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There are certain theorems which I learned earlier in my mathematical education (especially in Calculus 3) which I was able to calculate well, but to which I never truly understood the real world applications. The applications that were presented in my lecture were unclear to say the least and the textbook that we had was rarely sourced.
The theorem that I had the most trouble visualizing real applications for was Green's Theorem (as well as some others).
I am past Calculus 3 now, but I've always been interested in fully understanding that which I feel I should know. Can anyone provide a real world application or at least some clarification on how Green's Theorem can be utilized?
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Every once in awhile, Green's Theorem pops up at least conceptually for conservative fields like gravity. In that case, the right-hand side of the equation goes to zero. Kind of explains the path-independent nature of work and of potential energy. Never actually used it to solve problems.
Green's theorem is related at least tangentially to Navier-Stokes, which is important for continuum mechanics.
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>>8422052
OP here
I do remember Green's theorem being related to Stokes but I also remember Stokes being way easier and straightforward to use than Green's theorem.
So Green's can pop up here and there in the terms of gravitational theory, huh, thanks for letting me know.
I also heard from my professor that if one was to pour some fluid over a surface and you knew the equation of the surface and the initial conditions, then greens theorem could theoretically tell you the direction and magnitude(velocity?) of every particle in the fluid.
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Not sure if green functions are the same thing as green theorem but if it is, then its used in many-body quantum physics(perturbation theory). In general GF shows probability amplitude for particle to move from point x1 at time t1 to point x2 at time t2. Theres much more about it but im too lazy to explain.
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Why do balloons pop when punctured?
Why don't they just shoot around like when they're untied?
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kill yourself
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>>8421514
Balloons are basically just spherical rubber bands. When their structure is compromised, they "snap" the same way a rubber band does, but in a sphere, because balloons are just spherical fucking rubber bands. This is because balloons - spherical rubber bands - distribute their tension in a sphere instead of straight lines. Just like a spherical rubber band would. Because balloons are spherical rubber bands.
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>>8421532
This plus the fact that the material is unable to withstand the tearing forces. The mouth of the balloon is reinforced. A punctured area won't be reinforced. You may be able to puncture the neck of the balloon without it exploding since it is also partially reinforced, though less than the mouth.
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>We did it, we found Gravitaional Waves
Are these niggas serious?
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There's no such thing as gravity waves or the graviton.
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>>8421310
Have fun burger flipping.
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>>8421309
No, they're just shilling for the global conspiracy for a round earth.
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Light (apparently) bends because the line A and B must keep their distance maintained at all times.
Someone fucking explain what this means? I just want to understand and no one gives a good answer.
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Pls answer, I hope someone here is smart enough to explain.
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Come on.. anyone know???
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I can't even bump the thread?
Oldfag here again
Taking calc2 in the spring after 8 year hiatus from school need halp.
Where did they get "a" from? I know it something super easy but I just can't figure it out. How did they get a?
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>>8421216
do your own homework. This board has rules against shitposting to beg for smart people to teach you.
More constructive advice would be to go to your TA or professor office hours to have them give you real help.
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>>8421216
a=1 because x^2=(1)(x^2)
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Most recent Mathematical/Scientific problem that you solved?
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you wont scoop me that easily
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bow down
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>>8421117
calulating the net impulserate of a thorium .."glow sock"? is that what you call'em in english?
is that what you were going for OP?
either my IQ is too low to calculate this or I just don't know enough mathematical tools to figure this out. i hope someone can help.
here is the problem:
assume that you are investing in something, and you're using a high risk high reward strategy.
- you are investing your entire account every trial.
- you have a 70% chance of gaining 20% of your account, and 30% chance to lose 30% of your account for every trial.
as you can see, these probabilities and gains/losses will eventually be guaranteed (99%+) to make net profits with increasing trials (n)
however, it is risky in the short term with little number of trials if you don't want your account go below a certain value compared to the initial amount.
so in the early stages, by lowering the amount of money you invest each time, you should be able to decrease your chance of going below the value you don't want to go below, by increasing the number of failed trials it would take to achieve that, meaning an increase in n. therefore this should give you higher chance of success in the long run.
so how dafuq do you do this? how do you judge how much money to invest with to give yourself the best chance in the long term?
i know "best chance" is subjective, so lets define it.
for example if i want my account to be above 0.8* of its intial value at any time with about 85% probability, how should i go about lowering the % of my account that i invest with, while maximizing the potential profits at the same time?
formula for net profit (% of initial account) = 1.2^x * 0.7^(n-x)
x being number of successful trials
n being total number of trials
you can see here: >>8420308
formula to figure out x, in the form of A = B^x * C^(n-x):
x = [n * LogB(C) - LogB(A)] / [LogB(C) - 1]
Please be gentle, I don't know much math. Wtf is this stuff called anyways? Do people in finance schools study this sort of stuff?
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I forgot to mention binomial distribution is also heavily involved in this problem. Just a reminder
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>>8420985
Let's take a step back.
You repeat a random process that has 2 possible outcomes, A and B.
If A happens with probability N, and B with probability 1-N, how are the following things connected: number of repeats, A, B, and N?
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>>8421027
Are you asking me a question or giving a hint?
you can use cumulative binomial distribution formula to tell you the cumulative probability of >=# of A resulting from N and number of repeats.
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What is the speed of thought?
