/sci/ - Science & Math

So I'm a bit confused with the order of numercial methods. They both represent the computational time AND how fast the order decreases?

So say a method of order O(x) will converge slower than a method of order O(x^2)?

>>10112208
how fast the error decreases* sorry

>>10112208
>>10112213
In different contexts, yes.
O(f) is just the class of functions that does not grow faster than f does. For convergence, the behaviour around 0 is relevant, and obviously a quadratic function will decrease more rapidly in that region ( |x| < 1 ) than a linear one.

Am I okay in assuming 450m for the Head here?

Also what turbine would you lads use? I'm thinking Francis turbines

>>10112231
No........

Really brother?

>>10112229
so, higher order = higher computational time with faster convergence?

>>10112390
n-no, what's wrong fren?

So it would seem I have odorous hemorrhoids that started up maybe up to a week ago. If I ingest a substantial quantity of magnesium oxide, with the intent to have very loose stools, could this mend the problem after a couple days?

If del dot A is the divergence of A, what the fuck is A dot del?

Is there a term for a chemical that has the property that it promotes oxidation? There's chemicals with antioxidant properties but what about the reverse?

Any anons in the UK or more specifically at University of Edinburgh? Thinking of applying (from the US) for a masters or maybe phd related to EE, mainly the Signal Processing and Sensor & Imaging systems degrees, but maybe the Optical Medical Innovation one. Mostly just wondering what exactly is a 2:1 Honours degree (just a bachelors?) and do masters and phd students get funding often? because in the US a PhD is basically always funded either by the university or by you doing research for them, whereas a Masters can be funded but isnt as guaranteed

>>10112231
That seems like a more than enough head "pressure?" Why fifty hertz? Is that a standard in tha relevant country? You lose flow through friction. You will not lose pressure. You will not lose any flow in a series circuit. You will gain pressure. Right? Don't know shit about hydro turbines

>>10112471
Oxidizer? Antioxidants

>>10112406
Keep a food diary. Lay off nightshades. You can diminish to insignificant but not non-existence

>>10112695
Nightshades? And yes I’m hindsight it was clear I had not been consuming much fiber which was much of the cause.

>>10112457
a linear operator

Pretty rudimentary question, but how would I show that 5n^2 + 3n is O(n^2)?

When drawing Bode Plots why are we only interested in the imaginary values? Does the real part not affect the response? And if it doesn't why do we even bother with Laplace transform, wouldn't Fourier be enough?

>>10112653
I'm in the UK doing a PhD. First thing: the UK has a different grading system. Everything you do is given as a percentage, but there are different percentage tiers:
>0-40: fail
>40-50: third class
>50-60: 2:2
>60-70: 2:1
>70+: first class
The British system works in that the average person will achieve a 2:1, so exam difficulty/grading/curving is based on this concept. Usually any company you apply to requires at most (and at least) a 2:1 degree too. For Masters/PhD, they almost exclusively require you to get a first class (even if it says you require at least a 2:1), and for PhD usually a high first class. I'm assuming you're coming from an American system, and given that it is such a clusterfuck with grade inflation, then there is no universal GPA to UK-class system conversion, but for reference, a first class should be approximately "top 30% of the class".

Now, as for funding, Master's students almost never get funding, especially not if you're an overseas student (and you have to pay much more in tuition), unless it's a sort of masters+doctorate program. PhD students mostly get funding, but not everyone gets it, and a BIG thing to note is that "full funding" is not always full funding if you're an overseas student - If it says it covers "tuition + living costs", then the "tuition" part usually means EU tuition (I got mistaken for an overseas student in my first month, so my tuition was 18k instead of 3.5k, so they thought I had to pay it - note my wage otherwise is 14k a year, although engineering students usually get more). Therefore you should always ask the department in charge of admissions.

>>10112848
Complete the square

>>10112106
Why des my sweat smell like popcorn?

>>10112862
I'm not quite sure what you mean. I'm assuming that you need to find the fastest growing term (5n^2) and then remove the coefficient, which would leave us with n^2. Is that how to deduce the time complexity of some algorithm?

>>10112848
>>10112879

Just incase anyone sees this and wants to correct me if I'm wrong, I got:

5n^2 + 3n = (5n^2 + 3n) - 3n = 5n^2 - 5 = O(n^2)

not sure if that's correct though.

>>10112857
Ok thanks. I am not sure on my class rank as it isnt really readily available, but I think I am at least top 10%, probably higher for just my major (EE). The way you put it definitely seems like the price may be an issue though. I have heard that there are some internships for engineering PhDs which can help with funding too, but im not going to assume that will be a given. I'll just apply and see if I get any funding I guess

>>10112904
holy fuck lmao

>>10112956
I was just following the find the largest term/remove the coefficient rule, maybe you could tell me why I'm wrong instead of just saying that, I posted in sqt for a reason

>>10112393
> so, higher order = higher computational time with faster convergence?
No. Those are two different things.

Big-O notation simply describes the "shape" of the asymptotes of some function. Any function. It could be the function which describes the computation time or memory consumption or rate of convergence or whatever.

Typically, you're not interested in the exact function as that includes arbitrary constants determined by external factors, and also overheads which become negligible for large values of the argument. So you just state that the time/memory/convergence/whatever is O(x^2) or O(n*log(n)) or whatever it is, as that describes asymptotic behaviour of the function.

How do i find alpha in this overdamped parallel RLC circuit?
I need to find the value of the resistor and I planned on finding it through alpha = 1/2RC

>>10112971
For a polynomial, its order is just the largest term. f(x)=a*x^n+b*x^(n-1)+... is O(x^n), as there exists a constant M such that for all sufficiently large x: |f(x)|<M*x^n. Eventually, all of the other terms will become negligible compared to the a*x^n term.

E.g. for M=6
5n^2+3n - 6n^2
= 3n-n^2
= n(3-n)
<0 for all n>3

So 5n^2+3n<6n^2 for all n>3
=> 5n^2+3n = O(n^2)

Note that if a function is O(n^2) then it's automatically O(n^k) for all k>=2. But normally you want to make the strongest assertion you can justify, I.e. use the lowest order you can prove.

>>10113047
Thank you, that makes sense, appreciate the help!

>>10112867
Have you got a second opinion about the smell of your sweat? You may think it smells good due to a brain tumor pushing on the cavernous sinus. You may need to cut back on popcorn consumption.

>>10113020
Ohms law? This picture is shitty. Voltage divided by current equals resistance. Show to DIY

Does a weaker stress response lead to higher intelligence, or does more intelligence lead to a weaker stress response?

>>10113078
I don't know the current.

Can someone show me or link me a proof to the result [eqn]V \subseteq V^*[/eqn] for any vector space [math]V[/math] and its dual [math]V^*[/math]? Obviously I'm most interested in the infinite dimensional case, where equality is in general not assumed. (Equality in this sense, I believe, actually means that they're isomorphic; I get that a vector space and its dual are not necessarily isomorphic to each other, but I don't see how that translates to the dual being *larger* than the original space.)

Also related, but equality is only assumed for finite dimensional vector spaces and inner product spaces, correct? Or does the latter need to be Hilbert?

>>10113020
Could try finding the currents on the condensator and inductor by KVL in s-domain and from that get current for the resistor, from which you can solve for resistence.

>>10113145
You mean V**? How can one be a subset of the other if they're not even the same objects?

>>10113161
In the same way that [math]\mathbb{Z} \subset \mathbb {Q}[/math]. As I noted, equality is in the sense that you can I identify the sets with each other, typically in the form of an isomorphism.

>>10113145
You mean proof that V is isomorphic to some subset its dual space?

>>10113182
I believe that would be sufficient, yes.

>>10113187
Let E be a basis over V, and V" is V's dual space. If a is a vector in E, we take f(a) to be the linear operator which zeroes any vector orthogonal to a, and gives a when multiplied by a. Im f is a vector space isomorphic to V.

I'm having trouble drawing this out. x^2+y^2+z^2 = 4 is a sphere with radius 2, but where the fuck did that cone come from? When it says pointing down, do they mean the pointy end or the wide end?

>>10113198
>Let E be a basis over V
Of course, this is assuming a basis exists.

>>10113252
>show that V and the dual space are isomorphic without assuming an isomorphism can actually be constructed lmao

>>10113255
>>show that V and the dual space are isomorphic without assuming an isomorphism can actually be constructed lmao
Who are you quoting?

>>10112106
Why is x divided by x equal to 1 when it's undefined at 0?

>>10113303
x divided by x is not defined at 0. you can define it to be 1 at 0 to make it continuous, perhaps in applications.

