is the latter.

>>8338319
Ahh, I see. I was just assuming the answers would be different if you rearranged them like that. Thank you!

Why do I get epididymitis every time I'm constipated?

so like imaginary numbers are like a number but it has 2 dimensions right
so are there numbers above imaginary numbers like one with three dimensions like 1D:real 2D:imag 3D: ???

>>8338735
quaternions, octonions

>>8338735
The complex plane has the same structure as [math]\mathbb{R}^2[/math], but if you have a complex function of one variable you are obtain the mapping [math] f:\mathbb{C}\rightarrow\mathbb{C} [/math] which is like having a mapping [math]f:\mathbb{R}^2\rightarrow\mathbb{R}^2 [/math] and so is 4 dimensional. You can have functions of more than one complex variable though which gets you into further dimensions. https://en.wikipedia.org/wiki/Several_complex_variables

>>8338735
There is no equivalent in 3D specifically because you can't get nice calculation rules like with complexes in three dimensions.
You have to jump to 4D directly.

>>8338068
Does the proof end there or did you cut the rest?
He gets a continous curve, so now I guess he will define some other curve related to [math] \gamma [/math] but differentiable. For some retarded reason he just doesn't choose to give them different names, say [math]\gamma_1(t)=\gamma(t)[/math] for [math] t<N[/math] and
[math] \gamma_1(t)=\frac{t}{N}\gamma(N)[/math]
is now differentiable for [math] t\geq N[/math] and [math] \gamma_1[/math] doesn't intersect [math]\Gamma[/math] (in last sentence you use [math](**)[/math]).

Is [math]\sqrt{\infty}[/math] a real number?

>>8336702
Danke, will take a look at them.

does anyone have some integration table specifically for exponentials and other integrals that would initially be approached with integration by parts?

like int: x^n * exp(inx) and other foms similar to that

>>8338062
Bumping question

>>8338964
Yeah I cut it off. The last sentence is [math] \text{ Finally, because } \gamma(t), 0\le t \le N, \text{ can be uniformly approximated by a differentiable curve, there exists a curve } \gamma \text{ with all of the desired properties}. [/math]. He kind of just hand waved it I feel like. After I wrote this I realized the power of \mathrm{}.

Speaking functionally (as in, a real-world situation), wouldn't dividing something by 0 create infinity?

I usually ignore what happens to dx when doing integration by parts, but now I'm seeing something that says for me to find the integral of tan^-1 x dx, suggesting I have u = tan^-1 x and dv = dx.
If dx has to be integrated in this case, why can I get the correct answer when I completely ignore dx in other integrations?

>>8339034
No; because although lowering a positive divisor towards zero makes the result head towards positive infinity, raising a negative divisor towards zero makes the result head towards negative infinity.

So dividing something by 0.000000000... (infinite zeroes) ...000001 would create infinity, but as soon as the divisor no longer has a sign you don't know the sign of the output either.

>>8339088
>why can I get the correct answer when I completely ignore dx in other integrations?
If you like to ignore dx (you should get out of the habit of doing this, but that's beside the point...) then you can just think of the integrand as the product of arctan(x) and 1. You aren't doing anything differently when you set dv = dx. That's just the same thing as dv = (1)dx.

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which correlation is the strongest degree of relationship between two variables. +0.10, -0.67, -0.10, or +0.5

>>8339109
But when I integrate dx I get x.
So it clearly makes a difference.

>>8339117
b

>>8326795
2nd question is impossible, (you did a mistake because by isomorphism you have cardinal equality which is not met)

can't bother with writting as I always forget how to, but just check contradiction with pre-image of 0F by such morphism :

x = phi^-1 (0F ) then phi( x - x ) = phi(0E) = 1F
but phi(x - x) = phi( x) .F phi( -x) = 0F .F ??? = 0F
contradiction and it proves something even greater, no additive law can be made such that it can also be a ring law except for singleton groups/rings.

>>8331464
check the message just above this one, I sketched something for which you don't even need characteristics.