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>>8420915
It depends on IQ
Intellegent people like me can think faster than the speed of light.
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>>8420915
Strictly less than that of shitposting.
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>>8420915
electron speed
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FIVE HUNDRED DEGREES CELSIUS
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>>8420903
amazing thread bro. im so science rite now
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>>8420903
You got a problem with that?
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>>8420903
Five hundred is also the number cocks ur mom sucked while you were a fetus.
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>medicine is applied biology is applied biochemistry is applied chemistry is applied physics
If medicine is so easy, why didn't you go to medical school and go into one of the many specialties were you make a literal $300k starting, instead of living off a $25,000 grant to publish papers on some dumb shit nobody but the one other autist researching the same garbage cares about?
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>>8420661
You sound angry. Which med school did you fail out of or get denied from?
Also the reason why not many people decide to become Medical Doctors even if they could become one is because it doesn't interest them or they don't feel the costs outweigh the benefits.
>4 years undergrad
>4 years of med school
>1 year internship
>2 years residency
>70+ hour work weeks until that's all done
Same reason why people who'd make good EMT's don't do it. Friend is a great EMT but fucking hates doing it for these reasons.
>No benefits
>Shit pay
>Half of the people you try to help hate you for it
>DOA's
>Having to watch people die in your arms constantly
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>>8420688
>>DOA's
>>Having to watch people die in your arms constantly
Sounds like an easy work day, would not complain.
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>>8420661
Because no amount of money will ever make up for the 10 years lost in the meat grinder that is med school and the residencies that follow where you're literally a slave.
Also because some people have greater intellectual ambitions than shoving tubes up some old man's arse.
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>mathematician arbitrarily chose the expected value, E[X] of a given probability distribution X:S-> R to be the sum of all (value_i - mean)^2 times p_i because it is convenient to work with.
how is this allowed? Why not just take the absolute value of it instead of squaring it
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>>8420658
>derivative of |x| is a fun thing to work with
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>>8420660
it is true tho, how the fuck do you interpret the currently accepted E[X] in words? The squaring removes any meaning from it
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That's a very strange definition you have there. Pretty sure you mixed something up.
Reference?
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why are astrophysicists such hippies?
http://www.nature.com/news/the-scientists-who-support-donald-trump-1.20827
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>>8420551
so, the brainlets (economists, engineers) tend to have more conservative views (albeit still liberal in majority)? Interesting to see actual proof, but not surprising.
I don't even know why they include sociology though, embarrassing.
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>>8420565
>economists and engineers are brainlets
>not sociologists
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>>8420565
It's the differential equations. Mathematicians have the same pattern.
In response to my previous post offering advice to aspiring economists, a student emails me:
>Since the time allocation is limited, I can take only some math courses and the problem is that I am not sure which courses are most important for a successful economist and which course I should take first. Can you possibly suggest for me a list of math courses that a typical economics student should take step by step?
Here is one plan of action:
Calculus
Linear Algebra
Multivariable Calculus
Real Analysis
Probability Theory
Mathematical Statistics
Game Theory
Differential Equations
Note the differential equations
There is, of course, some flexibility about the order of courses, but you can absolutely not skip the differential equations. Differential equations separate economists from Marxist sociologists who suck dick. Check the prerequisites at your school to figure out the right sequencing.
Let me also recommend a book if you need a crash course for catch up or review: Principles of Mathematical Analysis, by Walther Rudin.
Greg Mankiw at 5:38 AM
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How do we take back race realism from /pol/? Surely we need a better representative then people who will dismiss the all scientific knowledge and other advancements of the west that doesn't fit their narrative as jewish and call you a ctr shill when you come up with an argument they can't oppose. So what do we do /sci/?
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Why even bother? No one takes that board seriously and even /b/ considers them cancer. There is literally nothing to gain by investing time and energy into that tumor.
You wouldn't invest time and energy in arguing with a down syndrome victim, would you?
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>>8420375
Butthurt BLM copkiller spotted. Why don't you run back to your twitter and cry about muh oppression some more ?
>even /b/ considers them cancer.
a board that uses the N word as much as saying "hi" considers /pol/ cancer? AHAHAHAHAHAHAHHA. you retards are alone in your hilarious dindu nuffin mindset.
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>>8420375
There are many nuggets of truth in pol if you can sift through all the shit.
How do you solve this?
Actually it's not homework, I need it for work. I tried looking up rules for logarithm/exponent equations but got nothing related to this
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>>8420308
This is a solution. It may not be unique though.
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>>8420308
0.7^k = 1.2
k = log 1.2 / log 0.7
(0.7^kx)*(0.7^10-x)
0.7^kx+10-x
0.7^x(k-1)+10 = 1
x(k-1)+10 = 0
x(k-1) = -10
x = -10/(k-1)
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>>8420318
>It may not be unique though.
Each value appears only once on an exponential curve, unless you include complex numbers.
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Is play something unique to mammals?
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>>8420300
Unique to Humans. The rest is anthropomorphism.
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>>8420300
It seems like mammals are the only animals born without all of their necessary survival skills hardwired in instinct, creating the need to play to develop coordination and stuff. And the evolutionarily least efficient animals are the only ones that evolved intelligent life
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>>8420306
You don't think what baby non-human mammals do could be called playing? Because it looks like they all play a lot, while a baby reptile or something never does that