SQT - Stupid Questions

Is this the Stupid Questions Thread?

I'm doing integral of e^(-st) t sin(t)dt from 0 to inf

and I get -2s/((1 + s^2)^2)

But wolframalpha says the answer is the positive version: 2s/((1 + s^2)^2)

I can't see where I'm going wrong. Can someone post the step-by-step?

>>8476704
you probably just fucked up a negative somewhere. Maybe the - in (-st)

>>8476704
how are we supposed to know what you did wrong when you dont show us any of your work brainlet?

>>8476704
just take the Laplace transform of sin(t) and differciate with respect to s.
ta da
differentiation under the integral sign is ur best friend

>>8476695
Underated

>>8476692
Write an arbitrary vector in a basis of eigenvectors of M, then swap all the eigenvalues out with the maximal/minimal eigenvalue?

>>8476692
since M is real symmetric its diagonalizable with eigenvectors e1,..., en with eigenvalues c1,..,cn

write x = sum of aiei

then
x^T M x
=(sum aiei)^T M (sum aiei)
=(sum aiei)^T sum aiciei)
=sum ai^2ci
<= sum ai^2max {ci}
=max {ci} sum ai^2

dividing by ||x||_2^2 gets rid of the sum

you can do the same thing for the minimum since
x^T M x
=(sum aiei)^T M (sum aiei)
=(sum aiei)^T sum aiciei)
=sum ai^2ci
<= sum ai^2 min{ci}

>>8476749
should be

>= sum ai^2 min{ci}

on the last line of course

>>8476749
>>8476751
thx

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Hey guys, not sure about my answer here. Can someone verify it for me? Thx. (Bottom question)

>>8476784
tan(x) isn't defined let alone continous let alone differentiable at π/2, thus rolles theorem isn't contradicted (the hypothesis of rolles theorem is that the function is differentiable in the entire interval, and endpoints are the same)

>>8476792

Ah ok that makes so much more sense. Thanks!

Figure the people who know most about matlab will be here. So I have a vector which is ('v1', 'v2', 'v3') and I can't get it to reference the whole strings, only one letter of it. So for instance it return vector(2) as "1". How do I fix this so that vector(2) returns 'v2' etc? Pls respond

>>8476728
I didn't ask you to find where I was going wrong, I asked to see YOUR work. Brainlet.

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I'm really struggling to understand what my professor means by problem 2. I'll show you the example she is referencing.

She says the key to solving these problems is "to consider some quantity M (Called a monovariant) that changes in a predictable way."

I think I solved problem 1.

When it is a 3d shape, the pieces you are breaking off are the 1 by 1 cubicles.

From what I've tried. If there an odd number of pieces (m*n*l is odd), then player 2 will win.

If there is an even number of pieces (m*n*l is even) then the first player will win.

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>>8476929
These are the examples she left us. This problem is very similar to the chocolate example 1.

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How to do this?

Also would I use the limit definition of differentiation?

How can I develop good math skills? I always forget about what I learned after a few weeks and I'm just clueless about past things that I've done. It's pathetic but I'm retaking precalc for a second time at my university and I can never remember the rules for equations so I just get stuck on problems and don't know what to do. Should I just start from the very beginning and relearn math?

>>8476973
Kys and hope you will be reincarnated into a non brainlet

I used a solution of water and hcl to dissolve iron oxide and pure copper. Then i let a ball bearing sit in it for a few days so it would be plated. The plating was copper colored, but opaque and very weak.

Was that because of dendritic alloy nucleation or lamellar alloy nucleation?

>>8476982
Sorry, was it because the plating was lamellar or dendritic or both?

>>8476692
How do I obtain cellular immortalization?

I know that hTERT and telomerase has a big part to play in it, but the papers I've read don't exactly go into the process of how they immortalized normal human cells in vitro.

>>8476692
"Upper bounded". Into le trash it goes.

Is there a good way to learn all the necessary alkane/alkene/alkyne reaction mechanisms for orgo? I slacked off for a bit and now I'm fucked because I only remember simple alkyl-halide mechanisms

>>8476929
Does the sum converge ?

>>8476958
do you know Cauchy Riemann equations ?

>>8476973
Practice, practice, practice, then learn how to summarise your learnings as though you were going to teach it to someone else. metaphors, analogies, etc, etc.

alternatively look into Scott Young's advice on his blog for other ways of learning deeper.

Why the fuck are there three SQTs?

>>8477160
not really relevant

>>8477331
Jesus fuck, you're right.

One of them hit the bump limit so this one was made while the older one still hasn't been deleted, and some other faggot made one while this one was still perfectly fine.

>>8477386
This thread was made later than >>8476351, just so you know.

>>8477396
Hey, my mistake.

OP is a faggot.

Should I take solid-state or atomic physics next semester? Can I take both or is one a prerequisite for the other?

I've just finished my first QM course.

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What the hell am I doing wrong?

>>8477450
Using mathematica

>>8476808
Did you include apostrophes when defining the vector? Because that will fuck it up. It should simply be defined as v=[v1 v2 v3], in which case v(2) will give you the value of v2.

It's not immediately clear to me why the set of deck transformations form a group under composition. I can't understand why an inverse exists according to the definition my book uses. Some other books define deck transformations to be homeomorphisms, and Hatcher defines them as isomorphisms, which makes it very clear why there exists an inverse, however in my book deck transformations are defined as continuous maps. I would assume it comes from coverings being locally homeomorphisms, but I can't piece it together. Is it a book typo to define them as continuous maps, or do I just need more caffeine to get my head on straight?

>>8477443
Depends what 'atomic physics' means. It could be a quantum field theory lite.

I'm biased, but would recommend solid-state. Good application of QM and an introduction to one of the largest active areas of physics research. Though an undergrad-level course might be bogged down with details of band theory and you only scrape the surface of cool stuff.

Hello /sci/, I don't like maths so I come to you with this question.

How do you calculate rolling a 3% item twice (or more times) in 10 attempts?

>>8477568
[math]{10\choose3}(0.03)^{2}(0.97)^{8}[/math]

if you're real unfamilliar with math, note that the first term is the binomial coefficient and NOT a fraction. 10 choose 3 is 120. This is for twice. If you want it for more than 2, the general formula is

[math]{n\choose k}(p)^{k}(1-p)^{n-k}[/math]

where n is attempts, k is successes, p is success probability.

>>8477576
i mean 10 choose 2, i'm tired. either way, your probability is around 3% of getting 2 successes at 3% each out of 10 attempts

http://www.wolframalpha.com/input/?i=(10+choose+2)(0.03)%5E2(0.97)%5E(8)

>>8477576
>>8477587
Ah I see.
I tried using http://www.danielsoper.com/statcalc/calculator.aspx?id=69 and got 3% too.
Is it the right calculator for that?

>>8477591
Yes, you're correct this is binomial probability.

Sophomore undergrad, took chem and bio all last year and doing ochem, physics, and calc right now. I've found out through a bit of stockholm syndrome I actually am autistic and love STEM.

My school is being paid by gubment and I'm not really going to be hurting for a job afterwards given I can just work at the family store, but I'm really tangentially interested in certain not-as-popular sciences, like Geology, Astronomy, (>implying phsychology is science), and just generally anything that gives me day-to-day knowledge of the world.

