Can we get a whole playlist dedicated to eliptic functions and eliptic integrals? It's such an interesting theme! I'd love to see more videos about that.
For those who are interested, elliptic integrals form the foundation of Hodge theory developed by Phillip Griffiths (he has a lecture on the subject here on RUclips which discusses elliptic integrals) which I highly recommend.
Finally got an idea how to look at elliptical integrals of the first kindy thanks! I also enjoy seeing the var thetas, the way you write them is just a little from being the theta you refer to tho 😆 the right part goes up to the height of an f before making a loop ϑ
The incomplete elliptic integral F(φ; k) is very similar, but the integral goes from 0 to φ instead of 0 to π/2, which woukd complicate the coefficients of the series expansion quite significantly, but calculating them is still doable.
11:13 Why not play mathematician and say "monotone convergence theorem"? All the terms in the sum are positive, so regardless whether the integral is finite or not you can exchange summation and integral
I couldn't understand. Can we change the sigma with integration symbol? Or why other terms than the sinus popped out and sinus remained? Isn't the sine term in the summation? so how can we separate it from the sum?
@@ugursoydan8187 The sinus is still in the sumation. It is just integrated first. The other symbols are constant in relation to θ so they can be brought outside of the integration. In short everything including the integration is summed.
you should do a video on the arithmetic-geometric mean, the details sound nerdy. also, it might be a more efficient way to calculate values of the function (i dont code)
I'd like to see a simulation with the exact solution versus the approximate (sin x =x) for large values of x. How fast do they diverge? At what angle of x? What are the differnces in behavior predicted?
Me: *OMG the title contains the word elliptic* Also me: *OMG FML THM proof by A. Wiles memories strike me again* Also, also, nice Dream reference, papa Minecraft Maths 2021 confirmed? :D
When doing the series extension at the start, you used that the inner derivative of (1-x)^... was -1. But when replacing x by k_2n*sin^2n(v), you didn't change this. Did you screw up bigtime or am I stupid?
Why beta , reduction derived by parts should be enough With reduction we should get I_{n}=(2n-1)/(2n)I_{n-1} I_{0}=pi/2 I_{n}=\frac{1}{4^{n}}\cdot (2n \choose n) \cdot \frac{\pi}{2}
Complete elliptic integral of the SECOND kind www.ams.org/notices/201208/rtx120801094p.pdf which gives you the perimeter of an ellipse using the AGM method (Arithmetic-Geometric Mean) and a modified AGM method.
try this: closed form solution of the elliptic integral of first kind: Integrate (1 + v sin^2(x))^(-1/2) dx = 2 csc^2(x) sqrt(v sin^2(x) + 1), make sure the v-value is negative
try this: closed form solution of the elliptic integral of second kind: Integral of sqrt(1+c*sin^2(x) ] dz = (2/3)*csc^2(x)*(c*sin^2(x)+1)^(3/2), just make sure the c-variable is negative, c=-k^2
hey pappa flemmy, since when is computing a period considered solving motion equations? like it might be, I dont know what are physicists interested in. But I would like to have some sort of formula for phi, don't care about T
When talking about periodic motion, it makes sense to talk about the periods, which is something easily measurable. In this case, T is constant whereas phi is not. But the formula he obtained concerns T and phi, so it is a valid way to express the solution. If you want the formula for phi, you need the inverse elliptic function.
@@ugursoydan8187 The integrands are positive measurable functions in their domain. Thus the partial sums form an increasing sequence of measurable functions, and the theorem applies.
Isee a double factorial being divided by a factorial AND a power of two? This is unacceptable. I will replace (2k-1)!! With (2k-1)!/(2^(k-1) * (k-1)!) And so we actually get something like (2k-1 choose k)/2^(2k-1) which is really interesting.
could you present your sponsor at the end of the video please? Because there are so many people that are watching only the beginning of your video and they leave as you start talking about your sponsor. I really like your channel and I don't want youtube algorithm not to suggest your videos just because you have little watchtime.
I heard this nonsense for 2:40. I see k(k) = ... But on the right hand side I see no k. I see something that looks like an eliptic integral but wrong and I see a Mandelbrot Iteration. My question: Is this an engeneer using AI?
I like that papa spent orders of magnitude more time explaining that 1= 2(½) than he did to explain that \Gamma(1/2) = \sqrt pi 😂
papa forgot the squares when doing the coefficients of the series, papa made a booboo
Peepeepoopoo moment
;_;
big booboo.
Tôi cũng thấy quên đạo hàm sin^2(x)
the board making noises because its excited as i am seeing some spicy Elliptical "integaral "
:D
when papa says integrül fhom ziro tu infiniti (even tho there's no integral like this in this video) my heart melts
:D
@@PapaFlammy69 Quack
Can we get a whole playlist dedicated to eliptic functions and eliptic integrals? It's such an interesting theme! I'd love to see more videos about that.
Cette homme est full of motivation , incroyable !
