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/sci/ - Science & Math

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6012655 No.6012655 [Reply] [Original]

I'm an expert on calculus. Ask me anything.

>> No.6012656

<span class="math">\rm{ ∫_{0}^{10} x^2(1+sin^2(sinh(e^x))) dx}[/spoiler]

>> No.6012657
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6012657

>>6012655
How do I get a Korean gf?

>> No.6012663

>>6012656
291.667

>>6012657
By learning calculus.

>> No.6012672

Have you ever attempted to a triple integral?

>> No.6012677

>>6012672
My PhD thesis involved research on triple integrals.

>> No.6012678

what's the functional for the wave equation, the diffusion equation, snell's law, and least action principle?

>> No.6012681

>>6012677
Jesus H Bomb, you actually are a expert!

>> No.6012690

>>6012678
The Lagrangian.

>>6012681
Thanks.

>> No.6012695

How do mathematicians justify dividing my zero ( the limit ) ?

>> No.6012699

>>6012690
what's the functional for snell's law?

>> No.6012714

>>6012699

sin(phi)

>> No.6012715

>>6012695
<div class="math">\lim_{x\to0}1/x = \infty </div>
You never approach it from the negative side.

>>6012699
<div class="math">\int_A^B n\,\mathrm{d}s</div>

>> No.6012717

>>6012715
mmm yes...
and now the wave equation and diffusion

>> No.6012745

Any advice for people who want to major in math?

>> No.6012746
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6012746

>>6012655

how do you divide by zero

>> No.6012748

>>6012745
>advice
>don't major i math

>> No.6012755

>>6012717
What wave equation? Classical or quantum mechanical?

>>6012745
Take an IQ test before majoring in math. If your IQ is too low to join mensa, stick with something less ambitious, e.g. a CS major. Math is very competitive and full of child prodigies like myself.

>>6012746
The result is infinity.

>> No.6012758

>>6012755
what's your salary?

>> No.6012760

>>6012755
This is bullshit and bad advice. Major in math if you love it and will work hard.

>> No.6012768

>>6012758
You might of heard /sci/ saying 300k starting. This is wrong. My starting salary was 500k.

>> No.6012773

please stop shitposting

>> No.6012774

>>6012768
ah ok, you are a master trole

>> No.6012780

>>6012656
How the hell would you even maneuver around that?

>> No.6012784

What is math?

>> No.6012786

>>6012773
>>6012774
What makes you say something like that? Are you trying to hurt my feelings?

>>6012780
It can be solved with techniques only understood by PhDs.

>> No.6012787

>>6012784
Math is a human invention. Often you see people saying math was discovered and not invented. This is wrong. For example imaginary numbers do not exist in nature.

>> No.6012788

>>6012755
classical
what the hell is the quantum one?

>> No.6012795

Are you doing your postdoc in calculus?

What do you see as the next big breakthrough in calculus?

>> No.6012796

>>6012788
Schrodinger equation is the quantum wave equation.

>> No.6012799

>>6012755
OR NEGATIVE!

>> No.6012801

>>6012788
The Lagrangian is
<div class="math">\mathcal{L}(x,t,f(x,t)) = c^2\left(\frac{\partial f}{\partial t}\right)^2-\left(\frac{\partial f}{\partial x}\right)^2</div>

>what the hell is the quantum one?
The Schrodinger equation.

>> No.6012806

>>6012787
what is an imaginary number?

>> No.6012807

>>6012788
you might have been referring to any of the various wave equations used to determine the wavefunction- the simplest of which is Schroedinger's. I'm not OP btw.

>> No.6012812

>>6012787

Numbers of what don't exist in nature?

I

>> No.6012814

>>6012806
When mathematicians use letters like x in equations they are imagining x is a number. So x is a imaginary number.

>> No.6012815

>>6012795
>Are you doing your postdoc in calculus?
After publishing my PhD thesis in calculus I am now doing research in trigonometry.

>What do you see as the next big breakthrough in calculus?
Triple integrals are one of the big unsolved problems. Personally I don't believe we will see a solution within this century. The next big breakthrough could be finding the derivative of e^x.

>>6012799
By convention the solution is defined to be positive. Think of square roots which are also defined to be positive.

>> No.6012820

>>6012815
>research in trigonometry
lel

>> No.6012829

>>6012806
Imaginary numbers are a very controversial idea and I would even call them crackpottery. Advocates of imaginery numbers claim they can square root negative numbers. That sounds ridiculous, doesn't it? What they don't want to see is that they are paying the price of having to break several axioms of math. Many mathematicians - including myself - do not believe that imaginary numbers will lead to any practical applications.

>> No.6012835

>>6012663
>291

Except the integral is clearly bounded between 333.333... and 666

>>6012780
pray you can find a good enough series expansion

>> No.6012843

>>6012786
You're not just trolling right? Like that would be solvable with very high level mathematics?

Because I often sit around racking my brain because I can't figure out some antiderivatives only to find out they don't have elementary solutions

>> No.6012850

>>6012656
464

>> No.6012852 [DELETED] 

>>6012829
actually, now that I think about it. Imaginary numbers make sense.