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how do you turn this?

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>>8339443
into this?

>>8339443
>>8339450
[eqn]\frac{81}{n^4} \left[ \frac{n(n + 1)}{2} \right] ^ 2 = \frac{81}{n ^ 4} \left[ \frac{n^2 + n}{2} \right] ^ 2 = \frac{81}{n^4} \frac{n^4 + 2n^3 + n^2}{4} = \frac{81}{4} \left( 1 + \frac{2}{n} + \frac{1}{n^2} \right) = \frac{81}{4} \left( 1 + \frac{1}{n} \right) ^ 2[/eqn]

>>8339480
Wtf? 1+1/n=(n+1)/n=n(n+1)/n^2

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>>8339486
Problem?

>>8339480
thanks senpai

Would an advance civilization take the time to make a white hole in order to feed their universe enough energy to go on forever, or would they leave it to avoid its heat death?

What is it about machine learning that demands so much math?

>>8339536
>meme learning

Stop.

>>8339536
it comes from desperation. when all else fails, hide behind the math.

I want to read about artificial intelligence and I would like some recommendations on books.

So far I have Stuart Russell's book. But I want to have more resources on the subject.

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what does this mean?
I'm a brainlet, pls halp.

>>8339658
I know there's one with a cartoon tasmanian devil that is very good for beginners

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3 Questions:
1. Example 3a: 3a is nonlinear due to not having x(sub t) -> x(sub t+ 3) right? Would it be linear if there was an x(sub t + 2) in the equation?

2. I don't understand constant coefficients. I thought I did, but suddenly my brain does the no goods.

3. Could someone summarize each point? The prereq for this class was linear algebra or differential equations, and I took linear algebra. Not confident I full understand.

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>>8339701
Here's a graphic.

The first part of the theorem says that we have some function, f(x). It says that this function has a domain from a to b and a range from m to M.

The second part states that the integral of f(x) from a to b is in between the values m(b - a) and M(b - a). In other words, the area under the curve must be between (or equal to) the areas of the rectangles m(b - a) and M(b - a), as you can see in the pic.

>>8339727
I see, thanks very much, it makes a lot of sense.
I thought for a second, the ms were functions

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Why did no one came up with a symbol for the word "otherwise" ? It is used a lot for piece-wise functions...

what does slope exactly mean?

>>8339794
should be _ , meaning it takes anything else if all predicates fail, and returns some arbitrary value

>>8339805
thanks

>>8339794
Mathematica just uses "True"

>>8339808
haskell also uses True, and has otherwise as synonym for it
but I wish it would be _ , because True feels out place and otherwise is too long

>>8339806
I just came up with that, don't think this is a standard
however, if you're wriitng a paper, please do this

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How do I do these problems?

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And how do I do this?

What would happen if I were to make a sandwich of plastic and lead foil of the same thickness as a slab of lead.

Would this sandwich be better or worse than the slab for protecting against radiation?

How do I sketch

r(t)=<4cos(t), 4sin(t), t-pi>

?

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>>8339825
for 6 pic related

Just download Calculus for Scientist and Engineers Early Transcendental, easily found on torrents

Go to chapter 12, it has examples like these
>>8339830
>>8339835

What can I expect in technology 20 yrs from now?

>>8339850
not much senpai
ww3 will happen

>>8339849
For finding intersection points would I just set the respective equations equal to each other and solve for t?

>>8339862
read the book I told you, lazy fuck you might learn something since apparently you aren't leaning shit from your class. Sleeping during lectures ?

>>8339874
I missed that particular lecture due to unforeseen circumstances

Just looking for some help as all before I get around to torrenting the book

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Multiple questions on this one.

- How can one verify the bijectivity of g?

- How can one build g and other functions that would be bijections from X to Y?

>>8339536
> What is it about machine learning that demands so much math?
Machine learning doesn't actually require that much math compared to some other fields.

I think it's more a case of machine learning being a "trendy" field so it's currently attracting a lot of mathematically-challenged programmers whose first impressions is "holy crap, so much math".

