Thank you for explaining where this came from, other videos simply chuck this formula at you and doesn't explain why you use it and just take it for granted.
This was absolutely perfect. I understood how to use Simpson's Rule but, until this video, I couldn't understand how we could possibly take the area under a curve by taking the area under a finite but greater number of curves. Anyway, thanks so much!
Thank you so much! I am reworking through my calculus book, and my book just kinda gives you the formula and doesn't even make an attempt to prove it for any reason, and I was completely lost as to even where to start. I tried doing some of this stuff, but namely I got stuck because I didn't make the observation that the definite integral -h to h of bx would always be 0. If I had seen that I wouldn't have been so frustrated. Pretty embarrassing I wasn't able to see that >.>
Great video! Just a note, It works really well, but only describes the case where odd pieces are parabolic stationary points - it doesn't have to be that case, and you can kind of get the maths to describe that from this, but it would be more complete to include that. Sorry for the pedantism :P
I have a question, perhaps a stupid one. Since we can shift the function in any way we like without a change of area, in order to make it symmetric about the y-axis, how can y_2 for the first parabola be the same as the y_2 for the second parabola? Wouldn't the shifts required for the two parabolas to be symmetric about the y-axis be different? Thanks :)
Just a question, isn't the simple formula of Simpson in the form "((a-b))/6)(y0+4y1+y2)"? (With (a-b)=h*n, being a the beginnig point, b the last, and n the number of equal devisions of that intertval.)
This looks like a helpful video, but it keeps pausing. I thought it might be my computer, but had the same problem at the library. Is there any way to fix this?
Great video! I just want to add, though, I believe that the parabolas aren't symmetric about the y axis - the parabolas are being shifted such that their two far ends will be equidistant from the y axis. The only way the parabola will be symmetric is if its endpoints of the domain (-x and x) result in an equal y output, along with the B coefficient being equal to zero in the equation.
There is a reason! Once you have the equations: yo = Ah^2 - Bh + C y1 = C y2 = Ah^2 + Bh + C Notice that yo can be added to y2 to eliminate Bh: yo + y2 = 2Ah^2 + 2C And the area beneath the curve is: x/3(2Ax^2 + 6C) So if we want to express this area in terms of yo, y1, and y2, we have to find where we can substitute them. Immediately, we can replace 2Ax^2 + 2C: x/3(yo + y2 + 4C) And C = y1. Therefore: Area under curve = x/3(yo + y2 + 4y1)
God bless you man
Haven’t seen a better explanation in my life. Love you man
I loved how you explained this topic so simply, very graceful
Thank you for explaining where this came from, other videos simply chuck this formula at you and doesn't explain why you use it and just take it for granted.
This was absolutely perfect. I understood how to use Simpson's Rule but, until this video, I couldn't understand how we could possibly take the area under a curve by taking the area under a finite but greater number of curves.
Anyway, thanks so much!
Thanks for making this video!! I was trying to decipher my books derivation, and it wasn't making sense, but this cleared it up!! Much appreciated
If not for these kind of videos on youtube, I won't be a top student. I owe you all my grades
It really helps to know where this long formulas suddenly jumps to mathematics, great thank you.
Better explanation than most!
Well done Patrick!
Thank you so much!
I am reworking through my calculus book, and my book just kinda gives you the formula and doesn't even make an attempt to prove it for any reason, and I was completely lost as to even where to start.
I tried doing some of this stuff, but namely I got stuck because I didn't make the observation that the definite integral -h to h of bx would always be 0. If I had seen that I wouldn't have been so frustrated.
Pretty embarrassing I wasn't able to see that >.>
I just had my numerical methods exam last friday, this would have helped me a ton :(
Thank you so much. I find this video very helpful and easy to understand the Simpson's rule. Keep it up dude, very appreciate it!
FROM EAST TO WAST U R THE BEST
West*
Her from Dukes lesson
same lad
It's great to know where the seemingly arbitrary 1, 4, 2, 4, 2, 4, 1 thing comes from. Thanks!
Awesome as always .. the best teacher I've Ever had !
Bruh, that took a while. Now I know why the professor didn't bother showing this in the lecture lol
This explanation is super crazy AWESOME. thank you so much
Nice explanation Patrick! As a tutor this is a great help.
Great video!
Just a note, It works really well, but only describes the case where odd pieces are parabolic stationary points - it doesn't have to be that case, and you can kind of get the maths to describe that from this, but it would be more complete to include that.
