I heard the music as more other-wordly than frightening - though mathematical notation can certainly be intimidating! Right now I'm struggling with a text on numerical analysis,, trying to create practical algorithms from rigorously precise derivations....
Thank you very much, this video let me know more how to calculate error function and how the z-table graph come from. Just want to remind that it is ease to miss the "x" before the summation signal in the final formula at 3:02.
+Alexander Bukk - thanks, I think the intermediate steps are important because it's not always obvious where the algebra will lead you. I don't go into as much detail as blackpenredpen (an excellent channel), but I try to make the thought processes clear.
Wow, thank you. you present a great piece of math. good expaination. I myself need the error function in the context of the mathematics of diffusion, such as instationary heat transfer with the Heavyside boundary condition. yes, modern programs know to evaluate the erf(x). but now i feel better because now i know as well. Thank you for that gift. it must have been very exciting to find this way to solve the problem. Best wishes from oversea.
You're most welcome, and thank you for the kudos! I suppose Taylor series are the basis for a lot of approximation techniques, but I liked the trick of finding a common ratio between successive terms of an infinite series, something I'd picked up many years earlier in a Diff Eq class. Best of luck in your endeavors!
thank you, glad you found it interesting. Nowadays even Excel has an intrinsic erf(x) (though I think they call it something else), but back then we had to roll our own.
I did with python! And your idea to find the r = Ak/Ak-1 was amazing. I did that for sin(x), cos(x) and etc... Look how easy it was: def erf(x): T = 1 Sum = 1 for k in range(1,10000): T = T*(-x**2)*(2*k-1)/(2*k**2+k) Sum += T return Sum*2/pi**0.5
Does anyone know if the first Z tables were made with something like this? I've tried finding a probability from the normal distribution using the error function power series alone, and it was labor-intensive for anything not close to the center. I think there must have been a better way, similar to this.
@@lesnyk255 Thanks. I'll just go with this. Amazing how a calc 2 technique can circumvent such a huge problem. I'm going to do the same thing to use for integral of e^u^2 instead of e^u^2/2 since that seems to be the most prevalent version of erf currently.
Background music is so on point. Math sure is frightening ;)
I heard the music as more other-wordly than frightening - though mathematical notation can certainly be intimidating! Right now I'm struggling with a text on numerical analysis,, trying to create practical algorithms from rigorously precise derivations....
What a background music!
Thank you very much, this video let me know more how to calculate error function and how the z-table graph come from. Just want to remind that it is ease to miss the "x" before the summation signal in the final formula at 3:02.
The content of this video was so great! I realy liked that you didn't skip any of the important steps (teachers always do)
+Alexander Bukk - thanks, I think the intermediate steps are important because it's not always obvious where the algebra will lead you. I don't go into as much detail as blackpenredpen (an excellent channel), but I try to make the thought processes clear.
0:17 Base Definition
3:25 Taylor series formula
4:25 Rk-th formula
6:00 algorithm
What is the music called? It would be great to play while studying.
It's by Tangerine Dream - last slide gives full credit to the band and the recording it was taken from.
Wow, thank you. you present a great piece of math. good expaination. I myself need the error function in the context of the mathematics of diffusion, such as instationary heat transfer with the Heavyside boundary condition. yes, modern programs know to evaluate the erf(x). but now i feel better because now i know as well. Thank you for that gift. it must have been very exciting to find this way to solve the problem. Best wishes from oversea.
You're most welcome, and thank you for the kudos! I suppose Taylor series are the basis for a lot of approximation techniques, but I liked the trick of finding a common ratio between successive terms of an infinite series, something I'd picked up many years earlier in a Diff Eq class. Best of luck in your endeavors!
The music is good. Far better than a lot of the upbeat and distracting crap you find on many other videos.
Man you're amazing and i love this Song!
thank you, glad you found it interesting. Nowadays even Excel has an intrinsic erf(x) (though I think they call it something else), but back then we had to roll our own.
I did with python!
And your idea to find the r = Ak/Ak-1 was amazing.
I did that for sin(x), cos(x) and etc...
Look how easy it was:
def erf(x):
T = 1
Sum = 1
for k in range(1,10000):
T = T*(-x**2)*(2*k-1)/(2*k**2+k)
Sum += T
return Sum*2/pi**0.5
Do you have facebook ?
I found that 10k iterations was more the enough hahaha
The music make you focus intensively THANK YOU
Thank you, that was the intent. It's too bad others who couldn't see that were put off by it.
personal preferences, just that it's the minority who likes it..
Melvin Ang
In my opinion, four or five complaints out of over 2300 views do not constitute an overwhelming majority.
The music was great. Make an abstract algebra playlist with a similar style and I will watch ahaha
Does anyone know if the first Z tables were made with something like this? I've tried finding a probability from the normal distribution using the error function power series alone, and it was labor-intensive for anything not close to the center. I think there must have been a better way, similar to this.
I don't know, but I would guess some kind of numerical integration like Simpson's or quadrature was used
@@lesnyk255 Thanks. I'll just go with this. Amazing how a calc 2 technique can circumvent such a huge problem. I'm going to do the same thing to use for integral of e^u^2 instead of e^u^2/2 since that seems to be the most prevalent version of erf currently.
@@mathnerdaid2770 Yes, e^[(u^2)/2] is pretty specific to the normal distribution in statistics. The version you propose is the general case.
that music though...
What's with the bgm???!!!
Thanks, very nice job!!
What level math is this??
Some calculus (Taylor/MacLaurin series, integration) - mostly algebra
The music omg.
thanks for this, but the BGM......
+Tianshu Ma
Sorry - BGM = ???
sorry, i mean the back ground music is like a horror movie. video is excellent by the way.
I've been waiting for scary face to jump out of screen
apparently this is a solution to my quantum hw problem but I've never heard of the erf func before so wtf.
It figures prominently in statistics, defining the Normal Distribution.
I don't want to use the shitty chart my teacher gave me and this is how I ended up here
The music is so creepy
This is awesome, some good applied mathematics here. This can definitely be used in microcontroller to speed up processing.
thank you!
THANK YOU!