>> No.6012856

>>6012773

Please stop shiptoasting.

>> No.6012857

>>6012843
lmao

>> No.6012863

General question for /sci/ in particular the Calculus phd. What are beautiful problems of this branch of mathematics? I recently learned about the problem posed by bernoulli, the curve of most rapid descent. It's quite sweet, are there other problems like this one? I guess maybe catenary curve, or the tautochrone are similar challenges.

>> No.6012864

>>6012801
yeah that's the one.
thanks :)

>> No.6012868

>>6012655
I've just started a calculus course, why would my professor not teach the class about derivatives? Why would this not be the very first god-damned thing she would mention?

>> No.6012869

so the diffusion one is
<span class="math">
\mathcal{L}(x,t,f(x,t)) = \left(\frac{\partial f}{\partial t}\right)^2+\left(\frac{\partial f}{\partial x}\right)^2
[/spoiler]
right?

>> No.6012871

>>6012868

Maybe you need a refreshment on functioms.

>> No.6012879

would you rather fight five duck sized horses or one duck size horse?

>> No.6012881

>>6012843
Did you utterly fail calculus 1 or something? sin^2(x) is bounded by 0 and 1 so the integral must be bounded by 10^3/3 and 2*10^3/3 so his answer is absolutely wrong. The correct answer seems to be exactly 500 but no one will be able to prove it

>> No.6012882

>>6012871
Fuck me, it's been a year and a half since pre-calc where some half dead old man bullshit his way through teaching the course. I couldn't agree more.

>> No.6012883

>>6012879

Shirley you mean one horse sized duck,

>> No.6012888

>>6012868
Well first she has to define and prove standard results of |R and it's axioms, sequences, convergence, limits, series, and metric spaces beforehand

>> No.6012889

>>6012883
I did.
and don't call me Shirley

>> No.6012892

>>6012879
>5 duck sized horses
>1 duck sized horse

Top lel

>> No.6012895

WHAT IS -1* i?

>> No.6012896

OP, why is the navier stokes equation hard?

>> No.6012910

>>6012829
This

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>> No.6012912

>>6012895
i

>> No.6012916

>>6012912
so i=invinciple

>> No.6012918

>>6012768
lul

>> No.6012929

>>6012910
yeah but now I can build a segway.
You can do it without imaginary numbers.
But it's much easier if you do it with.

>> No.6012930

Where do you fall on the spectrum?

>> No.6012937

>>6012930

I'm neurotypical.
I'm not OP.
But I knew you would want to know.

>> No.6012942

What online resource is best for telling a 15 year old mate of mine who wants to learn calculus??

>> No.6012944

>>6012942
Don't settle for anything less than Walter Rudin.

>> No.6012945

>>6012930
Not OP, but I have aspergers.

>> No.6012954

>>6012944
Which one of his books?
Also since im poorfag, how would I be able to obtain it for free?

>> No.6012958

>>6012954
Tbh if you're "mate" is worth a shit he should be able to derive all the important theorems from first order logic after constructing the real numbers and developing some set theory on the toilet.

>> No.6012980

are there any known applications for quadruple integrals (and higher)?

>> No.6012985

>>6012980
Quadruple Integrals represent the fabric of the universe; Quintuple Integrals represent the phenomenological structures of consciousness, which, according to modern Quantum Theory, are the core of reality.

>> No.6012988

>>6012985
neat

>> No.6013010

>>6012985
Bullshit.

>> No.6013011

>>6012954
gen.lib.rus.ec

>> No.6013015

>>6013010
>The solution to ∫∫∫∫∫e^x dx, which has eluded the greatest mathematical minds - from Euclid, to Euler, to David Ickes - likely contains buried deep within it the secret to consciousness itself.

>> No.6013022

>>6013015
> secret to consciousness
I believe it!

>> No.6013031

>>6013011
Thankyou anon

>> No.6013867

>>6013010
lul

>> No.6014201

>>6012715
>You never approach it from the negative side.
Can this be applied to women as well?

>> No.6014217

>>6012815
>triple integrals
>unsolved

>derivative of e^x

I know it's pretty much established by now that OP is master ruseman, but I'm honestly surprised no one else responded to this.

Personally, I lol'ed.

>> No.6014224

How hard is calculus?

>> No.6014228

>>6014224
Hard as my dick.

And spans a similar function space.

>> No.6015816

>>6012829
>dismissing imaginary numbers
>PhD in calculus
>choose one
>2013
ISHYGDDT

>> No.6015822

>>6012888

what the fuck for though, nobody, literally nobody gives a shit about these. fucking set theory and algebra and all that shit was the biggest waste of tuition ever.

>> No.6015827

>>6012829

oh ye? what the fuck is impendance plz
wtf are vectors plz
wtf are polar coordinates plz
what the fuck is arccos 5 pls
wtf is geometry plz
wtf is physics in general plz

>> No.6015842

An infinite number of mathematicians walk into a bar. The first mathematician asks the bar-man to give him a beer, the second one asks for half that, the third one asks for half that, and so on.