What are some of the more interesting courses you guys've taken that aren't part of your core majors? Is it worth dropping a couple grand to take something like geology over the summer?

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>>8476695

>>8477568
https://en.wikipedia.org/wiki/Binomial_distribution#Probability_mass_function

Why is v*dv/dx equal to acceleration?

>>8477675
It's the instantaneous change in velocity.

As in, at that point, at what rate is the velocity changing.

As in, at that exact point, by how much is it speeding up, or slowing down?

>>8476958
Graph it, look

>>8477545
>deck transformations
always isomorphisms

what book are you using?

>>8477675
because v(dv/dx) = (dx/dt)(dv/dx) = (dv/dt) = a

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How would I show this? I originally thought integration by parts would help, but then ended up with f ' (t) and didn't get anywhere

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Prefer tips over answers.

Can you predict the remainder when 111...1 (100 ones) is divided by 1111111?

>>8477932
Short answer: 11.

Long answer: 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 = 1000000100000010000001000000100000010000001000000100000010000001000000100000010000001000000100*1111111 + 11

>>8476929
What is your question exactly?

Set:
M=1/(a1+1) + 1/(a2+1) + K
M'=1/((a1-1)+1) + 1/((a2+1)+1) + K
Simplify M'-M, and you get
(a2-a1+1)(a2+a1+2) / a1(a1+1)(a2+1)(a2+2)
a2>=a1 => a2-a1+1>0 => M'>M
(a1 must be at least 1, as that's the room which someone is leaving, and all of the other terms are always positive).

So M always increases whenever someone moves to a room with at least as many people.

You can't use the sum of 1/a[i] because some of the a[i] could be zero, which would make 1/a[i] and thus the sum undefined. So you add 1.

>>8477940
Is there an intuitive way to figure this out?

>>8477970
Number of 1s in the long string divided by the number of 1s in the string you want to divide it by. The remainder is the number of 1s in the string of the remainder when you divide the long string by the shorter divisor string.

>>8477972
Thank you!

>>8477450
Help!!

>>8477719
>graph it
>look
>3-dimension
>wants me to graph
>bring this autistic in an exam

>>8476958
What does it mean when it says wrtx/y. Do I just consider x/y as a parameter?

just throwing this out there

For personal reasons I am under a lot of stress. From the moment I wake up my heart rate rockets and it is a struggle to keep it under control, I can hardly think straight, it is starting to become a problem itself at a time when I need to calm down and get things done.

What is the psychology behind this? How can 1 abstract thought have such a huge physiological impact? I've tried distracting myself but nothing can shake it off.

>>8478048
Stress modulates the adrenaline receptors, making you more excitable.
The excitability feeds anxiety, which will increase adrenaline in a positive feedback loop.
I've had the same thing last year during my master's.

It's best to try yoga and exercise, the endorphins may help. Try to control your breathing, long breathes will activate your parasympathetic nervous system. (don't bother meditating when you're to excited though)

You may want some chemical help; I'd recommend either to supplement L-Theanine or Ashwaganda. Don't use benzodiazepines, as they will fuck you up.

>>8478071
I was thinking about exercise, I haven't jogged in a while due to flu. I will go do that. Thanks.

>>8478044
If it says "wrt x", it means treat x as the independent variable and treat y as a constant.

>>8476692
How do I learn math? I'm a freshman in college and my math education was extremely poor and limited. The only thing I really understand is basic algebra and graphs.

The professor is really good at math, to the point that he can't even begin to comprehend just how far behind me and a lot of other students are. Even when he tries to explain, he uses proofs that involve things we don't know yet. If I don't learn math I'm going to fail.

What is the best way to teach myself? Is there some kind of progression? I need to be able to understand Logarithms by next week. So far all I grasp is that they're like reverse exponents or something.

>>8478111
log-base a-of(b) means "a to what power equals b?". That power is the value of that expression.

So log2(8) + log3(9) = 5

Also,

loga(b) + loga(c) = loga(bc)
loga(b) - loga(c) = loga(b/c)
loga(b^c) = cloga(b)
loga(b) = logc(b) / logc(a)

Those are all you really need to know.

>>8478048
>>8478071
update: it worked, I am still thinking about the personal reason, but the ridiculous resting heart rate and sensation of tightness around my heart and stomach is gone

Any idea what the science is behind this? I am not sure it is entirely due to endorphins, the positive feedback loop is a good theory. Exercise causes a bit of excitement so I hypothesize that my focus changed from my anxiety to my running. Maybe the endorphins reduced anxiety and helped in this process.

How do I draw in 3D?

My calculus III final is one month away and I still don't know how to fucking do it properly

>>8477450
HELP!!

>>8478158
Just get a 3D pen, duh

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>>8478230

x^2 = 25
x = sqrt(25)
x = +5 or -5

No problem.
But what if I try something different, like derivative.

x^2 = 25
d(x^2) / dx = d(25) / dx
2x = 0
x = 0

Which is obviously false!
Somebody help me please...
What's wrong here?

>>8478296
Is this bait?

>>8478298
No, unfortunately.
Can you please explain?

>>8478299
What's the formal definition of a derivative?

>>8478306
[math]\frac{d}{{dx}}f\left( x \right) = \mathop {\lim }\limits_{\Delta \to 0} \frac{{f\left( {x + \Delta } \right) - f\left( x \right)}}{\Delta }[/math]

>>8478310
not the formula, but as in the concept itself
What is a derivative with respect to its function?

>>8478315
Rate of change?

>>8478316
the slope of the tangent line to the curve at any given point where f(x) is continuous

What do you infer from this?

>>8478324
I got that the slope of the tangent line of x^2 at a given point is zero?
But not that the value of x^2 is zero?

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I don't where's the better place to ask this. But how do I interpret this VAR estimation?

>>8478327
You got [math]\alpha = 2x[/math] Which is the function at which

Let [math]f(x) = x^{2} - 25[/math]

You got from before that x is either minus or plus 5, in any case once you plug that into [math]f(x)[/math] you get either the point [math](5,0) or (-5,0)[/math]

Hence as [math]\frac{d}{dx}f(x) = 2x[/math]

[math]\frac{d}{dx}f(5,0) = 10[/math] and [math]\frac{d}{dx}f(-5,0) = -10[/math]

[math]At (5,0) tan\alpha = tan(10) = some constant \beta[/math]
[math]tan(2x) = \beta[/math]
[math]x = \frac{arctan\beta}{2} = \frac{10}{2} = 5[/math]

You can't just put the derivative equal to zero at point (5,0)

>>8478372

So I can't just take derivative of both sides of an equation like I can divide, add or multiply both sides by a constant?

I think I get it.

I can take an equation and add 5 to both sides, or divide by 5, or take the log of both sides, or square both sides, ....

I can do anything but take the derivative of both.

>>8477752
Gamelin. It's pretty bad but it's what we're using for the course. I managed to understand and convince myself that deck transformations need to be isomorphisms this morning after a good cup of coffee, as the alternative could break the [math]p\circ f=p[/math] component of the definition. I see other books like hatcher include isomorphism in the definition. Definitely would've saved me some time last night thinking about it with so little focus.

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Looking for some reassurance here. Is this the correct answer? Is it ok that I assume the squeeze theorem?

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How the fuck do I do this?

Anyone?

>>8478430
variable starts with a number, the instruction clearly states that you can't do that

>>8478430
sq3 = 9
not sp3 = 9

are you dyslexic?