If your previous experience is in webdev or databases, a lot of programming fields are going to be "so much math".

>>8339834
Worse.

A slab of lead is equivalent to a sandwich of lead foil and lead foil. Replacing some of the bits of lead with plastic is going to reduce the absorption.

>>8327392
>>8327403
>the denominator is representing the the number that it is being raised to 2. The 1 = what that number is multiplied by one.

The numerator is what you raise it to, the denominator is what type of root you take.

5^(3/4) = 4th root of (5^3)

The reason why n^(1/a) is the a'th root of n is because:

n^(1/a) * n^(1/a) * n^(1/a) * ... (for a terms)

by the rules of exponents, equals:

n^((1 + 1 + 1 + ... + 1) / a) = n^(a / a) = n

Now that we know n^(1/a) is the a'th root of n, what happens if you raise n to a power before taking the root?:

(n^b)^(1/a)

by exponent identity, this equals:

n^(b * 1/a) = n^(b/a)

If instead you raise n to a power AFTER taking the root, you get the same thing, so it doesn't matter the order.

>>8328438
You got the correct answer.

>>8328442
It doesn't matter whether it's log or ln. ln is just log-base-e and if the bases are the same between two logs then you can apply the identity you used.

>>8333119
I don't know about the first one, but the second one is:

F = AB + (AB)'C
= AB + C
= (1)(AB + C)
= (AB + (AB)')(AB + C)

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I didn't complete my A-Levels (only AS, A/A/A/B math/phys/chem/buss) while at school and plan on applying to UK universities

What can I expect to study in a UK university foundation course for engineering?
Can I just study from the AL textbooks (C3/4, Mech2, FM1, etc.)? If not, what textbooks should I read ahead in?
Is there any hope in being accepted into a good/top university like this?

Why is it bad practice to integrate with respect to a variable that is used in the bounds of the integral? What's an example of a situation where it could cause confusion?

In Boolean Algebra, why is thr complimentary axiom a + a' = 1 and not 0? Is it something that people decide on or is there some embedded logic in that choice? In arithmetic compliment equals 0

>>8340702
There is no "complementary axiom".

"x or (not x) = T" follows from the definitions of "or" and "not".

>>8340697
It's technically not wrong, it's just confusing to reuse variables.

>>8340763

Thats the term my prof use but i guess you are right, its not really an axiom

>>8340702
When is a + a' true?

Either a is true or a is false, and in either case, the expression yields true, therefore it can be reduced to 1.

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>>8319889
Anyone here into seismology?
I have a question.
3 days in a row my city has multiple level 5 or above earthquakes.
This city was thorn down by earthquakes in 518, 1505 and 1963.
Is it time to get my ass out of here?

>>8340840
>using + for or
>I shiggy diggy do

If you represent truth values as 1s and 0s then a or b = ab + a + b, and a xor b = a + b. But yes, you are right that in Boolean logic a or not a is always true. IT's called the law of excluded middle.

>>8340887
>using + for or

Learn boolean algebra.

>a or b = ab + a + b

a + b = a + b + p, where p is anything.

>a xor b = a + b

Not true.

a xor b = ab' + a'b

>>8340919
I'm talking about {0, 1} with the natural addition operation, friendo. 1 + 1 = 0, hence + is not or. Are you an engineer or something?

>>8340939
>Are you an engineer or something?

No, just someone taking an intro Computer Architecture course.

>>8340945
>>>/out/

Can someone explain to me Cantor's diagonalization argument? Specifically how exactly was the algorithm supposed to generate the whole R from a bijection with N.

>>8340238
Please.

>>8341055
>>8340238
AFAICT, proving bijectivity is mainly about showing that the two cases (g(x)=f(x) and g(x)=x) don't overlap, so that g(x)=g(y) iff x=y.

If f is a bijection, then if X and Y are disjoint then so are f(X) and f(Y). And f^n must also be a bijection.