The barman pulls two beers and says. "Hey, now, know your limits."

>> No.6015852

>>6012829
https://en.wikipedia.org/wiki/Imaginary_number#Applications_of_imaginary_numbers

>> No.6015860

>>6012814
No.

>> No.6015868

>>6012656

It's 5.

>> No.6015873

>>6012829

Quaternions are very practical.
Do you have any idea how much they've contributed to flight simulators? Transitioning across spheres? Go learn some more.

>> No.6015877

>>6015842
Heh

>> No.6015880

>>6015873

yeah it solves the gimble lock problem
without quaternions (they are damn awesome) we'd be stuck with the clusterfuck that is the Euclidean system. You wouldn't be able to so much as rotate about an arbitrary angle an arbitrary amount.

>> No.6015882

>>6015852

>wikipedia

Nice try dumb ass.

>> No.6015888

Why does calculus work?

>> No.6015890

>>6015880

nigger that's not even true. they were only a problem with shitty programming. vector calculus has an answer that doesn't use imaginary bullshit

>> No.6015899

>>6015890

They both achieve the same thing. Quaternions happen to do it faster.
It's not bullshit. There is a theorem and it is very practical. You're in denial because you don't -want- it to be true because you have a hard time comprehending it, whether because you don't like the concept or whatever.
The idea of negative numbers is also bullshit to most people. You can't have -4 apples. But I don't see you complaining about it. It's the concept that can allow pragmatics, following principles. Similarly square roots of negatives may seem evenly lunatic at first. But it has real useful applications. I learned a lot from them and I learned to love imaginary numbers and the possibilities it entails. Maybe if more mathematicians accepted the idea, we might even solve things such as dark matter.

>> No.6015903

>>6012656
slightly less than 500
<span class="math">
\int_{0}^{10} x^2(1+sin^2(sinh(e^x))) dx \approx \int_0^{10} x^2(1+0.5) dx
[/spoiler]
because the average of sin^2 over one period is 0.5 and sinh(e^10) = 2*pi*shitload, even for x>2 the contribution is negligible

>> No.6015913

>>6015890
Quaternions are actively used for point transformations as well. In both DirectX and OGL, they are graphics and mathematical libraries. You can also have a quaternion-based camera. It's very common to use because it allows a level of freedom that is beyond just solving the gimble lock problem and rotating about an arbitrary vector. It allows for interpolation, sphere transitioning, slerping, and more. It has the same properties as a normal 3d vector but with a 4th element and the application of complex algebra. You cannot call such practical and useful math "bullshit".

>> No.6015917

How do the Cauchy-Riemann equations change on hyperbolic geometry?

>> No.6015922

>>6015917

There are (at least) five models, each with its own metric.

I'm not OP.
I just knows a bit about non-euclidean shit.

>> No.6015924

>>6015842
>first mathematician drinks his beer
>all the other have to share a glass
according to an urban myth, the last sip from a 1liter bottle contains 50% spit
assuming a 25ml sip, a 1l glass (a german beer glass) and assuming that the mathematicians will drink exactly as much beer (not liquid!) as they ordered...
>mathematicians M2 to M6 quickly drain the glass
>M7 to M10 hunt down the last droplets of beer
>in search of the final beer molecules M11 and onwards exchange spit between each other

>> No.6015927

I have a problem understanding the whole concept of lim.
This due to the fact that we started using english written books and I have a hard time understanding some of the technical terms.

Just as an example(an exercise from my book):

f(x)=2x^2-5, find the equation of the straight line tangent at (2,3)

How do I proceed? A kind of step by step would be helpful.

>> No.6015935

>>6015927

Think of a limit as "what a number should be if it were to exist in a function".

For example, limit of (x-1)/(x-1) at x=1 is y=1. Graph it, and there's a discontinuity at x=1. We use L'Hopitel's rule to assert that the answer is its own derivative.

>> No.6015938

>>6015935
Also, I never quite got this confirmed; But isn't lim much the same as derivating functions?

>> No.6015944 [DELETED] 

how do I translate the graph y=1-(1/2x) to the right one x?

>> No.6015947 [DELETED] 

>>6015944
substitute the x for (x-1)?

>> No.6015950
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6015950

>>6015938

No. We use limits to derive them.
Derivatives are defined like so...

lim as x -> 0 : ( f( x + c ) - f( x ) ) / ( ( x + c ) - x )

The denominator cancels the x and -x out, so you're left with C. As such, you cannot divide by zero. But it approaches a certain number.

To be abstract, look at pic what formula does. It finds the slope as the function changes. Like (y2 - y1) / (x2 - x1). Refer to pic. It allows it to work on curvy functions.
With this formula of the limit differential, we discovered shortcuts such as the power rule.

>> No.6015951

>>6015950

Woops, sorry. That was a mistake.
The correct formula is as c -> 0, not x -> 0

>> No.6015953 [DELETED] 

>>6015947
>>6015944
no, the whole thing minus 1

>> No.6016328

>>6012755
>the result is infinity

2/10 jesus fucking christ