>>8478435
you're retarded

Suppose f(x) = {1 if x in Q, -1 if x in R\Q

I want to find the points (if any) that f is continuous. Now since the domain of f is R we have that every x in R is a limit point, so there are no isolated points / singletons (is this true?). Now, I don't think it is continuous anywhere, and I think the way to prove this is to construct two different sequences in the domain that both converge to some arbitrary point p in the domain, but do not converge to the same value. Could I make one of these sequences x_{n} = (3/n) + p, and the other t_{n} = (π/n) + p? And then of course f(x_{n}) converges to 1, f(t_{n}) converges to -1?

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Hey Brains,
I got two conjuctions (hope that's the right word) for
R x R, I have to conclude weather or not the conjuctions turn them into a vector space.
I already concluded the stuff for the + like conjunction, now I am stuck at the conjuction for vector and scalars.
In my notes it says I have to prove
while k and h are scalars and v and w are vectors that:

(k + h)v = kv + hv ,
(k ⋅ h) ⋅ v = k ⋅ (h ⋅ v) ,
1 ⋅ v = v ,
k ⋅ (v + w) = k ⋅ v + k ⋅ w

My question is now what + operation do I need to use the one I proven earlier or just the normal + operation?

>>8476958
Helb???

Hi, first time posting here. Why is it possible to write 2^n if 2*n+1 is less equal than 2^n?
Would be nice to get an easy explanation. Thanks in advance.

>>8478424

God no thats awful

>>8478424
sin(x)/x equal 0 only when x tends to 0. So your reasoning is false.

>>8478453
What are you doing? It sounds interesting but I've never heard of logic being modeled as a vector space.

My initial instinct here is that you're actually doing something with a cartesian closed category but I don't want to wander in aimlessly in case I'm way off base.

>>8478461
wat

>>8478484
I study in german and this is some basic stuff, it may sound interesting to you because I don't know the right terms.

Basically I have to check if
(x; y) ⊕ (x0; y0) := (x + x0; y + y0 + 1); λ(*) (x; y) := (λx; λy + λ − 1)

fulfill the requirements of a vector space,
So gotta check if the ⊕ follows the rules of addition and (*) of scalar multiplication

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Whats this

>>8478430
>>8478444
>comes in thread asking retarded question with a simple answer
>gets the simple answer
>gets treated like a retard

/sci/

>>8478492
Sorry, I just learned that I should've wrote this down in TeX. I mean why is it possible to change
2n+1 in 2n+1 \leq 2^{n} to 2^{n} ?

>>8478468
>>8478483
Can you help a brainlet out? I can't think of anything else to solve it

>>8478501
It doesn't matter whether you use TeX or not. But you /do/ need to explain WTF you're rambling on about.

>>8478526
Ok, I'll try this to explain in another way.
Let's say that 2*n+1 is smaller equal to 2^n.
I've seen someone turning 2*n+1 to 2^n. Why is this possible?

hi /sci/
Im not asking for help with my home work here, but im trying to do an algebra calculation on my phone calculator, and my computer calculator. but it doesn't work.

here is the line:
46200/230*√3*cosϕ=

Sorry for stupid question.
i think im filling in the cosinus wrong
but I've tried both cos, cosh and cos/cosh- with only wrong answers

>>8478453
these are the compatibility of scalar multiplication and vector addition. you would also have to show that vector addition is a commutative group

>>8478496
>Basically I have to check if
>(x; y) ⊕ (x0; y0) := (x + x0; y + y0 + 1); λ(*) (x; y) := (λx; λy + λ − 1)
>fulfill the requirements of a vector space,
>So gotta check if the ⊕ follows the rules of addition and (*) of scalar multiplication
the compatibility requirements you can directly check. (just write the compatibility equations down and substitute the definition of scalar multiplication and vector addition as by your definition and then check that it all works out as it should)

then you still have to check that vector addition is a commutative group. and since you have to hand in the exercise tomorrow morning (I have a strong suspicion of what uni you're studying at), I'll give you a hint: check exercise 1)i)of the last exercise sheet. (set g=-1)
you can save yourself a lot of calculation that way, otherwise you have to verify all group axioms.

>>8478550
Look, if you don't even understand enough to be able to ask a coherent question, there's no point in posting.

How do I visualise the fact that heating up a gas increases its entropy? I don't see how increasing temperature affects the number of microstates.

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Wtf did i do wrong here guys?

>>8478579
Holy shit. I'm leaving. It was nice to seek help. I guess I expected too much from you guys.

>>8478593
forgot to keep the cot in the first term

>>8478599
Oh fuck, stupid mistake. Thanks

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>>8476692
Can anyone recommend me what to read about terminology extraction? Learning from scratch. Thanks in advance.

Same question about Web3D, though it's more /g/ related.

>>8478593

you dropped the cot(x) in the first term

f'g +g'f

you did f' + g'f

>>8478597
he's kind of right, though. the first step in solving a problem is being able to clearly state the problem.

with very simple problems this is also often the last step, because in trying to precisely formulate what the problem is the solution will often become obvious.

either way, ambiguous questions are impossible to answer.

What are the requirements for a subject to be a science?

>>8477450
Mathematica wants you to capitalize Sin[x] and Cos[x]. Should work then.

>>8478451
you want to use the density of Q in R

f is not continuous at any x in R\Q since you can find a sequence of rationals approaching x that where f is always 1 but at x f is -1

>>8478574
Yeah your guess ain't far off, thanks for the tip.
Appreciate it.

>>8476987
HALP

First time learning Linear Algebra. Is Shilov's book hard or I'm just too dumb for it?

>>8478424

Let f(x) = 2x-1-sin(x). Then f'(x) = 2 - cos(x), and this is always positive, so f is strictly monotone increasing. Since f(0)=-1, and f(pi) = 2 pi -1 > 0 there is exactly one root, and it's in (0,pi).

>>8476692

If I have a line y=mx with m being a very small number, how do I calculate what the first point of 2 integers it intersects is? Can you do it without brute force? (I assume every line would have one)

>>8478807
Do you mean the first point (x, y) where y=mx and x and y are integers? If m is irrational, there's no such point, and if m is rational, then y and x are just the numerator and denominator when m is written in lowest common terms.

Surely you boys have done some MATLAB Euler's method right?

[eqn]\frac{d^{2}x}{dt^{2}} = -\sin(x) =-\left( x - \frac{x^{3}}{3!} +\frac{x^{5}}{5!}+\dots \right) [/eqn]

I define the linear model as the first term of the series expansion.

Rewriting:

[eqn] x^{\prime} = y[eqn]
[eqn] y^{\prime} = -\sin(x)[/eqn]

Given x(0) = 1 and v(0) = 0 write up an Euler's method and when you plot x and y it SHOULD be a circle.

My code seems right: (s is step size)

for i = 1:100
x(i+1) = y(i) ;
y(i+1) = y(i) -s;
end

But it isn't and now I'm fucked. This spirals out in the plot(x,y) and I haven't a clue where to go now. Please anon's you're my only hope.

>>8478899
>Surely you boys have done some MATLAB Euler's method right?

I did when I took ODEs. But I instantly forgot it.

>>8478899
i assume you've tried a smaller step size? you need a pretty small step size for euler's method to be accurate.