>>10112106
this webm crashed my fucking computer

anyway, why do embryos look the same?

>>10113349
Google Beauty Venus IPX219

>>10113349
simplicity, compactness, made of the same general materials, using the same basic mechanics.

>>10113349
They don't. This is from an outdated source. Humans don't have a tail during any stage in their development.

>>10113378
Ever seen a sonogram? Human looks like seahorse. But agreed, this is not only outdated but a bullshit source. Look the same is in the eye of the beholder.

I'm having a really tough time converting triple integrals in rectangular coordinates to spherical. Does anybody have any material I can go over? Most of the stuff I find online have constant boundaries. I know for sure my professor will have stuff with trig function boundaries on the exam.

Would it ever be possible to create a device that can communicate with animals? I feel like that could be possible if we ever really nail how the brain works.

>>10113471
Impossible. There's no way to verify that what we're translating is accurate unless there was an animal that could speak a human language.

Is there a way to practice pre employment assessment tests? I don't know what to do, I keep failing all the verbal and numerical reasoning tests

>>10113516
Practice the stuff they asked you? What did they ask you?

>>10113527
I don't remember exactly. But they're all questions about inferring information from passages or doing math tests about money and economics

>>10113471
>>10113477
Impossible is for pussies. Until it happens, a whip gets the point across. Birds can talk'ish. Apes use sign language. You don't need a translatior. I don't think animals have much to say. I knew of a man with a story of a windmill that required frequent maintenance. It would start making some "machine bitching" noise and they would go out and dick with it. The birds learned to mimic the sounds of the distressed windmill just to fuck with the people and watch them come out of the house. You are welcome.

>>10113552
>just to fuck with people
How would you know they're doing it to fuck with them? It could be they're just mimicking the sound.

>>10113584
I would not know but the guy who told me the story seemed to think they did. Are you calling birds stupid? Are you a bird hater! Are one of those bitches on the internet that likes to pick apart everything so you can appear smarter? Just fucking with you bro. Who knows?

>>10113594
I have definitely seen birds.. ?scissor tails? Messing with my dog. They would fly around in circles at the park to make her run. When she grew tired the would get really low to reinspire her and if she would lie do un, they would also land and take a break. Seems like legit fucking with a dog.

>>10112457
A vector field. Let [math]M[/math] be a smooth [math]n[/math]-dimensional manifold, then there exists charts [math](U,\alpha)[/math] about each point [math]p \in M[/math] such that [math]T_pM = C^\infty(M) \otimes \{\partial_i\}_i[/math] as a free [math]C^\infty(M)[/math] module, where [math]\partial_i = \frac{\partial}{\partial x_i}[/math] whence [math]\alpha(p) = x[/math] for all [math]p \in U[/math].
>>10113145
It depends on what topology you endow on [math]V^*[/math]. In general you can give [math]V^*[/math] the weak limit topology [math]f_n \rightharpoonup f \in V^* \iff |f_n(x) - f(x)|_V \xrightarrow[n\rightarrow \infty]{} 0[/math], and this gets you shit like the Dirac delta distribution, which is obviously not in the Schwarz space.
For [math]V \cong V^*[/math], [math]V[/math] needs to be separable. [math]V[/math] with uncountable basis need not have this isomorphism (see Schwarz functions on non-compact spaces).

How come we are adding 2 dydxdz integrals?
Why don't we add 2 integrals from dxdydz? What difference do they have that makes us add 2 integrals?

I learned in class that the current density J is equal to the sum of the conduction current plus the displacement current

J = Jc + Jd

Then I read today that the current density equals the free current + bound current.

J = Jf + Jb

What is the difference between the two equations? Does Jf = Jc and Jd = Jb or vice?

Here's a picture to get your attention

Why does duct tape get rid of plantar warts?

>>10113835
With bound you mean magnetization currents?

>>10113835
it's the context
current = free current + bound current is more general, and is also explicitly true
current = conduction current + displacement current isn't actually explicitly true. but it works if you ignore the "dE/dt" term in maxwell's eq and instead include the displacement current. in this case, conduction current refers to the total actual current (and bound current is usually approximated as 0, so it is the free current too).

bump
>>10112853

>>10113988
I don't know. Suffocation?

>>10113643
>depends on the topolgy
That's a homeomorphism. Anon's asking isomorphism.

>>10112853
> Does the real part not affect the response? And if it doesn't why do we even bother with Laplace transform, wouldn't Fourier be enough?
The easiest way to calculate the Fourier transform of the transfer function is usually to calculate the Laplace transform and substitute s=jw. Especially if the transfer function is defined by a linear ODE.

how the fuck do I calculate the inertia of a disc if its tilted

>>10113643
Hey animuposter, the previous thread died, could you mind explaining what an integrable polarization is? Same goes for leaves of the foliation, first time I hear these things in this context. Thanks

>>10112106
where to should i start to learn electronics in more math-oriented/autistic way?

I feel like such a brainlet for not understanding this, I don't get how I'm supposed to obtain the PDF from this.

>>10114373
oops, I'm so mindfucked by probability that I feel like resigning entirely.

>>10112106
I HAVE A BIO EXAM TODAY AND I ONLY STUDIED LAST NIGHT. PANIC. HOW DO PRACTICE GOOD TIME MANAGEMENT WITH KIDS, A JOB, A WIFE. I JUST WANT TO DO THE RIGHT THING.

>>10114375
Righty. So you have a circle |(x, y)|<=2 and x, y is definitely in this circle. Becausr the probability is distributed in this space uniformly, the chance is the area of the circle |(x, y)|<=1, divided by the whole area. So 1/4.

>>10114390
You converted it to polar coordinates, and then divided the two by their double integrals?

>>10114394
>integration
The area of a circle is πr^2. I'm not using integrals unless I have to calculate the expected value or something.

>>10114401
okay, but isn't the probability 1/2 since the radius of the outer circle is sqrt(2)?

>>10114324
>integrable polarization
A polarization is a Lagrangian subbundle [math]P\subset TM[/math] of the tangent bundle such that [math][P,P]\subset P[/math], where orthogonality is defined in terms of the symplectic form. Define [math]D = P \cap P^\perp \cap TM[/math] and [math]E = P \oplus P^\perp \cap TM[/math], [math]P[/math] is integrable if
1.[math][E,E] \subset E[/math],
2. [math]M/D \rightarrow M/E[/math] is a submersion of smooth manifolds.
When [math]P[/math] is integrable, you're able to "polarize" out coordinates in [math]P^\perp[/math] on [math]M/E[/math]. For instance, holomorphic quantization is achieved by taking the integrable Kahler polarization [math]P[/math] that polarizes out vector fields [math]X = X_i \partial_{p_i}[/math] after prequantization. This makes [math]P[/math]-wavefunctions holomorphic and momentum independent.
>leaves of a foliation
A foliation is a family of diffeomorphisms [math]\varphi_i:U_n \rightarrow U_m[/math] between opens sets in Euclidean spaces such that [math]\varphi_i^{-1}(U_m) \cong U^{n-m}[/math] for each [math]1 \leq i \leq n-m[/math], and each preimage intersect transversally with each other. A leaf is a (n-m)-dimensional subset of [math]\varphi_i^{-1}(U_m)[/math].
It can be seen that an integrable polarization gives a foliation [math]\varphi_i: (x,y)\mapsto (x,y_1,\dots,\hat{y}_i,y_n)[/math] of [math]M[/math], which you can think of as "integrating out" the set of coordinates [math]y[/math] on each local chart of [math]M[/math]. If [math]P[/math] is integrable and if [math]X_H[/math] is a Hamiltonian vector field compatible with it, then trajectories of [math]X_H[/math] lies within leaves [math]\varphi_i^{-1}(U_m)[/math] of the foliation given by [math]P[/math]. This is a purely differential geometric understanding of the fact that "trajectories stay in the level sets of constant energy for time-independent systems".

>>10114411
>diffeomorphisms
Maps*, not diffeomorphisms, sorry. They can't be diffeomorphisms if they're in different dimensions

I have to sketch a spectrum of the addition of a 1 kHz sine wave and a 2 kHz sine wave, in which the 2 kHz sine wave has double the amplitude of the 1 Hz sine wave. Pic related was the answer given, but I thought the bigger bar had to be at 2kHz due to the amplitude being bigger. Can someone explain what the correct answer is?

and just so I understand this, I find the area enclosed by the region in this problem too, right?

>>10114433
to show that f is a PDF, you need [math]\int_{\Omega}f = 1[/math]. Since the function is not constant, you can‘t answer the questions by area in this case.