Sorry for the pedantism :P
Loved this man…..
Such a beautiful explanation!!!
Wow, amazing!!! You make it so clear
I have a question, perhaps a stupid one.
Since we can shift the function in any way we like without a change of area, in order to make it symmetric about the y-axis, how can y_2 for the first parabola be the same as the y_2 for the second parabola? Wouldn't the shifts required for the two parabolas to be symmetric about the y-axis be different?
Thanks :)
Marvelous, simply marvelous
Patrick do you have any bernoulli differential equation tutorial? I stick with you because you really teach very well.
no, not at the moment, sorry
Bless you
Thank you so much for your videos
Wait so you use integration to compute the approximation of the the integral seems abit like chicken and egg
thank you so much for this video! It really helps
Just a question, isn't the simple formula of Simpson in the form "((a-b))/6)(y0+4y1+y2)"? (With (a-b)=h*n, being a the beginnig point, b the last, and n the number of equal devisions of that intertval.)
I don't think it's (a-b)/6 but (a-b)/3 because you don't know delta x yet(h).
Thanks man! Awesome proof vid!
YAY Numerical methods!!! plz make all the ones you can think of.
wow! so helpful! thanx Patrick! :)
why does the rule only work if the number of parabolas is even?
This looks like a helpful video, but it keeps pausing. I thought it might be my computer, but had the same problem at the library. Is there any way to fix this?
I think it's the computer or internet connection. I have no such issue.
Hello one question ,
in y0 +4y1 +y2 , where did the 4 come from? thankyou
minute 8
im a little confused, if you had n=2 how would you solve? would it be f(x)+4F(x1)+f(x2)???
"im a little confused, if you had n=2 how would you solve? would it be f(x)+4F(x1)+f(x2)???"
Yes.
Nice video! Thanks!
is this possible if the upper limit is smaller than the lower limit?
awesome! this really helps me!
is it possible that you do a video on diagonilization of a 3*3 matrix
Hi Patrick . how best to prepare for last year college maths exam.
works lots of old practice tests if they have them.
and i would ask someone at your actual school; it is hard for me to say
How many rules are in the math problems? Cool vid.
It's only about 6000 Math rules we have in Mathematics
@@qinisombulawa727 beautifully created
Great video! I just want to add, though, I believe that the parabolas aren't symmetric about the y axis - the parabolas are being shifted such that their two far ends will be equidistant from the y axis. The only way the parabola will be symmetric is if its endpoints of the domain (-x and x) result in an equal y output, along with the B coefficient being equal to zero in the equation.
thats brilliant
I am not comfortable when you set y0+4y1+y2 = the area expression. I don't see the rationale or physical/mathematical connection by doing so.
It's so beautiful!
at 8:00, why do you multiply y1 by 4? What is the "clever observation?"
There is a reason! Once you have the equations:
yo = Ah^2 - Bh + C
y1 = C
y2 = Ah^2 + Bh + C
Notice that yo can be added to y2 to eliminate Bh:
yo + y2 = 2Ah^2 + 2C
And the area beneath the curve is:
x/3(2Ax^2 + 6C)
So if we want to express this area in terms of yo, y1, and y2, we have to find where we can substitute them. Immediately, we can replace 2Ax^2 + 2C:
x/3(yo + y2 + 4C)
And C = y1. Therefore:
Area under curve = x/3(yo + y2 + 4y1)
Ur dumb
+Benito Kestelman
Aha, thank you!! I have also been trying to figure out why 4 was used and you have explained it very well!! :D
You are amazing
Beautiful
Didn't like the jump to the solution and trying to backtrack to "observe" it. Better to just derive it all the way through.
patrick how to use simpson's rule from - infinite to a number
Is There a geometrical explanation?
yes
patrickJMT do you know where to find it? By the way if found your explanation really helpful
Very clear!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! appeciate
That's awesome 😊👌👌
Thanx
Sir plz also explain 3/8 rule
very helpful , thxxxx^^_^^
Cool!
Thanks!!!
Why do we multiply Y_1 by 4 in Y_o + 4Y_1 +Y_2?
mind = blown
sir why we take n is even
makes it easier to explain
All i notice is that he is left handed
Ohhh, its fine! ;)
Sorry this my mistake
nice voice
Please be my teacher
you cheated tho
9:22
See my post then comment ok
Awesome as always .. the best teacher I've Ever had !
Ohhh, its fine! ;)