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Civil Engineering major here. Should I be ashamed and self hating of my career choice?

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>>8478932

s = 0.0001

>>8478944
looking at your matlab code, i dont know if it's right.

if your step size is S, then shouldn't it be something like this:

x(i+1) = x(i) + s
y(i+1) = y(i) + s*(dy/dx)(i)

by (dy/dx)(i), I mean "the value of dy/dx when x=i"

>>8478958

But x depends on y.

Is a strict graph with 6 vertices, and degrees 1, 2, 3, 4, 5, 5 possible?

https://www.youtube.com/watch?v=65KhNiYZajg
can all programmers do this?

>>8478899
if you are using -x in place of -sin(x), that only works when x is small. More fundamentally though, you are not doing the divided difference right. If you want
x'=y
y'=-sin(x), then you need

for i=1:100
x(i+1)=x(i)+s*y(i)
y(i+1)=y(i)-s*sin(x(i))
end

>>8478899
you are plotting a straight line

How do I get gud at engineering mechanics

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How do I write these three proofs? Could someone guide me?

is there an algorithm for knowing whether a graph is bipartite?
Specifically, how is it known that all n-dimentional hypercubes are bipartite? I get it has something to do with the fact that all adjacent vertices differ in only 1 bit in its binary string representation, but i can't quite complete the thought.

>>8479327
try to 2 color it

****In serious need for some help****

I got back my midterm for a Calculus class and I bombed it, mainly because I only ended up with a half hour of sleep within 36 hours due to staying up from election (I know I shouldn't have, but I couldn't control my impulse) and midterm being next day. I also had some family things that happened that day.

My university said that it was possible to appeal to get a midterm remade because of election, but I believe my professor is very unwilling to do that because some kids already emailed him about the night of election.

Is there anyway I could convince him to transfer all of this midterm's weight to the final? Any tips? He's from China, so there is kind of language barrier

Honestly so down that I threw away all my work for that class for the semester down the drain

>>8479016
have you even tried drawing the graph?

>>8479327
>>8479334
sorry I didn't read all your post. The idea is you can always split the vertices into two groups: those with an even number of 1s and those with an odd number

Is hiroshimoot trying to destroy 4chan with the new image server? It's unbearably slow, and I haven't made a script to replace all is.4chan.org with i.4cdn.org yet. How did he fuck up this badly?

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>>8479350
thanks, i think i get it. Do you think you could help me get started on pic related? Just on what the second set of vertecies should be(i'm guesing 9,10,6)? Is there only 1 possible second set of vertices? honestly i think i'm just having a definition problem.

>>8479364
Subtle.

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>>8479364
Wasn't too difficult.

>>8479426
what? i wasn't trolling. It's not actually >>8479432

>>8478760
Strang is an easier start.

>>8479432
Oy vey

Is hungerford's algebra a tough algebra textbook? Sets of 4-5 exercises take me anywhere from half an hour to 3 hours if I don't look up hints...

>>8479527
his graduate level one is tough, as tough as every graduate textbook should be

his undergraduate level book is fairly easy

>>8479527
"Algebra" is a very tough book, yes.
"Abstract Algebra: An Introduction" is not that hard.

He's written two and I'm not sure which one you're talking about.
If by some chance you're new to abstract algebra and you're actually trying to learn from the yellow Algebra book, stop. It's not an introductory text at all.

>>8479633
>Going to be majoring in computer science

I am so sorry to hear about your mental retardation

>>8476692

Hello Sciencers, physicists, chemists, oh my,

Can anybody tell me what a Sm^2 unit could potentially used for?

(Siemens meter^2)

It gives conductivity in mS*cm^2, but that doesn't make sense to me.

it's not mS*cm^-2 which would make more sense.

it doesn't make sense to me because it would imply that a larger surface area would decrease conductivity. what?

>>8476692
false

if x is length not equal to the m (of the m by m symmetric matrix M) then the expression in the question is undefined and therefore cannot be bounded by two numbers

>>8479649
Sm^2 is the reciprocal of ohm/m^2, which also doesn't make much sense as a basic physical property.

Materials have resistivity in ohm-metres (i.e. ohm-m"2/m), sheets in ohms (the resistance between opposing edges of a rectangular sheet of material depends only upon the aspect ratio; the dimensions cancels), wires (i.e. fixed cross-sectional area) in ohms-per-metre.

So ... ohm/m^2? Maybe change in resistance-per-length with some quantity with units of length, e.g. strain, i.e. ohm/m per metre of strain? Or per metre of ... something.

>>8477888

Bump! A rare interesting question!

>>8477888
Maybe suppose first that f>=0 on [0,1], so that F(a) = \int_a^1 t^(-2/3) f(t) dt is monotone increasing and continuous. Since f is continuous, there is an M such that f(t)<=M on [0,1], so F(a) <= \int_0^1 t^(-2/3) M dt = 3 M. Since F(a) is bounded above, and continuous, the limit exists.

For the general case, split f up into it's positive and negative parts... or consider (f(t)+k) - k where k is big enough to make f(t)+k positive on [0,1]

Why does the second derivative of 1/(1+x) using the quotient rule differ from when using the chain rule as in (1+x)^-1 ???

>>8479825
because you're using one of the rules wrong

>>8479350
>have you even tried drawing the graph?
I thought that was implied. I've tried yeah, but every try ends up useless for those specific criteria.
I can't manage to have both degree 5 vertices while also having a degree 1 one.

The handshake lemma tells me that the degree 20 could be equal to 2|E|, so I think it should have 10 edges?
Whether or not the graph is possible I still don't know. Maybe I'm just being retarded and keep drawing them wrong.

>>8477888
this is begging for a Cauchy's criterion solution

>>8479840
I was right, you can solve it that way. using the boundedness of f and uniform continuity of [math] x^{1/3}[/math]

CS fag here. I'I finishing up Calc I this semester and will be taking Calc II next semester, but what should I take after that? Linear Algebra? Diff Equations? I honestly don't know

>>8479888
Aren't ODEs part of calc II?

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Is it possible to calculate how this capacitor charges up? The parallel resistor is really throwing me off. The "standard" charge/discharge equations are easily derived from a RC-circuit with the resistor in series and leads to the time constant tau = RC, but it can't be the same when it's like this right?

>>8479911
Forgot to add that the capacitor is supposed to be completely discharged before closing the switch S.

>>8479298
Damn, I'm stuck on these too. How would you approach these?

>>8479911
write down the ODE

>>8479911
it charges instantaneously

>>8478424
How is sinx/x =1????

>>8479347
Yes, I know your professor. Buy him some wontons and a couple fortune cookies. The Chinese love that and he will surely allow you to transfer the weight of the midterm to the final.

I have a damped pendulum, described by [math] \ddot{\theta}=-\frac{g}{l}sin(\theta)-\frac{\gamma}{m}sin(\dot{\theta}) [/math]. How would I go on about reducing this to the two dimensional flow [math] \frac{dx}{dt'}=y, \frac{dy}{dt'}=-sin(x)-\sigma y [/math] by proper rescaling of [math] t = t' t_0 [/math] and for appropriate choice of dimensionless parameter [math] \sigma [/math] and the time-dependent functions [math] x(t'), y(t') [/math]?

I start by dividing with [math] \frac{g}{l} [/math] to make the first term in rhs dimensionless.