Continue de nous partager ces petites merveilles du monde des maths !
Amazingggggg, I've been waiting for this video for soooo long! Thank you papa.
amazing, we just did this in theoretical mechanics and I didn't understand anything :D
Thanks for elaborating on this, papa
I have no clue what's going on but I just keep watching anyway
Life is great :)
that background of fractals is looking beautiful
> nice approx even with early truncation
Engies: "this new tool is a blessing to our kind"
I'm only in first year and u explained this so well I can do it all!! You're great thank you for making videos:)
Thanks for solving the DE I asked some time ago without small angle approximation
Can’t wait for advent calendar!
:)
For those who are interested, elliptic integrals form the foundation of Hodge theory developed by Phillip Griffiths (he has a lecture on the subject here on RUclips which discusses elliptic integrals) which I highly recommend.
It’s been a while since I’ve used a series expansion for integration. Very nice
"just some elementary operations you can do in your first year of university" right :P I'll keep playing physicist *grumbles*
You probably won't see this until second year maths at university.
Finally got an idea how to look at elliptical integrals of the first kindy thanks!
I also enjoy seeing the var thetas, the way you write them is just a little from being the theta you refer to tho 😆 the right part goes up to the height of an f before making a loop ϑ
You forgot to square the coefficients in the very end =(
oh shit, you are right!!
Thanks, I thought I was going insane...
The incomplete elliptic integral F(φ; k) is very similar, but the integral goes from 0 to φ instead of 0 to π/2, which woukd complicate the coefficients of the series expansion quite significantly, but calculating them is still doable.
beautiful derivation. thanks
Wow. You're the most awesome man in the world for doing this.
"Why be right when you can approximate?" - engineer
"Because I am a "pure engineer"! " -
ngl slightly triggered by the "it's" in the title
What a coincidence, I was just working on some electrostatics and the elliptical integral came up when I was calculating potentials!
11:13 Why not play mathematician and say "monotone convergence theorem"? All the terms in the sum are positive, so regardless whether the integral is finite or not you can exchange summation and integral
oh you are right! =)
I couldn't understand. Can we change the sigma with integration symbol? Or why other terms than the sinus popped out and sinus remained? Isn't the sine term in the summation? so how can we separate it from the sum?
@@ugursoydan8187 The sinus is still in the sumation. It is just integrated first. The other symbols are constant in relation to θ so they can be brought outside of the integration. In short everything including the integration is summed.
This is actually so cool
Eventually papas intro will only be heard by bats
More elliptical integrals please!
Hey you missed the squares on the double factorials at the expansion at the end. Great stuff tho.
Ye, noticed that an hours ago too hehe ^^' As long as the final expression was right, then that should be fine though :)
you should do a video on the arithmetic-geometric mean, the details sound nerdy.
also, it might be a more efficient way to calculate values of the function (i dont code)
Yes, the connection between elliptic integrals and the AGM is super cool (and leads to deep insights on the non-linear pendulum)
Math so powerful it tears the blackboard apart.
Amazing
This guy is good.
I WANT MORE ELLIPTIC INTEGRAL VIDEOS.
Yooo papa flammy bro I just got the engineering clock in the mail finally ITS SICK
I tried explaining to my mom what everything meant now she thinks I’m retarded
Omfg, finally!!!! So glad it finally arrived;_;
xDDD
I'd like to see a simulation with the exact solution versus the approximate (sin x =x) for large values of x.
How fast do they diverge? At what angle of x? What are the differnces in behavior predicted?
I just don't understand anything, but it's beautiful, and that's enough 👁️👄👁️🤟
amazing
I hope your students also call you Papa Flammy while you slide around the classroom.
Those dark circles are do deep that when light hits them it achieves null completeness.
good explanation. does it have logarithmic singularity when k=1?
First semester physics prof: “we will assume sin(x) ~ x in this case”
Me: “wtf why, just do it exactly”
Me after watching this video: “Fair point.”
I hope that those weird sounds from your chalkboard wasn't the result of abuse!
Snecc's abuse!
Great video!😎
Woow! Great Job. Thanks to You 🙂
yes Papa flammy
Where did you get that shirt, that is amazing! haha
All the merch can be found over on stemerch.com/collections/why-be-right-when-you-can-approximate :)
You made a mistake at 15:15 2(n+1/2)=/= (2n+1)/2 but 2(n+1)/2
Great video either way
Papa will u do some videos with incomplete gamma function?
@12:00 wouldn't it have been easier to evaluate the Wallis integral the usual way with integration by parts and develop a recursive formula?
So who wants to break his heart and let him know that his Upsilons aren't Thetas?
24:28 Aren't the squares missing on the fractions you are writing here?
Me: *OMG the title contains the word elliptic*
Also me: *OMG FML THM proof by A. Wiles memories strike me again*
Also, also, nice Dream reference, papa Minecraft Maths 2021 confirmed? :D
When doing the series extension at the start, you used that the inner derivative of (1-x)^... was -1. But when replacing x by k_2n*sin^2n(v), you didn't change this.
