Explanation of Simpson's rule | MIT 18.01SC Single Variable Calculus, Fall 2010
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- Опубликовано: 15 сен 2024
- Explanation of Simpson's rule
Instructor: Christine Breiner
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
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Most professor just stop at the answer, but she went back to the question and summarize the whole thing again. Thank you!
Lovely! It s amazing
exactly! amazing
I really want to take a moment to be..extremely grateful.
I never expected such high quality education to be open and available for anyone with no cost. We are indeed blessed. We all should use this gift wisely.
thank you Doctor Christine, may your days be wonderful always.
This was a really really really good explanation. I do not think I could explain this any better. i am just going to play it for my students and fill in any gaps :). You have a new subscriber!
It's not her personal channel, She is an instructor at MIT so the video is uploaded by MIT OCW
This is where the power of MIT comes from. I highly respect you. Thank you!!!
Holy poptarts, I've spent hours agonizing over this stuff for an assignment. These online videos always explain it so lucidly.
Loved it when she says "Now, this might not look fun yet..." Of course it looks fun, Dr. Breiner!
you are fantastic! After just watching it once I sat down in the night befor going to bed and could derive everything myself! You are really a magic teacher! :-) Thanks alot and we are looking forward to seeing more of your great didactic masterpieces! =]
I now understand how that formula for simpsons rule cam about! Thank you!
Brilliant. I've been looking for a derivation/proof of Simpson's Rule and this has been by far the best explanation I've come across on the net. Christine is better at teaching the concepts than the actual lecturer. Very much appreciated.
This explanation was not necessary to work with Simpson's approximations, but there's just something special about seeing the machinery like this. Thank you!
Finally! A video explaining how Simpson's rule works. Other videos only explain how to apply Simpson's rule... Thank you!
Hi ma'am, I'm Debjit Patra from India, you're just awesome professor, after watching this video, I recommend all my friends to see your videos
Just wanted to say thank you for all your videos in Cal II. I had an A in the class by constant practice and your helpful video. I am glad I had You (Christine), Patrick and Krista's videos. Thanks once again and happy holidays.
Actually sooooooo talented at teaching this one video explained this concept so much better than the last two hours of worth of youtube videos i watched
Been watching for years now love the way you explained so clear. Thanks
Professor Breiner, this is a great explanation and derivation of Simpson's Rule in Calculus. Simpson's Rule is used to approximate definite integrals.
Simple and neat. Thanks a lot, prof. Breiner! You are my savior.
Amazing explanation! Crystal clear!!! Christine you are gifted.😘
The way she gave the lesson is so clear and logical, thanks a lot for this video
She has an extremely pleasant and clear handwriting too...
impressive,our prof just gave us the final expression without even explaining from where did it come I feel stupid when I try to memorize these rules .thank you so much for your astonishing efforts
this is one of the best maths videos ive ever seen. I would've still understood this if i was in high school
O Great Tremendous Way Explanation .......I Just wana Wow.....Such Great Style Of teaching i cant forgot ever in my Life.......
11:41 "We're getting very close to getting what we want." Didn't know it's so fun to study at MIT.
Excellent approach. Easiest of all I've seen. But some viewers might think that the formula is valid only when X1=0. It would have been better if it's explained that one can extend the formula for any number of such points on a curve by shifting the origin to the point in between each time, there by finding intergation of the curve between any two intervals.
Thank you so so much. Your teaching made me so happy to learn Math and this looked like so much fun. Thank you for going everything so detailed with your students and caring about them and their understanding. It means so much to us. (:
so perfectly explained, I think I actually understand it a bit better now, thanks so much. My teacher goes so fast, skips steps, abreviates like a madman and most of the time I feel like he is speaking a different language. Worst part he never does examples just explains the theory then throws problems at us and expects us to jump right in and do the work! I need to see it done at least once before I am comfortable doing it, thanks so much for posting this video. very helpful.
This was a really nice, straightforward presentation. Well done!
Wow! That was like listening to a well-played Bach prelude and fugue. Had no idea calculus could be delivered in such a lovely fashion.
IF you read ..you are an awesome instructor .You made it too easy and too simple to learn ..
This is really one of the best explanation videos I have ever watched :O
That was brilliant, a good teacher can take a horrible proof and dumb it down for students to grasp, you did exactly that! :)
You only one who give more explaing .you have great brain.
very helpful--you don't often see this--i think this wouod have been clearer if cb had defined a general quadrdic p(x) and its integral P(x)-- this might have allowed for a more linier presentation--the joy of youtube is being able to scrub back and forth to clarify
Excellent explanation!! MIT has the best teacher/s.
You cleared my concept about composite Simpson's rule. Thank you wish you good luck and keep up the good work 👏👏💖💖
You are amazing. my favorite teacher
6:58 why Ax^3/3+Bx^2/2+Cx jump to 2Ah^3/3+2Ch
This is fantastic. A wonderful explanation for a bit of mathematic sleight-of-hand.
Thank you very much, it's explained everything my teacher couldn't!
We just had a lecture on this this very same day and got back from it. Didn't understand crap. I watched this video and I have to say you blew me away, in a great way. I understood what we were doing, where they were coming from and to where we were headed. It's as though I'm discovering prescription glasses all over again! :D
Can anyone here explain me why, to apply simpsons' rule, we have to divide the function into n-EVEN no. of intervals? Also, how does the '2' come in the formula?