[math] \ddot{\theta} \frac{l}{g}=-sin(\theta)-\frac{\gamma l}{m g}sin(\dot{\theta}) [/math]. I then let [math]\sigma = \frac{\gamma l}{m g}[/math]

[math] \ddot{\theta} \frac{l}{g}=-sin(\theta)- \sigma sin(\dot{\theta}) [/math]

I finally introduce a dimensionless time [math] \tau = t \sqrt{\frac{g}{l}} [/math] and I realize that this must be an imaginary number since gravity is negative, so I conclude I make some mistake.

I am confused and don't know how to approach this. Any suggestions?

>>8480183
> gravity is negative
I don't know about you, but I choose my signs so that my constant parameters are all positive.
Pretty g is positive

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Here's the deal. I'm 18, and I fucked around during sixth form and barely got any qualifications. In GCSE I did fairly well and got a B in Maths and a A in both Chemistry and Physics. In A-Levels I became incredibly lazy, never did work at home, barely did homework, often skipped lessons and got a U in Maths, Physics, Chemistry, and a D in Computing.

Currently I work part time and I was thinking of going back to college for 2 years and getting proper A-Levels. I'm interested in studying Electrical/Electronic Eng or Chemical Eng at Uni.

The A-Levels I was thinking of doing are Maths, Chemistry, and Electronics. Physics and Further Maths seem a little too hard, especially since my self-confidence in academics is pretty low from all the past failures. Computer Science is also an option since it's so similar to Computing. Vocational ICT is also an option, which I know isn't engineering related but I know a dude who got into Uni of Birmingham with one easy vocational subject on the side, although his course was Urban Planning and dudes getting into mid-tier/decent Unis with mostly BTECs.

Should I change them or does this sound good?

Also I'm planning to use Khan Academy and text books from the actual courses to help prep. Anything else? Has anyone ever been in the same boat before?

>>8479957
I think he's thinking of the limit as x goes to zero.

>>8480252
Replace chemistry with physics. It's easier and more useful.

>>8479888
After Calculus II take Multivariable Calculus, Matrix Algebra, Intro to Proofs (do not take discrete math in the CS department) at the same time. Then take ODEs, Probability (again in the math department, not the CS crappified version), and Mathematical Logic. You can then follow that up with take Statistics, Numerical Analysis (math department), Linear Optimization/Programming (math department).

Or you could resign to being a brainlet like most other CS majors.

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>>8476692
How do I check the continuity for this?

>>8480306
>matrix algebra
Why not try finding a good linear algebra class. (Where the teacher actually teaches you what is going on instead of "lul look at these tricks!"

>>8480306
Not him, but will taking these courses as a CS major turn me into a pretentious fuck who calls other people "brainlets" for not having explored as many regions of math as myself?

I need to know this because I want to take most of these courses but I would actually like to enjoy life and connect with other human beings as well.

>>8480352
>Not him, but will taking these courses as a CS major turn me into a pretentious fuck who calls other people "brainlets" for not having explored as many regions of math as myself?

No, you'll still be a massive brainlet compared to actual math majors. You'll just be a part of the rare few who understand what's going on in your lectures.

>>8480324
whhere in the plane do you want to check the continuity?

>>8480204
Yes. You are right. This is embarrassing. Sorry.

>>8480365
A function is continuous if the limit f(blabla) as blabla goes to bananas = bananas

>>8480358
Your terminology seems to imply that you believe studying application towards a specific area of interest is intrinsically worth less than learning the mathematical theory behind said application even when the basis for a functional knowledge of theory is attained.

Is theory not an ample ground for self study, while application is made the primary focus in formal learning? Does practicing application never lead to new ideas in theory? Is the "purest" study always the best simply due to the descendant nature of applied fields?

>>8480324
The limit goes to zero
Use the taylor series expansion of sin to find the approximation of the the sin function you have there
Then solve by CST

>>8480382
I'm a unlucky son of a bitch and got calculus ll (series etc) right in the time of a curriculum change and now series is calc 4. Can you explain how'd I use taylor expansion there?

is it possible for a brainier like me to get as smart as you guys? i used to be smart then when i hit high school i stopped sleeping and went into dumb mode until I got to college. Now i want to be smart again.

>>8480377
OK, but continuous at which point? or in the entire plane?

>>8480385
you know sin(z)/z = 1 when z=0

let z=3x+3y
sin(z)/(z/3)=3sin(z)/(z) so the limit is 3

>>8480389
thats a bit naive

>>8479527
Hungerford's "Algebra" is a graduate text. It's truly excellent and highly recommended.

>>8480389
Sorry but that doesn't make sense to me. But this is indeed the stupid question thread.

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>>8479016
Ok, so correct me if I'm wrong here.

Using the Havel-Hakimi theorem I'm led to believe this particular graph isn't possible
>5 5 4 3 2 1
>4 3 2 1 0
>2 1 0 -1

Therefore a graph with six vertices and those specific degrees isn't possible, right?

>>8480385
Basically

[eqn]f(x) = \sum_{0}^{\infty} f^{(n)}(a)\frac{(x-a)^n}{n!} = f(a) + f'(a)(x-a) + f''(a)\frac{(x-a)^2}{2!}[/eqn]

[eqn]sin(x) = \sum_{0}^{\infty} (-1)^{n}\frac{x^{2n+1}}{(2n+1)!} = x - \frac{x^3}{3!} + \frac{x^5}{5!} ...[/eqn]

Hence

[eqn]sin(x) \approx x[/eqn]

[eqn]sin(3x +3y) \approx (3x+3y)[/eqn]

I can seem to figure out this integral, can anybody help?
[eqn] \int_0^{2\pi} \sin^{2\ell + 1}(\theta) \space d \theta \\
\ell = 1, 2, 3, 4, 5... [/eqn]

>>8480489
zero

I have to prove that the max amount of edges in a bipartite simple graph is [math]\lfloor n^2 / 4\rfloor[/math].

How can I start this? Induction?

>>8480590
I forgot, where n is the amount of vertices.

>>8480564
Ooops, I meant to state the bounds were from 0 to pi

>>8479963
I am assuming this is not serious right?

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So I'm having a little trouble with this problem.

The goal is to design a pressure vessel capable of holding as much gas as possible given a size constraint and a budget. It's really just an exercise in dealing with hoop stress and managing material

I'm kinda choking on how to optimize the volume and the pressure, however. I guess I don't see how to relate pressure and volume back to the stress and max amount of gas. Any tips?

>>8480592
wolfram alpha gives

integral_0^π sin^(2 k+1)(t) dt = (sqrt(π) Γ(k+1))/(Γ(k+3/2)) for Re(k)>-1

You can see the answer here too

https://en.wikipedia.org/wiki/Lists_of_integrals#Definite_integrals_lacking_closed-form_antiderivatives

I think these are done by recursion. Relate the 2*(n+1)+1 case to the 2*n+1 case somehow... by parts?

On a Cartesian plane I have 2 points. They both show a rate of change of a third point. How do I find the third point's rate of change?

>>8477926
Im thinking squeeze theorem.

>>8478158
make an axes at 90 deg. then the third leg at 45 downwards. straight lines must be parallel to your axes. This is the easiest i've found.