>>10113683
Bump

>>10114179
The topology dictates the closure-ness of your space and hence what elements are in it.
Please actually study functional analysis before posting.

>>10114411
Thanks for the complete answer. I’ll try to understand this even tho it seems a bit abstract even for a guy who’s into differential geometry

>>10114404
Radius don't matter, area do
>>10114530
>The topology dictates the closure-ness of your space and hence what elements are in it.
I'd like to remind you we're talking about general vector spaces. It's closed under linear combinations.
A complete vector space has elements because of its topology, but anon's question was about a random vector space being contained in its dual, or as he later clarified, being isomorphic to a some subspace.
And this isn't functional analysis.
>>10114411
Me on the left.

>>10114609
>general vector spaces
What I said is valid as long as [math]V[/math] has a metric, and once it does it's in the realm of functional analysis and completeness is necessary. I've demonstrated what he asked in this case.
Granted without metrics there's not much that can be said, and his problem can't be tracked even with topology. That's why I did not comment in full generality. In order to do so one has to demonstrate that [math]{\bf Hilb}[/math] inherits an injective duality endomorphism functor from [math]{\bf Vect}[/math], which is IMO not at all trivial (meaning I don't how to do it).

Any engineers out there willing to answer some questions about their career for me? A paper worth 25% of my grade relies on it.

Can someone verify if this is correct. I'm trying to rewrite Ampere's Law with the H field. I'm saying the magnetic field summed at each point along a curve C is equal to the conduction current plus the displacement current inside a surface S

>>10113243
>When it says pointing down, do they mean the pointy end
Yes

How am I supposed to study metabolic pathways? I’m trying to learn about the three phases of cellular respiration but don’t understand anything desu. I’m not used to studying anything other than math

so,
>big bang
>within fractions of a second, fields start interacting with the surrounding space, forming mass, expanding space and time
>fast forward ~ 13 billions years or so
>delivered pizza, tits, beer and all that
>fields still interacting with spacetime pushing the universe further apart and wider

have i got it right sci?

>>10113349
IIRC, there was a controversy behind this image because the similarities between the embryos are exaggerated (the similarities are still there though, just not as pronounced as is drawn here).

Also, the developmental process is highly conserved across all animals, the same genes tend to regulate body plan formation for most species.

>>10112106
>Euler
“Oi”-ler or “U”-ler

>Euclidean
“Oi”-clidean or “U”-clidean

>>10115366
Oy-ler, Ewww-clid.

>>10114734
make a thread or ask /engi/ engineering general

what does dx/dy mean? specifically if i were to put in the numbers for this what would d be? what do i use this for?

How the fuck do I get the maths equations on this board to show up properly in chrome on desktop? it shows the if i am using chrome on my phone but on desktop it only shows the "code"

>>10115693
dx/dy means "the limit as x approches 0 divided by the limit as y approches 0"

>>10115716

>>10115704
disable adblock

Why is the matrix that induces R
cos -sin
sin cos

Would it be a mistake to take a final level pre-calculus course after learning everything from pre-algebra to pre-calculus on khan academy? I haven't been in school for a few years.

God im so fucking dumb, can someone explain to me why im wrong and in which way?

>>10116222
Here you go

>>10116239
thank you so much anon, I should probably stop heavily drinking

Can someone explain the paths idea? Aren't they approaching the same point?

>>10112867
1. popcorn smell is, partially, rancid butter. Leave some salted butter out for a couple weeks and you'll see what I mean. Butyric acid is similar to rancid skin/sweat smell (short chain organic acids)
2. you've probably got some sulfur, or garlic/onion leeching out of your skin. Actually, it tends to come from your lungs more than your skin; see if it becomes more potent when you mouthbreath

What should I think about when making an RRL?
What constitutes credible and non-credible sources aside from the obvious wikipedia and blogposts?
In RRL I often here pros and cons, pros and cons of what?

My undergrad thesis submission is in 2 days an answer would help.

thanks in advance, animegirl.jpg

>>10115693
In the most stupid sense, it's a ratio of how much x changes to how much y changes. It's essentially a slope of a straight line that touches a function at, strictly, just one point.

>>10116389
Hit up Science-Direct, google scholar and sci-hub and look up articles and studies related to your thesis. Talk about how how they relate to your paper.

>>10116395
>sci-direct, sci-hub
thanks anon, so many sources. I cant even think where to begin with. animegirlthumbsup.jpg

>>10116407
sci-direct is what I use as a search engine, along with google scholar
sci-hub is for actually getting the papers since they're locked behind a paywall

>>10116413
>His uni isn't subscribed to every publication you'll ever need
Must be tough living in a third world country

>>10116294
Remember how in Calculus you had a left limit, and a right limit? You can similarly have left derivatives and right derivatives. In complex variables, you don't just have those two options of how to approach a point, but infinite ones.

Does anyone know any good youtube education playlists for game theory? I've got a bit under two weeks to cover picrelated, I don't think it will take two weeks to cover but I want to do very well for this exam
Thanks lads

>>10112106
What is this figure called?

>>10116529
Trapezium. Unless it's just a random four-sided polygon.

Do women naturally have longer hair?

>>10116534
It's not that, it has 3 dimensions. Four sides made out of Triangle rectangles.

>>10116536
No, it's purely cultural, usually long hair is related to atractiveness, so females use to leave it long.

So the answer is their hair is as longer than of a man as they let it be.

>>10116529
Nonregular tetrahedron

>>10116616
I guess that's it, i hoped it had it's own name, since it's a very specific shape i need for a game.

Is dimethyl ether soluble in hexane?

why is integration so much more difficult than differentiation?
As in, why is it that integration is the more complex operation? Why isn't differentiation as complex as integration?

>>10116670
Same reason finding roots is worse than taking squares, desu.

>>10116670
Because there is an algorithm for differentiating compositions of "simple" functions (using the chain rule and the product rule), but no such algorithm for integration.
It's the same question as why expanding is easier than factoring or crypting than decrypting.
Abstractly, it is the problem of applying a map vs inverting it. Applying a map just requires you to follow a rule. Inverting a map requires you to check the entire domain for inverses. They are very different operations

What's the smallest 1-connected cubic graph? Brute force got me to pic related but I'm unsure if this is correct and/or if there is some sort of proof/more formal approach to solving this problem

How do you even begin to tackle this problem?
I know that it's the case that if a matrix is full rank, then its rank is the smaller of its number of rows and columns (and thus it has a nontrivial nullspace if it's not square), but I have no idea what to do if neither matrix is full rank.

>>10116980
>rank
Is that the dimension of the row vector space? If so, I think it was either 7, 5, 4 or 3.

>>10116980
Think of rank as what dimension does the image span? So A has rank 4, and it's a map into R^5, therefore 1 spanning vector is "lost" by the map. Now B has rank 3, but the image of B is determined by how it acts on the basis of R^5, so the image will depends on if one of the vectors that doesn't get sent to zero by B is in the image of A or not. So BA can have either rank 3 (if the image of A contains all basis vectors that don't get sent to zero by B) or rank 2 (If the image of A has a vector that does land in the kernel of B, which is possible since rank A =4 <5)

how do I summarize the first and second mendelian laws in a phrase?
I know them, I just terrible at words

Which is some required math knowledge for high-level chemistry?

>>10112106
How do I figure out my career path? Should I take a career test.

Btw, I'm 19 and deciding which college I should apply to next year

why aren't tensors just called matrices?

Trying to prove that if [math]f\geq 0[/math] is Lebesgue integrable on [math] [a,b] [/math] (unbounded), then [math]cf[/math] is also Lebesgue integrable.
The definition for Lebesgue integrability I'm using in this case for [math]f\geq 0[/math] is that [math]{^{N}f(x)} = \begin{cases} f(x),& 0\leq f(x) \leq N \\ N,& f(x) > N \end{cases} [/math] is measurable for all [math]N[/math] and [math]\lim_{N\to \infty} \int_{a}^{b} {^{N}f(x)} [/math] converges.
My attempt: for [math]c>0[/math], let [math]N^{\prime}=cN[/math]. Then [math]{^{N^{\prime}}cf(x)} = \begin{cases} cf(x),& 0\leq cf(x) \leq N^{\prime} \\ N^{\prime},& cf(x) > N^{\prime} \end{cases} [/math] is also measurable, since measurability of a function is closed under multiplication. Further, since [math]\lim_{N\to \infty} \int_{a}^{b} {^{N}f(x)} [/math] converges, [math]\lim_{N\to \infty} \int_{a}^{b} {^{N}cf(x)} = c\cdot \lim_{N\to \infty} \int_{a}^{b} {^{N}f(x)}[/math] , which is the desired result.
I think the argument is similar for [math]c<0[/math] and [math]c=0[/math], but I'm not sure if I'm overlooking anything.