As to how you would build such a g() ... well, they give you an example right there. Assuming that you already have an f() such that "x in f^n(X)\f^n(Y) for any n" is decidable.

>>8341052
> how exactly was the algorithm supposed to generate the whole R from a bijection with N.
It isn't. The whole point is that a bijection between N and R is an impossibility. Cantor's diagonalisation argument is proof by contradiction.

Given *any* countably-infinite list of elements from [0,1), you can generate another element from [0,1) which is guaranteed not to be in the list.

I.e. any such list is incomplete, i.e. no such bijection exists, i.e. the cardinality of [0,1) is greater than the cardinality of N.

How does knowing whether a series/sequence/function diverges or converges help us at anything in math? Like what is it's purpose?

>>8341358
If it converges, it has a limit. If it diverges, it doesn't. That's fairly useful if you were planning on using the limit for something.

>>8341272

I know that there is no bijection N -> R, but how was the diagonilization supposed to show that:

>Given *any* countably-infinite list of elements from [0,1), you can generate another element from [0,1) which is guaranteed not to be in the list.

I am looking at the method where there's a set of binary numbers and from these set of number we generate another number, by taking the complement of the n-th digit from the n-th element in the set to be the n-th digit of our new number. From this he showed that no number in the set is equal to this one.

I wondered, how was this supposed to show anything at all? Maybe the set was simply incomplete? Or is it using the fact we have a set S that is a subset of R that have a bijection with N, but we can always find some x that is not in S but in R, therefore the cardinality of R is bigger.

Is reading Apostol's Calculus worth it if I've already taken calc 1-3?

I ask because they were really watered-down engineering versions of the courses, and I'm betting I have some gaping holes in my knowledge. Should I just move on to real analysis?

How big a poo is the biggest physically possible?

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Working through some math problems now, and I'm stuck on this one. Pic related.

I know the answer is 4.139kg, but I do not know how to get there. If I find the average rate, I get 4.143kg, but it's highly unlikely that's the correct approach.

Anyone, please?

>>8319901
>makes a post in the thread anyway

>>8341604
Know any calculus?

The sentence "a baby gains weight at a rate proportional to its weight" can be written as the differential equation
[eqn]\frac{dw}{dt} = kw \implies \frac{dw}{dt} - kw = 0[/eqn]
where w is the weight, dw/dt is the rate of change of the weight, and k is a constant of proportionality. We can solve for w to get:
[eqn]w = w_0 \, e^{kt} [/eqn]
We know that [math]w_0 = 4[/math], so we can use the second condition to find [math]e^t[/math]
[eqn]4.4 = 4 \, e^{14k} \implies e^k = (\frac{4.4}{4}) ^ {\frac{1}{14}}[/eqn]
Now we can plug this back in and solve for w at 5 days:
[eqn]w = 4 \, (\frac{4.4}{4}) ^ {\frac{t}{14}}[/eqn]
[eqn]w(5) = 4 \, (\frac{4.4}{4}) ^ {\frac{5}{14}} = 4.139.[/eqn]

>>8341660
Currently learning about this stuff.

I'm still not sure I grasp it 100%, but I feel a bit more comfortable with it after reading your post. Thanks.

>>8341470
>Maybe the set was simply incomplete?
No, if you assume a biyection you basically get an enumeration like in the argument. And his proof shows that given any enumeration/biyection from N to [0,1) you can build a number that isn't on your list, as opposed to what you assumed.

>>8341470
> Maybe the set was simply incomplete?

There's no "maybe" about it. The point is that, because it makes no assumptions whatsoever about the composition of the set, it applies to any enumerable set. IOW, you simply cannot enumerate the reals; any mapping f : N->R fails to be surjective.

> Or is it using the fact we have a set S that is a subset of R that have a bijection with N, but we can always find some x that is not in S but in R, therefore the cardinality of R is bigger.
That's a necessary condition, but not a sufficient one.

Consider: f: N->N defined by f(x)=2*x generates a set S which is a subset of N that has a bijection with N, but we can always find some x which is not in S but in N. That doesn't mean that card N > card N; it just means that we chose the wrong f.