>>8479298
>>8479942
its 5am here so please forgive me if i make no sense

first, there are several mistakes in this.
in 1, it should require B and C to be non-empty, and C should be in V
in 2, it should be for every continuous f

for the first one, just take the complements. U (resp. V) is the complement of the adherence of C (resp. B).

For the second one, if A is connected, let f be continuous from A to R. Then f(A) contains c1 and c2. (-infty, b) and (b, infty) are open sets of R, and their preimages are nonempty open sets of A. 1b says that A can't be the reunion of these two sets. Then b has a antecedent.

If A is not connected, then 1a is true. Let f(x) be 0 if x is in B and 1 if x is in C. f is continuous and its image is not connected.

For the third one, let x be a point of O. Let C be the connected component of x. take an open neighborhood N of x (O is open). Then C u N is connected, and since C is maximal, N is inside C. Then x is in the interior of O

>>8480590
just separate the vertices into two groups. one contains a vertices, the other n-a.
every vertice in the first group can have at most n-a neighbours (since they must be in the second group) so the max number of vertices is a*(n-a)

study this function for a and you will see its max is n^2/4

>>8480489
integrate by parts, get a relation and then use induction
you can also look for wallis integral on wikipedia

I'm trying to study for this occupational engineering test but I'm not so sure the type of math I should be studying.
The questions seem to revolve mostly around real world scenarios, like the famous 2 trains meeting questions and working with unit conversions (from gallons to fluid ounces and such)

What kind of subject is this? Good books?

>>8480834
I followed everything up to studying the function for a. Does that imply derivatives and further procedures?
It might sound like a cheap excuse but in class we were mostly taught to tackle these problems through logic over anything else. Think of how Euler's theorem works, not because of deep formulas, but rather the logic of graph theory.

I'm thinking there's a more "worldly" way of arriving to that formula through logic, like how you put the a*(n-a) together through simple deductions, but I can't put the pieces together.

>>8480671
Check your text for a formula relating pressure, geometry (wall thickness+shape), and stress. Figure out the relationship between wall thickness and volume based on the shape.

>>8480381
You need to learn theory in order to learn the more powerful applied topics. There is only so much you can do without knowing Algebra and Analysis.

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which chemotherapy agent would be best to contrast and compare its effects agent orange?

>>8480928
to agent orange*

>>8480297
physics is easier than chemistry? I haven't done either in so long so I don't quite remember

I'm in my junior year of a physics degree from a decent (top 30 in USA or something like that idk) school. I'm above average in my class but I'm nothing spectacular. I want to go to grad school but I'm not convinced that I want to go for physics.

I loved the gen chem sequence and have the space in my schedule to take a full year of p chem and o chem next year, which I'm seriously considering (or at least doing one of them).

What chem disciplines for grad school are open to me with a physics BS? What about if I take p chem and/or orgo chem?

Does anybody have any experience with this?
What about engineering grad programs? BME, Chem E, etc

>>8480893
it does imply derivatives but the function is just a quadratic in a, there's no tricky business

i doubt there's a more straightforward way of doing this

>>8480954
i wouldn't know honestly
i haven't started physics yet.

Anyone knows a good book on agrometeorology? we are being told to use the professor's book, but I hate when it happens because I can never tell if it's a good book or if it's the professor wants to simply sell us a product.

>>8480975
The no-calculus approach:

Put (n/2+k) vertices in one group and (n/2-k) in the other. The total number of vertices is (n/2+k)+(n/2-k) = n. The number of edges in the complete graph is (n/2+k)*(n/2-k) = n^2/4-k^2.

As k^2 cannot be negative, the maximum value this expression can have is n^2/4, which occurs when k=0 (i.e. each group contains exactly half the vertices).

>>8480954
Chemistry requires a ton of memorisation, but less maths. Physics requires learning a handful of laws, then applying them.

You could probably fit the entire physics syllabus on one sheet of A4. Everything else is just explanations of how you apply that knowledge to specific problems. I.e. it's stuff which (in theory) you could work out for yourself. Even if you can't work it out for yourself, it's easier to remember stuff which makes some kind of sense than stuff which is "here's a fact, commit it to memory".

>>8480998
are you doing a-levels currently or...?

>>8480975
I see. I'll try to see what I can do.

>>8481212
Ok this is interesting.
I don't really know how you got n(2+k) for one group and n(2-k) for the other though. I'm guessing k is an arbitrary value in this case, but the + and - functions for each group seem like a bit of a leap. If I had to take a gander I'd say they came from decomposing the initial equation somehow? It'd make sense since their addition returns n.

This shit is probably textbook for any respectable CompSci student but I'm fuckin dumb.

>>8481212
i guess it depends on what you consider calculus, either way you're just maximizing and for a quadratic it can be done without taking a derivative by just putting it in vertex form:

a(n-a)=-a^2+an=-(a-n/2)^2+(n/2)^2 tells you you want to take a=n/2 if n is even and floor(n/2) if n is odd

>>8476692
Can anyone give me a comparison of Linear Algebra Done Wrong vs Linear Algebra Done Right?

Brainlet here. Had some interest in complex systems science. Learned about the edge of chaos.
Wikipedia has an article with critique of it. Too lazy to look for it, and probably too low IQ as well, so my question:
Is the edge of chaos debunked or what?

>>8481404
It's just splitting the two counts into sum and difference. If one group has k more vertices than the mean, then the other must have k fewer.

Expressing it like that just means that the product expands to a difference of squares.

More generally, if you have a function y=x^2+b*x+c, note that (x+b/2a)^2 = x^2+b*x+b^2/4, so you can re-write it as y=(x+b/2)^2+(c-b^2/4), which clearly has its minimum at x=-b/2, at which point y=c-b^2/4.

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well?

>>8481398
nope
regular gen chem
after this i start physics

>>8481518
sqrt(x^2)=|x|

>>8481518
look at the line

a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4

There he applies the quadratic formula like if t was a constant but t is actually a function of a... and b.

It is like having the polynomial 2a^2 and then separating it as a^2 + a*a and then treating that a that is multiplying the other a as a costant and then completing the square.

>>8481534
That is no problem, it's true for any a,b.

>>8481543
a^2 + a*a = 0
a^2 + a*a + (a/2)^2 = (a/2)^2
(a+(a/4))^2 = (a/2)^2
a+(a/4) = a/2
1 + 1/4 = 1/2

Yup, sureeee. Completing the square with variables as coefficients works.

>>8481549
Completing the square is fine, it's dropping the square that's the problem.

>>8481549
Oh, what you did was nonsense by the way, the first line implies a=0.

>>8481554
>Completing the square is fine, it's dropping the square that's the problem.

No, the problem specifically starts when the proof completes the square treating t as a constant when it is a variable of a.

>>8481559
The point is that it was nonsense. I was completing the square using a variable of the polynomial as a coefficient to illustrate by the proof (which does a more sneaky version of this) is wrong.

>>8481563
... is this some kind of troll?
a^2+a*a=0
implies that a=0
Then in your last step you divide by a=0 which is not great. The conclusion is not that completing the square is nonsense, your manipulations are nonsense.

>>8481565
Why are you being so weird. Fuck, the point here is the completion of the square.

For all I care change the expression to 5a^2 + a*a = 0

The thing is that you cannot treat variables as constants, fuck. Do you have OCD or some shit? Focus on the problem.