How are my chances to find a good job in Japan with a PhD in material physics?

>>10117443
Seems about right. Your teacher might want something a bit more rigorous tho.
c=0 is trivial.
c<0 is just showing that -f is measurable and invoking the first result.

>>10117512
Thanks.
>Your teacher might want something a bit more rigorous tho.
This is where I'm curious. What could I make more clear?

>>10117542
>is also measurable, since measurability of a function is closed under multiplication.
Isn't that what you want to prove to begin with? Go the extra mile and show that the the sets [x such that f(x)=a] and [x such that cf(x)=ca] have the same measure then derive that result.
>the limit times c is equal to the limit of cf
I'd first claim that the measures for any N are equal, and then draw that to the limit.

>>10117559
>Go the extra mile and show that the the sets [x such that f(x)=a] and [x such that cf(x)=ca] have the same measure then derive that result.
I'm pretty sure we showed this already in class for bounded functions. The truncation is bounded for each [math]N^{\prime}[/math], right? So this should follow naturally so long as I say it that way?
>I'd first claim that the measures for any N are equal, and then draw that to the limit.
Not sure I follow.

>>10117485
Above average.

(but the average is practically 0, so...)

>>10117581
>your teacher lets you use the fact that measurability is closed under multiplication to show cf is measurable
What even is the point then?

>>10117604
we first considered bounded non-negative functions, then unbounded non-negative functions, then general functions - positive, negative, bounded/unbounded. It seems unorthodox based on how I've seen this material be taught in other books.

>>10117617
It very much is. Honestly can't help you without knowing what to assume and what not to. Just using what you originally posted should be fine.

>>10117485
What kind? Theory or experimental?
>>10117582
>the average is practically 0
Are you stupid? There's a massive condensed matter community in Japan. They even have their own journal with an h-index rivaling that of PRB.
Stop talking out of your ass please

>>10117632
It's not that, anon's a westerner seeking good employment in Japan. That's hard.

>>10117625
I'll try my best. This is the book he's using to teach http://www.math.nagoya-u.ac.jp/~richard/teaching/s2017/Nelson_2015.pdf . I haven't been able to find any other book that takes this approach.

>>10117637
>postdoc is hard
Not in Japan no.

>>10117640
>http://www.math.nagoya-u.ac.jp/~richard/teaching/s2017/Nelson_2015.pdf
>not a book about measure theory
>no, a book literally about Lebesgue measure and integration
Drop out of college.

>>10117653
sometimes wish I did at times like this

Could anyone help this brainlet. I rewrote it so that x is in the middle, so I use chain rule twice? All I need is a set of instructions, I’ll do it myself.

>>10117808
could do product rule on [math](xe^{-x})(\sec(x))[/math] or anything like that I'm pretty sure.

>>10117808
x=e^ln x
y= e^(x-lnx)sec x
Chain rule for the former, then product rule.

How to instantiate a quantifier in a quantifier in which they both use x?
e.g (∀x)((∀x)Fx→Fx)
Would it be
(∀x)(Fa→Fx)
(Fa→Fb)?
But shouldn't a instantiate for all instances of x?

>>10117854
(∀x)(Fx→Fx)

You guys know the classic interview question "You have eight marbles and a two-pan balance. All the marbles weigh the same, except for one,
which is heavier than all the others. The marbles are otherwise indistinguishable. You may make
no assumptions about how much heavier the heavy marble is. How many weighs will it take to find the heaviest marble?"

If the question was rephrased to instead ask "Describe an algorithm that finds the heavy marble in three weighings.", how would you answer it then?

Is there a general formula that can find the exact value of a trig function that isn’t wolfram alpha. I’m talking about finding the value of a function that looks like:

[eqn]Sin[\frac{m}{n}*\pi][/eqn]

Where m and n are integers. The closest thing I can find is randomly using a sum-to-difference formula to try and break up the original trig function and hope that you can make the numbers work. On top of that, it’s a really repetitive way to find values. For example, if m = 1 and n = 96, you have to perform a bunch of sum to difference substitutions to break down the original Sine function. Wondering if there is a quicker way.

Crossing fingers that I didn’t fuck up the latex

>>10117867
Divide the marbles between each balance. Take away all the marbles in the pan that goes up, and redistribute the remainder. Repeat until there's one marble left.
>>10117875
There are some infinite sums out there that approximate the sine function. Google and pick one.

>>10117898
Oh, I know the process to solve the question, I'm just wondering what the exact syntax would be to actually answer the question "Describe an algorithm that finds the heavy marble in three weighings."

>>10117875
Multiple angle formula.
sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)
cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)
=>
sin((n+1)*x) = sin(n*x)*cos(x)+cos(n*x)*sin(x)
cos((n+1)*x) = cos(n*x)*cos(x)-sin(n*x)*sin(x)

Apply recursively until n=1 and you end up with an expression involving sin/cos of pi/k. Then you apply the above in reverse: sin(k*(pi/k))=sin(pi)=0, cos(k*(pi/k))=cos(pi)=-1; expand out the LHS using the multiple angle formulae (and sin(x)=sqrt(1-cos(x)) or the converse) to get a polynomial with sin(pi/k) or cos(pi/k) as roots.

Consequently, if the argument of a trig function is a rational multiple of pi, its value is algebraic (a root of a polynomial with integer coefficients). But note that there's no closed-form solution for polynomials of degree 5 or above.

>>10112106
Need help here, nothing I do works.
>Used Q = M x Cp x ΔΘ, get far off result
>Figure "hey, let's use latent heat exchange equation instead"
>Use Q = M x λ, get far off result
>Try rearranging both and achieve nothing, try playing with magnitude and converting to kelvins, nothing.
I don't get it, I've fully read the lecture notes and power-point slides well over ten times now and it doesn't clear any of this up. The annoying thing is that the answer will be so frustratingly obvious that I'll want to eat a razor by the time I'm done following it.

>>10118033
first you have to calculate the energy from the specific heat to change ice from -41.7 to 0 degrees, then you add to that the energy from changing from ice into water

>>10118041
Thank-you, I've got the result.

>Let [math]f\in \mathcal{L}[a,b][/math] and define [math]G(x) = \int_{a}^{x} f[/math] for [math]x\in[a,b][/math] Is [math]G[/math] continuous?
What's the intuition behind this? Is it supposed to be some hint towards FTC from Riemann integration?

In terms of torque and efficiency, are there any benefits to using a pulley to motorize a wheel instead attaching a motor directly to the fulcrum?

I'm a Physicslet.

>>10112106
Can any of you faggots explain “weighted average” to me.

>>10118302
>faggots
Why the homophobia?

>>10118217
Yes. [math]G[/math] is absolutely continuous in fact.

>>10117898
>>10118004
Thank you anons

>>10117875
use de Moivres and Tyler series

>>10118305
Meant in endearment.

Some one help with my basic calculus

If 3x+y=9, then what is the maximum value of xy.

>>10118375
>If 3x+y=9, then what is the maximum value of xy.
What have you tried?

>>10118384
Nvm I got it.

xy max = 5.0625

Can someone explain how you get from 1) to 2)? I know it's simple algebra but I still don't get it

>>10118302
It basically means how much one quantity contributes to the over-all average. Say you've got a quantity A and another quantity B but you don't think B is as important as A and you want to make this apparent. You multiply them to fractions but the sum of those fractions need to equal to one. For example, (0.75A +0.25B) /2. Here, A contributes to 75% of the mean while B contributes a measly 25%.

>>10118465
Express x2 in terms of x1 from the 1st eqn, substitute it in the second.

>>10118563
I thought about doing that but it looks like it'll create a gigantic term and i was wondering if that could be avoided

>>10118590
Yes, it will create gigantic terms, but simplifying them isn't too complicated.

Whats 9 + 10?

>>10118990
Depends on the binary operation.

Dumb question but how many iterations should i do if I were to trace this algorithm in a table?

>>10118297
Reasons to use a pulley rather than direct attachment include:
- Changing the gear ratio, trading torque for speed or vice versa.
- Allowing multiple gear ratios by having multiple pulleys
- Allowing the motor to be placed away from the axis
- Torque limiting (if the load jams, the belt will slip).

>>10119156
At most n-1.

>>10119170
That's why I'm an idiot an posting in sqt - what is n in this instance?

>>10119177
The number of numbers in the array.