Cantor's diagonalisation proof relies upon the fact that it doesn't say *anything* about f, ergo it applies for *any* f. It's not that some specific f doesn't enumerate the reals, but that no such f can exist.

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What was the point of squaring in this?

>>8341946
In squaring what?

How does binary space partitioning work?

>>8342076
As in BSP trees for 3D graphics?

Given a plane and a viewpoint, anything on the same side of the plane as the viewpoint cannot be obscured by anything on the opposite side, and anything on the opposite side cannot obscure anything on the same side.

So you recursively partition the space with planes which don't intersect any object (if necessary, by cutting objects in two so that the each half is on one side of the plane). Then you can render the scene by depth-first traversal, traversing the child on the opposite side of the plane to the viewpoint before that on the same side.

>>8342253
I still dont get how this works

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What am I supposed to be using to solve these trig functions? What is the point of reference?

We are not allowed to use a graphic calculator.

I'm just not understanding what I'm supposed to do with the trig identities. The other problems I am ok with, but when they throw the trig identities into the mix, I'm not sure what to do, or how to solve.

Please help

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I must be retarded
can someone help me calc the point of impact?

>>8343113
A moves 100/*80(80+50) ~= 61.5
B moves 100/*50(80+50) ~= 38.5

>>8343094
> What am I supposed to be using to solve these trig functions?
Knowledge of their value and asymptotic behaviour at specific angles.

This particular problem only requires knowing the value of sec(pi/2):

As x->1/2, pi*x->pi/2, cos(x)->0, sec(x)->infinity
IOW, the limit doesn't exist.

Some problems may require the fact that sin and tan have unit slope at x=0:
x->0 => sin(x) -> x, tan(x) -> x

>>8343187
where do you get pi/2 from? it's nowhere in the problem

>>8343187

>Knowledge of their value and asymptotic behaviour at specific angles.

how the fuck am I supposed to memorize all these for all these different trig functions

>>8343195
> where do you get pi/2 from? it's nowhere in the problem
The problem involves the value of sec(pi*x) as x->1/2. When x=1/2, pi*x will be pi/2.

>>8343199
> how the fuck am I supposed to memorize all these for all these different trig functions
By not being a complete retard?

Seriously, if you can't even remember the values of the trig functions at 0/90/180/270, you need to abandon anything involving math and take up sociology or gender studies or something.

>>8343199
>all these different trig functions
THERE ARE LITERALLY THREE OF THEM
AND THEY CAN ALL BE REDUCED TO A SINGLE ONE
LIKE
WHAT THE FUCK MAN

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>>8343349
>only 3 trig functions
>csc, tan, sin, cos, sec

Ok so how do I manipulate the unit circle to go from sin to cosine to tangent to secant?

>>8343368
Come on Léa, csc is 1/sin
tan is sin/cos
sec is 1/cos

that's only cos and sin left.
But cos is just sin shifted by pi/2

So really you only need to know one

>>8343388

so if sin pi/2 = (0, 1) can you tell me what cos would be or how I would convert to sec, for example?

>>8343404
>Stupid questions thread

Jesus christ. You aren't supposed to take that literally...

when subunits link together to form a polymer what molecule is produced as a by product?
Is it water?

>>8343444

depends on what you're linking together and in what context

In case you can help: >>8326351

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I'm redoing calc1 atm and everything has been childsplay up until now, but this exercise has me pulling my hair out.

I am supposed to solve this via mathematical induction.

>>8344477

By the induction hypothesis:
S <= 2 sqrt(n) where S = 1 + ... + 1/sqrt(n)
S^2 <= 4n

Let s[ ] denote square root. Now we just check if
S + 1/sqrt(n+1) ?<= 2sqrt(n + 1)
But this is true iff S <= 2s[n+1] - 1/s[n+1] = (2(n+1) - 1)/s[n+1] = (2n + 1)/s[n+1]
iff S^2 <= (n + (n + 1))^2/(n + 1) = (4n^2 + 4n + 1)/(n + 1) = (4n(n + 1) + 1)/(n + 1) = 4n + 1/(n + 1)
done

>>8344477
Obviously
[math]\sum_{i=1}^n \frac{1}{√i}\leq 2n [/math] so the proof is trivial

>>8344510
Thanks! I knew I wasn't seeing something.