>>8481577
This still implies a=0 and you'll run into the same issue.
The problem is that you arrive at an absurd conclusion, namely 5/4=1/2, but you arrive there through faulty reasoning.
But in the absence of progress on your side I'm going to assume you're trolling, maybe from the start, or maybe later to cover up your abysmal mathematical ability.

>>8481518
Second to last line doesn't follow from the one before it.
(a-t/2)^2 = (b-t/2)^2 => (a-t/2) = ±(b-t/2)

NOTE: plus or minus.

Note that t/2=(a+b)/2, i.e. the mean of a and b.

So clearly (a-t/2) = -(b-t/2), i.e. the differences between each variable and their mean are of equal magnitude and opposite sign.

>>8481577
> The thing is that you cannot treat variables as constants
Wrong. I'm guessing that you're just butthurt that the flaw in the proof was identified instantly (well, ~9 minutes, which is almost instantly on /dpt/) and you're hoping to squeeze a bit more mileage out of it.

>A friction force tangent to the surfaces of contact occurs both during the interval leading up to impending slippage and while slippage takes place
>during the interval leading up to slippage
Why is that a thing if there's no actual contact for friction to occur?

>>8481607
Well, you're closer but traditionally a=+-b means that a takes either value, but a and b were set from the get go, so a will only take one value. So a=b or a=-b would be more accurate, a=+-b is fine when a is an unknown though.

>>8480974
Anybody?

What grad programs are open to a physics major, specifically in the chemistry field?
I have the option to take p chem and/or o chem next year (and actually get a chem minor)

What about BME, chem E, etc?

What is the logic behind denying that climate change is a thing?

>>8481728
In short;
It allows heavy industry to flourish without worry of economic backlash or subsequent taxation.

>>8481673
I'd suggest talking to your uni's student services or academic services or whatever you call them. They'll be able to answer your question and actually help you along.

How do you call lines / traingles with a 45, 135, 225, or 315 degree angle.

>>8481728
Money.

>>8481644
> So a=b or a=-b would be more accurate, a=+-b is fine when a is an unknown though.
It's fine even when both are known. A proof only requires that all statements are provable; it doesn't require that they're as specific as possible, or even that they're relevant.

Two of the fundamental inference rules of propositional logic are:
a |- a∨b
b |- a∨b
IOW, if you know that a is true, it's correct to say that "a or b" is true. Likewise for b.

Beyond that, while the statement
(a-t/2) = -(b-t/2)
would be true, it isn't a /direct/ consequence of the preceding statements (you'd need some additional steps). Whereas
(a-t/2) = ±(b-t/2)
is a direct consequence of the preceding statement.

More importantly, it directly addresses the the mechanism behind the "proof": the fact that there are two different ways that (a-t/2)^2 can be equal to (b-t/2)^2, one of which is true while the other is the basis of the "proof".

>>8482153
What I'm saying is that for any pair (a,b)!=(0,0) only one equality is true. And generally
(a-t/2)^2=(b-t/2)^2
implies that
|a-t/2|=|b-t/2|
which is not exactly the same statement as
a-t/2=+-(b-t/2)
although, the +- could be fine if we use it to denote ambiguity.

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What did you do to counter act the American educational system, concerning additional course supplements and tutorage?

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>>8476692
Gaps in my math education boys, doing simple sets and bam.

Can somebody explain A to me?

Is the set just all square roots less than 10 that are natural numbers?

How solve?

>>8482592
Says that if x is in n, then x is between 25 and 45 and if sqrt(x) is in n, then it's value is less than or equal to 10.

X will only be a whole number

>>8482596
Sorry, let me try that again.

It says x is a natural number between 25 and 45. X is in A if the square root of it is less than 10.

So the elements of A. = (25,26,27...,38,39,...,42,43,44,46)

Fill in the gaps with the other whole numbers

>>8482598
Thanks anon, that was more helpful than you know.

Wouldn't the square root have to also be a whole number?, so the only values would be 25 and 36? or does it not matter?

>>8482604
Yes, you're right. I apparently can't read tonight. Says sqrt(x) is in n. So then it would be 25 and 36.

So A is a subset of U, which is a subset of N

>>8481738
I will, but pretty much everything I've ever asked my advisors about they've been wrong about.

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How do you go about solving this?

What was that book called that had a bunch of old and obscure ways to solve integrals?

Does it exist actually? I heard it from one of my calculus professors a long time ago.

[eqn]\int f \ \text{d}\mu := \sup\left\{\sum_{z \in s(M)} z \cdot \mu(\text{preim}_s(\left\{z\right\})) \ \vert \ s \ \text{a simple function with}\ 0 \le s \le f \right\}[/eqn]

so how does one actually calculate this crap in practice

>>8483265
you dont

I'm supposed to write my research paper like a review article.
I've never read or written a review article before and Google shows me abstracts only.
Can someone link me a good one to reference?

If water expands when it freezes, wouldn't the ice caps melting actually LOWER the sea level?

>>8479432
"pure coincidence"

>>8483568
Water is densist at 4 celsius, after which it expands again, but that's all beside the point.

The ice caps aren't floating. They aren't being help up (entirely) by buoyancy forces. If they were, then you would have a point. Good question anyway I guess. If you have an ice cube on an island and it melts and runs into the ocean, the ocean level rises. That's simplified, but you get the idea.

>>8483618
The Arctic ice cap is mostly floating. Antarctica is a land mass.

People often confuse "melting ice caps" and "rising sea level" as the former causing the latter, which isn't the case. Global warming causes both, but the rising sea level is mainly a consequence of water expanding as it gets warmer. Addition of land-based ice (Greenland, Antarctica) to the oceans is secondary.

>>8483568
the rise of the sea level is mostly due to thermal expansion of water, not to the ice caps melting

In my calc class the teacher went from
[math]\frac{dy}{dx}=f(x)[/math]
to
[math]dy=f(x)dx[/math]

Why can you multiply by the dx? I thought [math]\frac{d}{dx}[/math] was an operator and you couldn't separate.

>>8483875
the rising sea level is mostly from ice on top of land falling off the land and into the sea

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Is a physics degree a meme or is it actually good?

>>8484034
If you want to go into research, major in pure math
If you want to go into industry, major in engineering

>>8476692

Is it worth it to study math as a "brainlet" (little above average IQ), or should I contemplate suicide.Also: Are there any learning methods that are especially useful when you're learning math? Thanks in advance, Brainlet.

wtf is the difference between work done by the system and work done on the system?

>>8484066
How do electrons in states move so quickly that they seemingly "teleport"

>>8484094
missquoted

>>8484001
ask your teacher just for the fun of watching him/her not realize how to justify it

I don't really know anything about torrenting or anything like that, but could someone recommend some software where I can manipulate surfaces in 3D space? I think it would help a lot for calc 3.

>>8484123
what do you mean by 'manipulate'?

you can plot 3d things in sage https://cloud.sagemath.com/ and spin them around/zoom in places

>>8484129
That sounds exactly like what I need. Thank you!

How else could one manipulate these objects?

>>8481673
I can't say whether the uni admissions will agree with me or not but: physical chemistry has a pretty big crossover with physics, so would probably accept you based upon your physics qualifications. However organic chemistry is a completely different kettle of fish, barely any maths involved and requires its own specific set of skills.

Just know that if you don't "get" how to do organic chemistry, its incredibly hard to make yourself learn.