>>10119178
Yeah, got it, wasn't listed on the spec for some reason so that threw me off. How would iterating i and j work?

>>10119202
It goes through the digits and swaps if the following is smaller than the latter.

>>10119239
So there will only be a maximum of 3 swaps if n = 5, as j caps the if at n - 2?

>>10118553
> For example, (0.75A +0.25B) /2
The /2 shouldn't be there. For an average, you divide the weighted total by the sum of the weights, i.e. (0.75A+0.25B)/(0.75+0.25) = (0.75A+0.25B). This ensures that if all values are equal, the average will be equal to them.

>>10119256
No because I goofed calculating the iterations earlier.
Σ from 1 to n-1 should be correct. If n=5 you can have
4 3 2 1 0
3 4 2 1 0
3 2 4 1 0
2 3 4 1 0
2 3 1 4 0
2 1 3 4 0
1 2 3 4 0
1 2 3 0 4
1 2 0 3 4
1 0 2 3 4
0 1 2 3 4

>>10119267
I appreciate the effort you went through to do that, but I'm still a little confused on how this trace actually works - what would the adjacent values for i and j be set to after each step?

>>10119156
>>10119170
>>10119177
>>10119202
>>10119239
>>10119256
>>10119267
>>10119270


I can’t tell if you’re being serious or trolling. “Number of digits”? “At most n-1”?
It’s bubble sort, you’ll drown in explanations if you simply google it.. As soon as you do that, you’ll also see that this implementation is flawed because both loops start from 0, which does superfluous work.
Anyway, what do you mean by “trace iterations in a table”? If you want to know how many swaps are performed, you can do that most easily by noting that the instructions swap all pairs of entries in the array for which the predicate A[i] < A[j] is true.
For one complete run of the algorithm, you have n times (n-1) runs through the inner loop, so if you want to tabularize it, your table will be, for example, 20 lines long for an array with five entries.

>>10119276
Not trolling, just sleep deprived and a bit of an idiot - appreciate the help though, I'll just do some reading to now flood the threat with brainlet questions!

>>10119276
Advanced shitposting desu.

>>10119256
There will be five passes (i=0,1,2,3,4) with a maximum of four swaps per pass (j=0,1,2,3).

But for 5 items, there won't actually be more than 4+3+2+1=10 swaps (which occurs if the list is initially in reverse order). In fact, the outer loop only needs to go up to n-2, and the inner loop only needs to go up to n-2-i.

After the first pass, the largest item will be in the last place. Every comparison which considers that item will always swap it to (or leave it on) the A[j+1] place, which will be the A[j] place on the next comparison, so it "bubbles" to the right (hence the name). After the second pass, the two largest items will be in the last two places (in their correct order), and so on. After k passes, the k largest items are guaranteed to be correctly ordered in the last k places.

After n-1 passes, the n-1 largest items are guaranteed to be correctly ordered in the last n-1 places, which means that the smallest item has to be in the first place simply because there's nowhere else it could be. So the last pass is redundant.

If you trace all 5*4=20 iterations starting with the list [5,4,3,2,1], you'll see the pattern described above. Every comparison with i<n-1 and j<n-2-i results in a swap, none of the other comparisons do. So there are n*(n-1) comparisons and n*(n-1)/2 swaps, but the number of comparisons could be reduced to the number of swaps. Other O(n^2) sorting algorithms (selection/insertion) sort typically have n*(n-1)/2 comparisons and n swaps (i.e. each element is only moved once).

I know my proof writing is shit, but did I get the general problem right? Specifically part b.)

>>10119344
[math] g(-M) \leq g(f(x)) \leq g(M)[/math]
How do you know this?

>>10119352
You know what, I don't know. I just blindly applied g to the inequality.

>>10119344
Jesus fucking Christ anon what is this.
>g(x) is defined for all x, y belongs to R
Remove the y.
Trivialize the whole thing to g:R ->X for some X contained in X, and claim that f: X-> R is bounded since f:R->R is.
b)>every function defined for every x in a closed interval is bounded
That's wrong. You can't prove wrong things.

>>10119358
thanks for putting up with my autism anon, so for part b.) I need to come up with a counter example?

>>10115937
As [math] \mathbb{R} [/math]-vector spaces, [math] \mathbb{C} \approx \mathbb{R}^2 [/math] by the map [math] a + ib \mapsto (a, b) [/math], so [math] \text{End}_\mathbb{R}(\mathbb{C}) \approx M_2(\mathbb{R}) [/math] as rings. But [math] \mathbb{C} \approx \text{End}_{\mathbb{C}}(\mathbb{C}) \subset_{\text{sub-ring}} \text{End}_\mathbb{R}(\mathbb{C}) [/math].
So [math] \mathbb{C} [/math] is a subring of [math] M_2(\mathbb{R}) [/math]. [math] i \in \mathbb{C} [/math], corresponds to the the map [math] z \mapsto iz [/math] in [math] M_2(\mathbb{R}) [/math], which is just the matrix [math] \Bigg( \matrix{0 & -1\\ 1 & 0} \Bigg) [/math] (because (a, b) is sent to (-b, a)).
As the corespondence is actually a ring homomorphism, the complex number [math] a + ib [/math] is the matrix [math] \Bigg( \matrix{a & -b\\ b & a} \Bigg) [/math].
In particular, rotation by [math] \theta [/math], which is multiplication by [math] \exp(i\theta) = \cos{\theta} + i\sin{\theta}[/math] is the matrix [math] R(\theta) = \Bigg( \matrix{\cos{\theta} & -\sin{\theta} \\ \sin{\theta} & \cos{\theta}} \Bigg) [/math]. As an application of the ring homomorphism property, we get the nice fact [math] R(\theta)R(\phi) = R(\theta + \phi)[/math].

>>10119361
Yeah. I'll solve the first part for you:
We define f:R->[0, 1] by:
f(0)=0
if IxI<1, f(x)=IxI
if IxI>1, f(x)=I1/xI.

>>10119367
My mistake.
f(0)=0
if 0<IxI<=1 then f(x)=IxI
if 1<IxI then f(x)=I1/xI

>>10119372
so could you do g(0) = 0, g(x) = 1/x otherwise, then g will blow up to infinity for g(f(x)) and is therefore not bounded

>>10119378
Yup.

>>10119367
>>10119372
Thanks for defining f at zero separately. Can’t be too cautious.
Why so complicated though? I’m asking sincerely. Anything that includes the neighbourhood around 0 works with your choice of f. Take sin, cos, Artanh, whatever.

>>10119383
> works with your choice of *g*
Sorry4typo

>>10119383
Uh? Ah, there's no particular reason for that. I just forgot those.
I was low key trying to remind him of the 1/x function.
Yes I do know spoilers don't work here.

A bit related to pumping water. I am having trouble understanding the last 2 paras in this tiny pdf.
http://www.pumpfundamentals.com/How%20high%20can%20you%20suspend%20water%20in%20a%20pipe.pdf

I CAN'T MEMORIZE ALL THIS FUCKING CHEMISTRY SHIT WHAT THE FUCK DO I DO AAAAAAA

>>10119366
That was very helpful, thank you

Help, I can't remember if you can multiply two ordered pairs.
Let x,y,a,b be Integers.

Is (x,y) * (a,b) = (x*a, y*b)?

>>10119929
It depends on the context, but generally speaking you can't do this. For example if those intended to be vectors/points in R^n, then no.

This is a question about Linear Algebra.
I've fallen behind a bit in this class so I am trying to catch up. Due to this there are some holes in my understanding.

Basically, I need to do a proof that a nonzero vector in R3 has a set of orthogonal vectors in R3 that is a 2-dimensional subspace.
It's the first part that I am having trouble with. I am not sure how to get the set of orthogonal vectors. How do I find it? The vector given to get the orthogonal from is V = (v1,v2,v3) (belongs to) r3 and is a non-zero vector.

Do I just assign it any number I want, then try to find the orthogonal? For example, could I just set it to v = (1,-2,0) and then create another vector to take the dot product of? If so, how would you know how many to create like that?

Sorry if this is a super basic question. I don't really need to know it for a grade, I am just trying to catch up and understand this stuff.

>>10120032
Theorem:
Let a be a nonzero vector in tridimensional vector space V.
Guide to proof:
Show that there exist two vectors u and v that are orthogonal to a.
Then, show that the set of linear combinations of these two is also orthogonal to a. In other words, for any scalars k and l, (ku+lv) . a=0.

>>10120061
Ugh, I wrote everything wrong.
Show that there exist u and v belonging to V such that a. u=0, a . v=0 and u . v=0, and that for any non-null x if a . x=0 then either u . x=/=0 or v . x=/= 0.

