Simpson's Rule - The Derivation

[@muhitthemagician7651]

God bless you man Haven’t seen a better explanation in my life. Love you man

[@anneupp9421]

I loved how you explained this topic so simply, very graceful

[@MrRumblefrog]

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.

[@JasonConner84]

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!

[@Josiah_Cornett]

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

[@mich6010]

Better explanation than most! Well done Patrick!

[@calambuhayjr.josevirgiliog2094]

If not for these kind of videos on youtube, I won't be a top student. I owe you all my grades

[@duchieu083]

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!

[@karthikr7956]

It really helps to know where this long formulas suddenly jumps to mathematics, great thank you.

[@abdelrahmangamalmahdy]

FROM EAST TO WAST U R THE BEST

[@jayant9151]

West*

[@insidetrip101]

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 >.>

[@ulquiorrashinigami]

I just had my numerical methods exam last friday, this would have helped me a ton :(

[@jonathanblack5940]

It's great to know where the seemingly arbitrary 1, 4, 2, 4, 2, 4, 1 thing comes from. Thanks!

[@kushalsharma707]

Her from Dukes lesson

[@louispender9347]

same lad

[@rawansaif7044]

Awesome as always .. the best teacher I've Ever had !

[@thomasledgerwood9643]

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

[@lostlatinlover]

Nice explanation Patrick! As a tutor this is a great help.

[@whiteboarddude3566]

This explanation is super crazy AWESOME. thank you so much

[@user-kt3mb8ug8r]

Loved this man…..

[@won20529jun]

Wow, amazing!!! You make it so clear

[@mariobaeza8114]

Such a beautiful explanation!!!

[@mitchellschoenbrun]

Marvelous, simply marvelous

[@ltroop343]

Bless you Thank you so much for your videos

[@fourierbird]

at 8:00, why do you multiply y1 by 4? What is the "clever observation?"

[@benitokestelman4545]

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)

[@FAHayekSays]

Ur dumb

[@sreyasingh3755]

+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

[@mimiarina9425]

thank you so much for this video! It really helps

[@mastermime1000]

Thanks man! Awesome proof vid!

[@nikkiactub]

Patrick do you have any bernoulli differential equation tutorial? I stick with you because you really teach very well.

[@patrickjmt]

no, not at the moment, sorry

[@tahsintahsinuzzaman781]

Bruh, that took a while. Now I know why the professor didn't bother showing this in the lecture lol

[@andyapi42]

Hello one question , in y0 +4y1 +y2 , where did the 4 come from? thankyou

[@andyapi42]

minute 8

[@zaidan56]

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.

[@davidlee8166]

awesome! this really helps me!

[@DarkNinjaStudent]

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 :)

[@RajeshKumar-rg5lf]

is this possible if the upper limit is smaller than the lower limit?

[@1manband22]

wow! so helpful! thanx Patrick! :)

[@jayjayf9699]

Wait so you use integration to compute the approximation of the the integral seems abit like chicken and egg

[@rafaelmelo2576]

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.)

[@SniperMonkeh]

I don't think it's (a-b)/6 but (a-b)/3 because you don't know delta x yet(h).

[@melannieruiz4259]

im a little confused, if you had n=2 how would you solve? would it be f(x)+4F(x1)+f(x2)???

[@SuperMerlin100]

"im a little confused, if you had n=2 how would you solve? would it be f(x)+4F(x1)+f(x2)???" Yes.

[@nelsonwetmore]

YAY Numerical methods!!! plz make all the ones you can think of.

[@alexandredamiao1365]

Nice video! Thanks!

[@tshidzolinda912]

is it possible that you do a video on diagonilization of a 3*3 matrix

[@VictorE1030]

why does the rule only work if the number of parabolas is even?

[@derek3719]

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?

[@BSplitt]

I think it's the computer or internet connection. I have no such issue.

[@halhauder79]

Hi Patrick . how best to prepare for last year college maths exam.

[@patrickjmt]

works lots of old practice tests if they have them.

[@patrickjmt]

and i would ask someone at your actual school; it is hard for me to say

[@roaahedaya1779]

That's awesome 😊👌👌

[@nickcochran6343]

It's so beautiful!

[@alwayslovelbjkyle6430]

thats brilliant

[@thejspace302]

Why do we multiply Y_1 by 4 in Y_o + 4Y_1 +Y_2?

[@TheWolfXCIX]

You are amazing

[@djmpvae27091978]

How many rules are in the math problems? Cool vid.

[@qinisombulawa727]

It's only about 6000 Math rules we have in Mathematics

[@sadbutitstrue2323]

@@qinisombulawa727 beautifully created

[@11crazykitties]

Beautiful

[@ChechoColombia1]

Is There a geometrical explanation?

[@patrickjmt]

yes

[@ChechoColombia1]

patrickJMT do you know where to find it? By the way if found your explanation really helpful

[@alphamega3306]

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.

[@firstnamelastname4685]

Very clear!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! appeciate

[@ashishsasmal7523]

Thanx

[@tiffanywong579]

very helpful , thxxxx^^_^^

[@khushimaurya4590]

Sir plz also explain 3/8 rule

[@truthjunkie3]

Didn't like the jump to the solution and trying to backtrack to "observe" it. Better to just derive it all the way through.

[@AHMED5014993]

patrick how to use simpson's rule from - infinite to a number

[@thesage1096]

Thanks!!!

[@muhammadsadiq1792]

sir why we take n is even

[@anneupp9421]

makes it easier to explain

[@banderfargoyl]

Cool!

[@iwilld0it]

mind = blown

[@nikkiactub]

Ohhh, its fine! ;)

[@saimafa5579]

All i notice is that he is left handed

[@laughtale1181]

nice voice

[@sonicworld7904]

Sorry this my mistake

[@jayant9151]

Please be my teacher

[@spectralanalysis]

9:22

[@gian2kk]

you cheated tho

[@sonicworld7904]

See my post then comment ok

[@rawansaif7044]

Awesome as always .. the best teacher I've Ever had !

[@nikkiactub]

Ohhh, its fine! ;)