Did you screw up bigtime or am I stupid?
Nope. He can do this. Theres no need to derribate again.
Content starts at 4:40 btw
Why beta , reduction derived by parts should be enough
With reduction we should get
I_{n}=(2n-1)/(2n)I_{n-1}
I_{0}=pi/2
I_{n}=\frac{1}{4^{n}}\cdot (2n \choose n) \cdot \frac{\pi}{2}
Oh finally, the monster integrals is back again, but papa flammy, does this integral flamming the internet? Or just for entire math vision? :^)
Complete elliptic integral of the SECOND kind www.ams.org/notices/201208/rtx120801094p.pdf which gives you the perimeter of an ellipse using the AGM method (Arithmetic-Geometric Mean) and a modified AGM method.
17:12 isnt it supposed to be n instead of k in the double factorial
try this: closed form solution of the elliptic integral of first kind: Integrate (1 + v sin^2(x))^(-1/2) dx = 2 csc^2(x) sqrt(v sin^2(x) + 1), make sure the v-value is negative
try this: closed form solution of the elliptic integral of second kind: Integral of sqrt(1+c*sin^2(x) ] dz = (2/3)*csc^2(x)*(c*sin^2(x)+1)^(3/2), just make sure the c-variable is negative, c=-k^2
make some good use out of those, and the derivative matches directly
talking is overrated, skill is underrated
have you ever plotted the elliptic integral inside function, the sqrt(1-c*sin(x)^2) stuff
Nice video, you forgot to square the terms in front of the k's though in the final answer
hey pappa flemmy, since when is computing a period considered solving motion equations? like it might be, I dont know what are physicists interested in. But I would like to have some sort of formula for phi, don't care about T
When talking about periodic motion, it makes sense to talk about the periods, which is something easily measurable. In this case, T is constant whereas phi is not. But the formula he obtained concerns T and phi, so it is a valid way to express the solution. If you want the formula for phi, you need the inverse elliptic function.
So, now RUclips shows ads on videos with paid promotion?
WOOOOOOOOWWWW!!!!!
That Mandelbrot set is kinda hot ngl
Everything okay, just in the end you didn't square the factorials to get the numbers!
Are you alright? That crashing in the beginning was prolly a bit wonky lol
11:54 why sin^2n(v) left from the sum?
You can change the integral sign with the sum using the monotone convergence theorem, no phycisist required ;)
how can it be? why is that correct?
@@ugursoydan8187 The integrands are positive measurable functions in their domain. Thus the partial sums form an increasing sequence of measurable functions, and the theorem applies.
@@juanpabloc.4002 Not always
@@gytoser801 in this case it does.
Bravo génial
arithmetic-geometric mean formula for the elliptic integral pls papa
"just some first year elementary operations"
bro i took intermediate algebra my first year of college
Why is it called an elliptic integral?
When are we able to interchange the integral with an infinite series?
Whenever the dominated convergence theorem applies.
I wanna be like you! 😖❤️❤️❤️
no show the AGM convergence property
8:04 quick maths
In the last step you forgot to square the numbers in the denominator.
imagine how the world would look like if we instead had 1/gamma and half of that stuff canceled...
can i request for ur next video, why 1>0? xD
The squeaking board... yeah you might want to ask an engineer for help with that. ;)
I see you've heard of Dream hahhah
wat?
Please tell me the application of elliptic integration in civil engineering
16:14 Beta function not need to divide by 2, factoria(1/2)=sqrt(Pi)/2.
mathworld.wolfram.com/BetaFunction.html
Sorry, confusion between factorial and gama function :)
omg i've never been this early haha
Isee a double factorial being divided by a factorial AND a power of two? This is unacceptable. I will replace (2k-1)!! With (2k-1)!/(2^(k-1) * (k-1)!) And so we actually get something like (2k-1 choose k)/2^(2k-1) which is really interesting.
:)
could you present your sponsor at the end of the video please? Because there are so many people that are watching only the beginning of your video and they leave as you start talking about your sponsor. I really like your channel and I don't want youtube algorithm not to suggest your videos just because you have little watchtime.
I would love to!!! But sadly, most sponsors require me to say the message during the first 4min of the video :(
@@PapaFlammy69 ahh i get it, sorry. And you can't say at the beginning you're going to say a longer message at the end neither, I guess
Hello maths boi's 👋👋🤘
AYE
22:20 2 times 2 times 2 does not make 4 haha
Of course it has no sense to do an exact value if an approximate one can do the job. It would be a waste of time.
π Pa
24.999999
papa flam do u have a discord server i wanna post shit engi memes
si-(t)
First?
2nd
corverge slow no fun
I heard this nonsense for 2:40.
I see
k(k) = ...
But on the right hand side I see no k.
I see something that looks like an eliptic integral but wrong and I see a Mandelbrot Iteration.
My question: Is this an engeneer using AI?