>>10120032
> I am not sure how to get the set of orthogonal vectors. How do I find it?
How do you check for orthogonality? Which operator do you use..

> Do I just assign it any number I want, then try to find the orthogonal?
> [...] how would you know how many to create like that?
You're trying to create a basis for a 2 dimensional subspace, right? How many basis vectors do you need for one of those?

>>10120083
From what I can gather, it's orthogonal when setting the dot product of two vectors = 0 then finding the values that make it 0.

2? So do I just make two orthogonal vectors?

>>10120093
>dot product of two vectors = 0 then finding the values that make it 0.
Yes.
>2? So do I just make two orthogonal vectors?
You want two vectors that are orthogonal to your (v1, v2, v3); they don't need to be orthogonal to each other (just not linearly dependent).
Say I wanted you to get one of those vectors x in the form (0, x2, x3). What are x2 and x3 in terms of the values of v?

I don't want to make a new thread for this, and I figured this is a stupid enough question. Should I go?

>>10120106
Do you mean what we'd need to multiply the v vector by to get the x vector or what the individual values of x2 and x3 would be?
If it is the former, would be it (0,1,1)?

Is it worth my time to take physics?
I plan on majoring in CompSci but if I like physics a ton I may just major in it.
Stupid fruitless endeavor or good idea?

>>10120118
No, the question is what are x2 and x3 so that [math](v_1, v_2, v_3) \cdot (0, x_1, x_3)^\mathrm{T}[/math] is zero?
If you can find it, that's your first basis vector.

>>10120118
>>10120123
Ignore the T, that's my mistake -- it should be on the other vector ( the dot product of u and v is [math]u^\mathrm{T}v[/math]

>>10120032
Let a be a nonzero vector belonging to a three dimensional vector space imbued with an inner product. Then the set of vectors orthogonal to a forms a two dimensional subspace.
Since the space is three dimensional, there exists some vector b such that cannot be written as ka, where k is some scalar. By the properties of the inner product, <b, a>=n, for some n. Since <a, a> >0, we can find some scalar l such that l<a, a>=<la, a>=n, and then <b-la, a>=0, and thus found a nonzero vector orthogonal to a.
You should be able to finish.

>>10120132
I don't think the plugin is working on my browser.

>>10120152
All I wanted you to see is that (0, v3, -v2) and (v2, -v1, 0) are two possible choices for the basis of your subspace.
If you want a more general approach, follow >>10120135 's advice.
If you want to develop a visual intuition for three dimensions, stick a pencil orthogonally through a piece of paper. The pencil is the normal vector, the paper marks the 2 dimensional subset.

>>10120135
>show that the set of vectors spans a plane
>>proof: since the set of vectors spans a plane
brainlet
>>10120032
Let v=(a,b,c) be a non-zero vector. In particular, we can assume WLOG that c is not zero, and again WLOG we can assume that v=(a,b,1), just by normalizing it. Then the vectors u=(b,-a,0) and w=(0,-1,b) are clearly orthogonal to v, and it is not hard to check that all 3 are linearly independent. In particular, v,u,w span the space R^3. It is also not hard to check that any linear multiple of u and w, that is, sums and multiplications by scalars of them are also orthogonal to v, hence the linear subspace U generated by u and w is 2-dimensional and is orthogonal to v, and any vector in R^3 that does not belong to U can be written as a linear sum of v and an element of U. Hence, taking the dot product of this sum with v will yield a non-zero scalar, and hence it is not orthogonal.

QED

>>10120213
>implies I'm assuming the result
>works with nigger coordinates
Unbelievable.

Can you use ultrasonic cleaners on lab glassware? It will be used under strong vaccum and 250C temps if that matters.

>>10120231
well, the retard that asked the question didn't even know how to make the vectors so it's a double whammy

>>10120247
> strong vacuum, 250C
> cleaning device that requires being filled with liquid water
???

>>10120255
No not cleaning it under vac/heat. The glass will be used under vac and heat, not just room temp storage. Didnt know is the cavatation from the cleaner would weaken the glass and make it shatter when it's being used.

Through current division, the current i_0 is supposedly i_l * 10/(10+40).
I thought current division was current*(equivalent resistance/resistance path)
Shouldn't the path just be 40?

>>10120601
(i0+il)*10 + i0*40 = 0
i0= -il*10/(10+40)

You forgot a minus sign

I've been feeding my interest in astrophysics for years now via brainlet sources like educational programming, videos, and books that aren't too terribly difficult, but in the end I am still left with this question:
Is there compelling evidence which supports the big bang theory or is it just our current best fitting model for universal genesis? I have a minimal understanding of Planck Time and the processes that took place during, but the proceeding moments seem very speculative.
TL;DR why is the big bang our best model of the beginning and is there a solid contending theory?

If the influenza virus is known for mutating often, then why doesn't it cause tons of cancer? Presumably most mutants aren't actually able to self-propagate, but if they can still infect cells, their DNA may cause cancer instead.

>>10120840
>muh ideology conflicts with science
>plz give me something to cling to to say it's bullshit

>>10120852
Lurk more or reread the question.
There's no mention of ideological differences, you just clung to that because I used the word 'genesis'. I haven't come across compelling evidence that the big bang is the correct theory as to how the universe began. Most programs and books simply mention Planck Time and call it a day. Some explain PT a bit, and I have no problems with it or the following universal processes that took place.

I guess I could refine my question to "is there compelling evidence for the assumed singularity from which matter sprang?" Like with quantum mechanics, where traditional physics models break down, I assume the pre-PT time just doesn't fit with our current understanding of math and physics, and I am seeking the aide of someone with a better understanding on it

Can I get a hint on how to calculate [math]\int_{\mathbb{R}}\frac{e^{itx}}{\cosh{x}}dx=\int_{\mathbb{R}}\frac{\cos{tx}}{\cosh{x}}dx=\int_{\mathbb{R}}\frac{\cos{tx}}{\cos{ix}}dx

>>10121056
Not without a [/math] you can't.
But seriously, it's all e functions. express it as that and do the limit yourself.
[math]\mathrm{cosh}(x) = \frac{e^{ix}+e^{-ix}}{2}[/math]

>>10121209
limit? there aren't any limits
also he'll need to know sin(x) is odd for that first one

>>10121210
Right, you just evaluate at the borders of [math]\mathbb{R}[/math].
Maybe you read it differently than I do -- to me the question is about computing the integral, not how those transformations are done.

How do I go about finding all functions [math]f:\mathbb{R} \to \mathbb{R}[/math] that [math]\forall x[/math] satisfy the condition [math]f(2015x + f(0)) = 2015x^2[/math]

>>10121583
Derive it, then integrate it. If g(x)=2015x+f(0), find df/dg.

>>10121583
[math]f [/math] is clearly differentiable.

Let [math]g(x)=f(2015x+f(0)), h(x)=f'(2015x+f(0))=2015x, k(x)=f''(2015x+f(0))=1[/math].

Then [math]g(0)=0[/math] so [math]f[/math] must have a zero at [math]f(0)[/math], [math]h(0)=0[/math] so that zero must also be an extremum, and [math]k(0)=1>0[/math], so in particular it must be a minimum.

Note that [math]f(x)[/math] is just a linear transformation of [math]g(x)[/math], so up to moving the plane around, they behave the same. Hence since [math]f''(x)=1[/math], then we can write [math]f(x)=\frac12 x^2+bx+c[/math]. Substituting [math]f(f(0))=f(c)=0[/math], we get that [math]c=0[/math] or [math]c=-2(b+1)[/math]. Then [math]f'(f(0))=0[/math] implies [math]c=-b[/math]. Then you get that there exists only two functions.

>>10121583
You're given f(g(x)) = kx^2
Just replace x by the inverse of g.

If there is a badly done experiment, and 1 independent variable is being tested, BUT there is another variable that isn't being controlled for, can it be said that there are 2 independent variables?

>>10121757
A variable and a stochastic element.

Am I going nuts? I thought this was how to use long division to generate a sequence from a generating function. However, whenever I look up long division of a polynomial, I can't find where I know this from.

>>10121836
you need to look at where your function is defined and what operations long division is valid for
you're equation is actually valid because if you sum x^n from 0 to ... you get your equation assuming x is less than |1| (so it converges and it's not infinite)

>>10121836
What?
(1-x)(sigma x^n)=-x^(n+1)+1 by induction.
Therefore sigma x^n=(1-x^n+1)/(1-x), which usually diverges, but x^n converges to zero if IxI<1, so sigma x^n=1/(1-x).