This is a way more complicated question than you might think. The typical calculus teacher answer (I'm a calculus teacher, hi) is just to say "you can't, but it sure looks that way." In physics we usually say "fuck that" to mathematicians and pretend we can do it anyway.

There actually are ways to ground calculus that allow for treating differentials like the fractions they resemble, the classic approach though relies on a roundabout argument you can look up if you'd like, a more classic answer would be to define (dy/dx)dx as dy.

Are you doing this in the context of integration or linearization?

tl;dr: no you can't. But the first line does imply the second.

>>8484001
dy and dx can be considered infinitesimals, in which case dy/dx is just their ratio.

>>8484129
How did they graph surfaces by hand before computers?

Where's a rigorous proof that if you have [math]\frac{dx(t)}{dt} = z(t)[/math] then [math]\frac{d^2x(t)}{dt^2} = z(t)\frac{dz(t)}{dx}[/math]. My problem comes from considering a proper composition as the derivative function is different from the derivativative operator. I mean, taking the derivative with respect to x doesn't seem to make sense in your average chain rule definition.

>>8484573
Plox haelp

>>8483265
You check that for all everyday cases (ie. piecewise continuous functions on segments), it yields the same results as the Riemann integral.
This can be done by noticing that step functions are also simple functions and that both definitions agree on simple functions. So far, so good.
After that, you notice that any nonnegative integrable function f on a segment [a,b] is a uniform limit of step functions (f_n), so that the Riemann integrals converge to the Riemann integral of f: [math]\int_a^b f_n(x)dx \underset_{n \to \infty} \int_a^b f(x)dx[/math]. But a sequence of functions that converges uniformly on a segment is uniformly bounded by some constant M. By the dominated convergence theorem, the Lebesgue integrals also converge to the Lebesgue integral of f [math]\int_{[a,b] f_n d\mu \to \int_{[a,b]} f d\mu[/math]. Since the Riemann and Lebesgue integrals agreed on f_n, they also agree on f.
That gives you the result for piecewise continuous functions on segments. You can use that to prove that they also agree for piecewise continuous integrable functions on intervals (that don't have to be closed or bounded).
That tells you that you can pretty much do what you used to do

>>8484573
d^2x/dt^2=dz/dt=dz/dx*dx/dt=dz/dx*z

[eqn]\frac{dz(t)}{dx} = lim_{h \to 0} \frac{z(t+h)-z(t)}{x(t+h)-x(t)}
frac{dz(t)}{dx} = lim_{h \to 0} \frac{z(t+h)-z(t)}{x(t+h)-x(t)} [/eqn]

does this work?

>>8484695
You are taking the limit of the quotients of two functions but not the actual derivative as the argument insdude z, needs to be the same as the the quantitites in the denominator.

>>8481728
Most people I've talked to don't "deny" anything. They'll happily agree that climactic changes are occurring. Their issues are more about that this shift is poorly understood, the cause of it cannot be proven to be primarily human action or more specifically greenhouse emissions, and even if it could there's every reason to believe the environmental prtection measures supported by many in politics will do nothing useful.

That last point is actually one I strongly share with them. We've been burning fossil fuels for over a century, and our output of these emissions only keeps going up and up. If we've already been doing this for so long as to begin the positive feedback loops that lead to climactic collapse as many claim (or at least they did for some time, they may have dropped that one), a couple countries promising to cut emissions is nothing more than a gesture. Even if it was a significant cut in emissions, as in much larger than any of the agreements pledge to, it wouldn't matter so long as shitty, overpopulated developing countries keep churning out emissions like nothing happened.

How do y solve
[math]\frac{d^2x(t)}{dt^2} = x(t) - x(t)^2 [/math]

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Any idea how I would prove the two sides are logical equivalents?

The if and only if is cooning me, tried starting from the righthand side, tried all sorts of wizardry but I am just too stupid.

>>8484807
Looks mighty separable
[math] \ddot{x} = x - x^2 [/math]
[math] \int \frac{\ddot{x}}{x-x^2} \, \mathrm{d} t = t [/math]
[math] \int \frac{1}{x-x^2} \, \mathrm{d} x = t [/math]

>>8484854
cept twice of course.

>>8484854
How you changed from the second line to the third one?

When does a complete bipartite [math]K_{n,m}[/math] graph have a hamiltonian cycle?

I know the requirement when it's just a complete graph with n vertices, but being bipartite probably has some extra criteria I can't figure out.

Hey need a quick refresher on log rules. If I have zlogb(x) - ylogb(n), can that also be written as (z/y)logb(x/n) ? Basically what do I do if I have a coefficient in front?

>>8484902
zlogb(x)-ylogb(n)=logb(x^z)-logb(n^y)=logb(x^z/n^y)

Does Mars experience a greenhouse effect because of the massive amount of CO2 in its atmosphere?

>>8484854
You have two dots on the x though... not sure how you get to the third line

>>8484854
you can integrate it once at least...

x' x'' = x x' - x^2 x'
1/2 (x')^2 = 1/2 x^2 - 1/3 x^3

>>8485185
https://www.wolframalpha.com/input/?i=x%27+%3D+x+sqrt(1+-+2%2F3+x)

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Hey guys, need help with pic related. I got it to where I could show 0/0, but L' Hopital's rule isn't really getting me anywhere.

>>8485212
Let y=1/x. Then the limit equal to
[math] lim_{y\to 0^+} sin(y)/y^{3/2} [/math].

>>8485212
[math] x^{3/2} sin (1/x) = /frac{sin (1/x)}{1/x} x^{1/2} [/math]
first term tends to 1

>>8485212
[math] x^{3/2} sin (1/x) = \frac{sin(1/x)}{1/x} x{1/2} [/math]
first term tends to 1

>>8484888
>>8485178
yeah i fugged up.
It'd be
[eqn] \iint \frac{1}{x-x^2} \, \mathrm{d} x^2 = \int t \, \mathrm{d} t [/eqn]
Which is integrable by partial fractions the first time, and just logarithms the second?
I'm probably missing something for the second integration

>>8484849
Just write a truth table it is enough because there are only finitely many combinations for values with p and q and testing them all is a perfectly good proof.
(And probably the easiest way to do this.)

>>8485076
> Does Mars experience a greenhouse effect because of the massive amount of CO2 in its atmosphere?
But there isn't a massive /amount/ of CO2. There's a massive /proportion/ of CO2 (96%), but it's a massive proportion of a rather small total.

Having said that: anything with (almost) any atmosphere will experience some degree of greenhouse effect.

Most gases absorb long wavelengths more than shorter wavelengths, so they'll absorb more of the radiation coming in than going out, meaning that the surface temperature will be higher than it would be with no atmosphere.

>>8484747
> Their issues are more about that this shift is poorly understood, the cause of it cannot be proven to be primarily human action or more specifically greenhouse emissions
IOW, believing what you wish to believe, and considering any evidence to the contrary as being disputed or unclear.

There are many unknowns in the overall picture, but the greenhouse effect is basic physics, and the rate at which fossil fuels are being (and have been) converted to CO2 is quite well known (the world expends a fair amount of effort in tracking the production, consumption, import, and export of various energy sources).

We know how much CO2 we've been putting into the atmosphere, and we know what effect that has in isolation. Responding with "but our knowledge of climatology isn't 100% complete, there could/might/may be other factors, yadda yadda" is just evasion.