Should we make a new thread?

>>8344571
Nah.
Good run tho.

I am currently taking probability class and just how do you get used to it?

>>8344605
You don't. Prepare your anus cause it's gonna be rough.

>>8344632
Why?

>>8344843
There's no purpose behind the difficulty of probability theory, it's just there.

>>8344934

Surely anyone whos deep enough in it will have some sort of epiphany like oooh thats how it is

>>8344959
You'd think that, wouldn't you?

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Really dumb question, but I am unsure how to enter in the direction here?

The angle has to be below the x-axis, so I would put 36 degrees correct?

Please someone help

hey lads can you help me with my hw ? :^)

>>8345587

No

>>8345541
yes correct, if you think the answer is 36 degrees below x-axis then you can put 36 in the box

>>8333199
DE models spring with a period of 2 seconds. Your time step is 4 seconds. Ya goof'd.

>>8345661
I think it is, but I'm not sure. Can anyone else confirm if it's 36 or -36?

>>8345541
>>8345661
>>8345688
It was 36, thanks anons!

>>8320753

this is a meme right? I mean what you've written is so alien to me. More generally, why is it that every post that is remotely related to quantum mechanics seems to be written in jargons.

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What do?

>>8319889
Hey, /sci/. /k/ here.

So I want some Ammonium Nitrate. The closest thing available to me is Calcium Ammonium Nitrate. All I was able to find about how to get rid of the calcium is the very vague instructions, "dissolve the CAN in water and filter off the chalk, then boil it to evaporate the water". No luck so far.

Can anyone explain more about what's actually going on there, and why it will or won't work? What I might be doing wrong?

>inb4 why
I need some pure Ammonium Nitrate to fertilize some plants

>>8345926
wtf did I do wrong in this problem? any anons know?

>>8345926
>>8345930
I think you have to input the nearest degree, not the exact expression desu

>>8345905
Epsylon is infinitesimal, hence b+eps = b.

>>8345930
You forgot the arccos().
A.B=|A|*|B|*cos(theta).

>>8345905
It depends upon what sort of proof is being sought. But in the absence of any further information:

Proof by contradiction. Assume a>b, set a=b+k for k>0, set eps=k/2, b+k>b+eps => a>b+eps.

Why is the determinant of a 2x2 matrix ad - bc?

In general, for a matrix nxn, what is the determinant?

>>8347060
The determinant is the factor by which areas, volumes, etc are scaled.

It can be calculated as the dot product between any row or column of the matrix and the same row or column of the cofactor matrix.

>>8347109

I just found it by taking the identity matrix, but I am still wondering what exactly is it? Currently trying to translate this to

(ax1 + bx2....)

this is called an algebraic expression right?

>>8347180
If you're trying to get a sum-of-products expression for the determinant of an NxN matrix, the sum has n! terms, each a product of n values.

For large matrices, that gets unwieldy (and inefficient), so you'd normally use recursion (or iteration), caching the determinants of the submatrices.

det(M) = sum[j]((-1)^(i+j)*M[i,j]*det(submatrix(M,i,j)))

where submatrix(M,row,col) is the matrix obtained by removing the specified row and column from M. Note that i can be any row without affecting the answer. (-1)^(i+j) is just [1,-1,1,-1,...], i.e. the signs alternate.

So for a 5x5, you calculate 5 4x4 determinants, each of which needs 4 3x3 determinants, each needing 3 2x2 determinants. If you multiply that out, you get 5*4*3=60 2x2 determinants; but there are only actually 10 distinct ways to obtain a 2x2 submatrix from the bottom 2 rows, i.e. each 2x2 determinant gets used 6 times.