>>10121687
This needs some explanation.
>Let [math]g(x)=f(2015x+f(0)), h(x)=f'(2015x+f(0))=2015x, k(x)=f''(2015x+f(0))=1[/math].

Why are the derivatives h(x) and k(x) respectively 2015x and 1? Shouldn't they be 4030x and 4030 instead?

>Then [math]g(0)=0[/math] so [math]f[/math] must have a zero at [math]f(0)[/math], [math]h(0)=0[/math] so that zero must also be an extremum, and [math]k(0)=1>0[/math], so in particular it must be a minimum.

Why is this part relevant?

>Hence since [math]f''(x)=1[/math], then we can write [math]f(x)=\frac12 x^2+bx+c[/math]

Based on what exactly can we write this second part?

>Substituting [math]f(f(0))=f(c)=0[/math], we get that [math]c=0[/math] or [math]c=-2(b+1)[/math]

Where does c=-2(b+1) part come from?

>Then [math]f'(f(0))=0[/math] implies [math]c=-b[/math]

Why exactly can we imply that?

>Then you get that there exists only two functions.

Based on what can we say that there exists two functions? And how can we determine what those two functions actually are?

>>10121867
>Why are the derivatives h(x) and k(x) respectively 2015x and 1? Shouldn't they be 4030x and 4030 instead?
Note i didnt write h(x)= (f(2015x+f(0)))', etc
>Why is this part relevant?
only the extremum and minimum part are irrelevant, but it was a flow of ideas, i didnt edit the reply
>Based on what exactly can we write this second part?
uniqueness of second order derivatives
>Where does c=-2(b+1) part come from?
doing the substitution
>Why exactly can we imply that?
do the substititution
>Based on what can we say that there exists two functions? And how can we determine what those two functions actually are?
literally do the substitutions

next time you reply to my posts, use your brain, retard

Can someone with matlab make a .m of this script? Mine expired and I need to submit this,

% ENGR 405
% ILA 17
% 6 November 2018

% Given a vector and eval statement, in a script, create the cell array, a , that will let the eval statement produce y = 1 4 9

clear all; close all;
x = [1 2 3]
a = cell{ x, 1, 2, 3}
y = eval([{1,1} num2str(a{1,2}) a{1,3} a{1,4}])

mixtape.moe is a file-sharing site if needed

How easy is community college and how stupid are the people going there?

>>10121983
Nigga just copy it in a text file and save it as .m

I'm getting more and more scared because I'm stuck on a question that is literally ninth grade level
>a car travels back and forth between points A and B
>to go from A to B, the car's speed is 60 km/h
>then to go from B to A, the car's speed is 90 km/h
>what is the car's average speed?
Apparently it's 75 km/h but I'm exhausted and I don't get it because wouldn't the car take less time to go from B to A if it's travelling faster?
I'm a physics major and I feel like I have fucking down's syndrome right now

Should I take a math paper to work on for this year (filthy, stupid undergrad)? It'll probably drive me to suicide, because mostly I was never able to get a grade higher than C, and even then I had to tear my ass apart in order to get something done or pass.
My skills are at the level of calculating the determinant and maybe recalling Rolle's theorem.

>>10122035
From A to B is goes through a distance AB, and takes a time m=60/AB, by the definition of speed. From B to A it goes through a distance AB, and takes a time n=90/AB.
Since it goes through a distance 2AB in a time m+n, it has speed 2AB/m+n. Substituing, 2AB/(60/AB+90AB)=2AB/150AB=75.
It's easy but the formal demonstration is weird.

>>10122061
Thank you anon.
There's another one I'm stuck on:
>a plane is flying at 150km/h
>it goes back and forth from A to B, the distance AB = 308
>the wind blows from A to B, it affects the plane's speed
>calculate the speed of the wind, knowing that the plane takes thirty more minutes to travel from B to A than from A to B
I calculated the plane's speed without the wind, and the speed increased/slowed down by the wind but I don't understand how I'm supposed to get the speed of the wind from that since dividing the plane's speeds will give me an acceleration (I think)
Again sorry for being dumb

>>10122061
Distance is speed times time, so AB=(150+k)(m)=(150-k)(m+30), where k is the how much the wind's speed affects the plane's speed and m is the time the plane takes with wind in its favour.
Since AB=308, 308=(150+k)m and 308=(150-k)(m+30). That's a normal two variable system and I'm feeling lazy.

>>10122103
Do you post "answered to the wrong post" if you answer yourself on accident?
Meant for >>10122075

>>10122061
>time 60/AB
Fucking knew I was confounding something here.
Time AB/60.

>>10122103
Thanks again.
How come I finished all my abstract algebra exercises easily but I get stuck on retarded shit like this? It happens often, too.

>currently at community college working on bachelors
>could transfer after next semester to a full university
>will still need a few classes (calc 3, physics 2, chem 2) at that point
Besides cost, is there any advantage to taking these at the 4 year vs staying at the CC?

Faraday Law states:
>The electromotive force around a closed path is equal to the negative of the time rate of change of the magnetic flux enclosed by the path
in which I don't understand the first part:
>The electromotive force around a closed path
my understanding of electromotive force is that it's just a fancy way of calling a voltage (because of a mechanical analogy between voltage and force)
but a voltage is a difference of potential between two points - so what sense does it make to say something like "voltage around a closed path"?

If I had anal fissures (which are now mostly healed and pain-free) and now my asshole is leaking horrible smelling orange/yellow discharged liquid, how might I make this stop so I don’t have to skip classes anymore?
>four of them are mandatory

>>10112106
Can anyone reccomend good calc 2 youtube videos/youtube channels? Tried kahn academy but it doesn't click with me

I was having a conversation with my friend earlier today when the conversation made a question pop into my head

given a total of money, what is the optimal composition of coins which sums to that amount?
I'm trying to solve it using basic single-variable calculus, but I'm almost certain this is a multivariable question that's beyond me

truth be told I'm not entirely sure how you would begin finding this answer either

>>10122583
https://en.wikipedia.org/wiki/Change-making_problem

>>10122583
>tried to solve a diofantine equation with calculus
This fucking thread sometimes.

>>10121209
Did you perhaps mean to type cos instead of cosh? Regardless, I don't find [math]\frac{e^{itx}+e^{-itx}}{e^{x}+e^{-x}}[/math] much easier to integrate. I've probably forgotten too much complex analysis by now.

>>10122595
Yes, I put ix instead of x in the exponent, sorry.

I'm told to sketch the region of integration for this integral.
Is this correct? Is there a website can sketch stuff like this?

>>10112106
Why is 0.05 used as the critical value in T-Testing for biology?

>>10122667
industry standard, a solid 5%

Basically, it allows biologists to pump papers under the guise of accuracy

for my intro complex analysis, one of the problems is to show that there's no feasible way to define infinity + infinity or infinity - infinity as a limit using convergence properties of the extended complex plane. Sorry for being a brainlet, but how would I go about doing this? Spamming the triangle inequality isn't really helping as far as I can tell.

>>10122648
>is this correct
yes
>is there a website
no

also, it's usually obvious

>>10122704
just try defining what it could be

suppose infty-infty = a for some a in C. What consequences does it have? what if instead you suppose infty -infty=infty?

>>10122704
There *is* but you'd have to have an infinity for literally every angle and you'd have to show that the limit of a sequence is the limit of the angles of the elements and the limit of the module.
Further, lim f(z)+lim g(z)=/=lim f(z)+g(z), and multiplication also no longer works.

>>10122720
For example, if infty-infty is defined to be any number in the extended complex plane, say a, then if b=/=a, we have b+infty=infty, hence infty-infty=b=a, contradiction

Why is the env gene a good characterizer for HIV virus?

If [math]|G|=p^{3}[/math] for some non-cyclic group with [math]p[/math] prime, how do I show that [math]g^{p^{2}}=1[/math] for all [math]g\in G[/math]? I was thinking something along the lines of Lagrange's theorem but am not too sure how to proceed.

>>10121583
let y=2015x+f(0)
f(y)=(y-f(0))^2/2015

f(0)=f(0)^2/2015
f(0)(f(0)/2015-1)=0

f(0)=0 or f(0)=2015

I have f(x), g(x). The domain of both functions is all real numbers.
Can I just say that the domain of f(g(x)) is all real numbers given that it is a composition of two functions whose domains are both all real numbers? Do I need to prove that g(x) is a real-valued function, or should I just leave it as is due to the fact that this is just the start for a calc I problem which would ignore imaginary values for g(x) anyways.
Sorry for my brainletism

>>10122918
For each element in the group, its order could only be 1, p, p^2 or p^3 because of Lagrange's Theorem. Assume it's order was 1 or p. Then, p^2 is a multiple of both of those, so g^(p^2) will also result in the identity. If the order of g is p^2, then you are done immediately, by definition of order of an element. Why can't it be p^3 be the order of any element, though? Read your hypothesis carefully, it would result in a direct contradiction with a specific condition.