If you haven't found the answer yet, you can look up Simpson's rule: the derivation by PatrickJMT. It is the complete version, and from there u can see why it HAS to be even number of intervals, and you also see where the '2s' come from.
hope it helps.
Thank you Jeanna Friske!
NOW PEOPLE, THIS. RIGHT HERE. IS HOW YOU TEACH.
Very straightforward explanation! Thank you :)
Excelente explicación. Acordar el área entre -h y h, permite simplificar mucho la comprensión de la fórmula.
Best math proof i have understood
Our Calculus professor upload this video on the Internet, I totally understand now
Just wondering what the significance of adding p(h) and p(-h)? Is it simply for manipulation ?
she make the theorem very easy to understand
Respected sir,
please answer
1) Simpson's 1/3 rule it gives exact value of polynomial of degree ?
2) The degree of precision of Simpson's 1/3 rule is ?
Wow..this is the best tutorial to understand Simpson's and how it works..Addition of Composite Simpson's would have made it more useful ..Thanks xx
it seems that she is empowered professor in calculus thanks a lot
I was searching for derivation on RUclips
I wanted to what exactly is this
Like why are we calculating like that
This is the best explanation. Thank you so much
what about if the interval is larger. means to know coefficients A,B,C we need only 3 equations not more than that.if we got more then how?
Nice.... I like that you do little bits of error checking along the way.... i try to emphasise that to students.... doesn't always get through.
she explains it in a simple manner
Thank you ,that was a very clear explanation.
And the main attraction is, after finishing the proof, you went back to the problem and again give explanation briefly.
@OpenTheTrollGate it didnt turn into h/3(2Ah^2+4c). it became h/3((y0)+(y2)-2(y1)+6(y1)) since she substituted the 2Ah^2 and C
I get how this works but when do you use it? Looks like you can only derive Simpson's if you already know how to perform definite integration. This is unlike the Trapezoid method which doesn't require any knowledge of integration but allows you to use a laborious method while you wait for integration to be invented. So what is Simpson's Rule for? If it only comes into existence as a by-product of defintite integration, isn't it a step backwards when you could just integrate between two limits?
Amazing professor, thank you so much!
Very nice teacher and very good explanation.
u must be a god! i mean u really understands math not just saying numbers and symbols but u can see what behind that
she sooo coooool!
She sure can teach the hell out of anything
I'd love to give it like again
Amazing lesson, but what about the coefficient of 2 in between the 4s?
Thank you; this issue nhas been nagging my intuition for years. I can now put it to rest.
thank you MIT!!
such clear direction. I'm skipping math as I write this because my classes don't even compare.
Simple method with great Mind...
I loved this explanation; I really needed some way to explain the rule. Yet I don't get how come the power rule did not result in a constant after integrating the quadratic function.
Thank you very much. you professor made it easy to understand. Thanks again.
I find perfect video. Thanks MIT
But how about the coefficient of 2 in the Simpson's rule?! And why n must be even??
What if n=4, should the coefficients be 1 4 2 1, or 1 4 4 1 ??
So if there were 5 points involved (4 regions) instead of 3, then multiple parabolas are needed. Parabola one passes through the first 3 points (y0,y1,and y2) and the second parabola passes through y2,y3, and y4. So we have h/3(y0+4y1+y2)+h/3(y2+4y3+y4). Combining those 2 is where the 2y2 comes from.
This is also why there must be an even number of regions. A parabola needs 3 points to be defined, so the first parabola needs 3 points (being 2 regions). The next parabola also needs 3 points for its 2 regions, but since it uses a point from the last parabola, only 2 more points need to be added.
Wow great explanation I never say that often.
Is it possible or worthwhile to extend this to estimating areas with cubics instead?
+John Smith It is, and it's called Simpson's second rule. You can also use higher degree polynomials, but the initial interval size also increases. For the second rule, you need 3 initial intervals (n is multiple of 3). So even though a higher polynomial will give a better approximation, the interval is larger, so the precision does not increase linearly. For very high degree polynomials, the error gets very large. If the precision and performance are both critical, you often need to find the "sweet spot" for a specific application.
I think Simpson's rule is originally a result of Archimedes plus area of trapezium
I'd prefer if you didn't start with the answer and try to work your way back as a goal. Just solve it and reduce it to come up with the rule.
Much appreciated. very well explained. Thank You!!!!
Great explanation
Why we need to approximate it by a quadratic function and not by cubic or quartic etc
Because it's simpson's 1/3 rule and in case of simpson's 3/8 we use cubic function.
I understand the whole thing except, to the B thing. Im just confused about why won't there be a B term :(
That was a great example of teaching:) Thank you a lot!
a great explanation, thanks.
when we evaluate, why do we have a "(2Ah^3)/3 + 2Ch" were does that 2 come from???
Symmetry - Ax^2 is a parabola with its vertex on the y-axis. The area on the left side of the y-axis will be exactly the same as on the right.
This goes for C also. C is just a horizontal line.
Very very helpful. simple and worth while.
No wonder great explainers like Feynman and Sal Khan come from MIT.
problem is what if its not over interval -h to h...
Excellent Teacher. Please Kindly keep it up.
Which is most likely why she is teaching at MIT. ;)
Vay...vay...vay...vay .....bravo Dr.Breiner
Brilliant! Thank you so much!
Beautifully explained
I thank my lectures.
Thank you
Thanks for the explanation.
Maravillosa explicación...