>>10123103
Just claiming the domain of f(g(x)) is the Reals is fine.

>>10122409
What the path integral is calculating is the Riemann sum, namely the potential difference over each line element and then summing them all up.

>>10122579
the organic chemistry tutor, patrickjmt

>>10123150
but what if we had a wire loop? shouldn't the potential be exactly the same at every point of the loop?
where does the voltage from the changing magnetic flux go then?

>>10123164
Uh. I think I'm dumber than you but I know mechanic type electricity and I think in terms of hydraulic pressure= EMF (voltage) flow is amperage. Restrictions are resistors. Water and electricity work the same in my imagination and I'm usually not very surprised by either. All i know is ohms law.

>>10122409
> but a voltage is a difference of potential between two points - so what sense does it make to say something like "voltage around a closed path"?
When it encloses a changing magnetic field.

An electrostatic field is a potential field (the gradient of a scalar field). An electromagnetic field isn't a potential field. If you follow a closed loop around a changing flux, the voltage keeps increasing, so the "potential" at the end is higher than at the start, even though they're the same point.

>>10122565
Do not take NSAID

>>10112106
As a kid, I've always been very dumb on math. Now, I feel like I could understand and get on with it better. Recommend me a book about Maths.

>>10123194
>If you follow a closed loop around a changing flux, the voltage keeps increasing, so the "potential" at the end is higher than at the start, even though they're the same point.
sorry, this still confuses me
if we had a changing magnetic flux and a closed loop made of an ideal conductor, where would the voltage be produced? Since the conductor is ideal, the potential has to be the same everywhere along it. So if we picked some point A on this loop, and measured voltage difference between it and current point B while going along the loop, it would be 0 everywhere.

>>10122918
Lagrange's theorem bounds the orders of the elements so that for any [math]g \in G[/math] we have [math]g^{|G|}=1[/math]. But this is not good enough, however, it acts as an upper bound. We have the following criterion (easy to prove):

>a finite group is cyclic if and only if there is an element of order |G| in the group.
We also have the lemma:
>If [math]g^M=1[/math], then [math]M[/math] divides [math]|G|[/math]

These two are enough to show it:

Any element of G has to have order [math]1,p,p^2,p^3[/math] by the second lemma. But G is not cyclic, so it cannot have an element of order [math]p^3[/math]. So every element has order [math]1,p,p^2[/math]. In particular, [math]g^{p^2}[/math] for any g

>>10123197

>>10123222
> Since the conductor is ideal, the potential has to be the same everywhere along it.
"Potential" isn't a thing when you have a varying magnetic flux. "Potential" implies that the path integral of the electric field between two points depends only upon the points themselves and not upon the path taken. That isn't the case when a varying magnetic field is involved.

The total voltage around the loop would be the same regardless of the presence of any conductor. An ideal conductor would have infinite current. In practice, you wouldn't be able to have a changing magnetic flux if it passed through a loop made out of an ideal conductor. The current through the conductor would generate its own magnetic flux which would act to oppose any change in total flux.

> So if we picked some point A on this loop, and measured voltage difference between it and current point B while going along the loop, it would be 0 everywhere.
Not if you actually had a changing magnetic flux enclosed by the loop.

>>10123197
Euler's Elements of Algebra
Hammack's Book of Proof
Lang's Basic Mathematics

>>10123319
>Lang's Basic Mathematics
Lang is a meme.

If I'm doing a problem and I know the direction of P, but nothing else, how do I calculate sigma_b?

>>10123195
Wasn’t planning on it but thanks just in case

>>10123456
taking all components parallel to P on your surface

>>10112106
>Consider the outward propagation of a spherical laminar flame into an infinite medium of unburned gas. Assuming that SL, Tu, and Tb are all constants, determine an expression for the radial velocity of the flame front for a fixed coordinate system with its origin at the center of the sphere. Hint: Use mass conservation for an integral control volume.

I might be mistaken, but wouldn't the conservation of mass just be d(m_dot)/dr = 0, and proceeds no differently since area would still be constant in the control volume?

How would I take the derivative of something like:
[eqn]
(Cu)^T (Cu)
[/eqn]

My best guess is to define some other vector, c = Cu, which leads us to use
[eqn]
\nabla (c^T)c
[/eqn]

Then, the gradient of this with respect to c would be just 2c. The part I'm stuck at is now how would I convert back to taking the gradient with respect to u?
Would I have to do [math] \nabla_u 2(Cu)[/math]? If so, how would I take the gradient of that?

Hi I'm a unicuck terribly failing my Differential course.
It's turning into a downwards spiral because the prof is going really fast over a bunch of new concepts every week when I don't even have my fundamentals done.
I really want to recover, and I understand that the only real way to do that is to find a resource that simplifies and boils down DEs to their very essence; providing an opportunity for rapid learning to catch up with the rest of my class.

I know I have no one better to turn to but you, the anons of /sci/, for said resource.

Can someone help me with finding Vout and when the diode is on or not?
D1's voltage is 0.7 to turn on, Iin varies between -6ma and 6ma, R1 = 1kOhm and R2 = 2kOhm

>>10124068
>Iin>0
Diode off

>Iin<0
>|Iin|*R1<.7
diode off

otherwise diode on

>>10123952
You got some more of those details? What kind of differential equations course is it, ordinary, partial? Is it about numerical methods or is there a special application with its own specialties?
Post some synopsis or a problem set as an example.

>>10124125
The course is introductory. It's part of the Engineering major. I'd say it's in the same level of general ed CALC2 or 3.

Could someone clear up some cosmology for me?
The universe is flat (by observations that I don't understand). This means that (I'm not sure why)

[math] \Omega_{total} = \Omega_{m}+\Omega_{\Lambda} = 1 [/math]

If we ignore radiation. As the universe expands the amount of dark energy increases, while the amount of matter is the same only more spread out.

How is it that the universe can remain flat (k = 0) when more dark energy is created through expansion?

>>10124143
In that case I’ll recommend the MIT opencourseware for their 18.03 course — the video lectures are excellent, and you’ll find enough references to other material to keep you occupied for a while. Here’s a link: https://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/

with this picture in mind how much force does one rubberband apply to the watermelon when stretched over it?
furthermore how much force is needed to destroy a human head in the same fashion
im working on a project and i need to know if this is possible

How do i get lewy body dementia by proxy

How to solve this? Without derivatives or integrals (we haven't learned them yet). Teacher told me that I should estimate something but I don't get it. Help me please.

>>10124263
I estimate there are 300 black pixels in your image.

What have you tried? Do you have an intuition about how rapidly each factor approaches its limit? Can you tell the sign of the expression?

>>10124263
idea:
both the nth root of 3 and 2 are going to tend to 1, the nth of 3 a bit slower since it is a larger number, so the expression in the parenthesis is going to tend to 0 from above. However, the square root of n is going to tend to infinity, however, exponentials beat polynomial expressions, so it's not going to be fast enough growing to not tend to 0

>>10124263
You just determine which term is of the greatest value/magnitude that will either approach 0 or infinity faster than the other terms and thus make the limit either 0 or infinity in this case

>>10124263
>>10124416
it really depends on the tools you have. As i said, if you can use that exponentials beat polynomials, then: mutiply your expression by the conjugate:
[eqn] 1=\frac{\sqrt[n]{3}+\sqrt[n]{2}}{\sqrt[n]{3}+\sqrt[n]{2}}[/eqn]
You get that your expression is equal to [eqn]\frac{\sqrt n}{\sqrt[n]{3}+\sqrt[n]{2}}\leq \frac{\sqrt n}{\sqrt[n]{2}+\sqrt[n]{2}}=\frac{\sqrt n}{2\sqrt[n]{2}}=\frac12\sqrt n\cdot 2 ^{-\frac1n}[/eqn]
But [math]\sqrt n[/math] tends to infinity slower than [math]s^{-\frac1n}[/math] tends to 0, since the latter is an exponential. Then simply show (perhaps by induction) that your limit is always above 0, so you can sandwich the limits and use the sandwich theorem

>>10112106
Which book do you recommend about "heat treatment"?
(Tempering, Martempering, Austempering)