An introduction to numerical integration through Gaussian quadrature

[@draxonful]

Thanks for the detailed explanation! Really helps for our numerical methods module at uni! Best regards from Germany!

[@quanttube]

This absolutely magnificently beautiful Mr. Lambert. Thank you so much for posting this.

[@sumitmukherjee249]

That graphical depiction was really interesting.

[@el-shammahrushwaya9677]

why didnt you work out the ws and xs, wasnt that the whole point of using this formula?

[@CodeVault]

24:05 You forgot to cut there ;) Otherwise, the only helpful video I found about this topic, really made me understand what's up with Gaussian Quadratures. Thanks!

[@SpartacanUsuals]

Thanks for pointing this out. Best, Ben

[@MatheusSilva-dragon]

You explanation is better than my teacher's pdf file!

[@tusharbommala8150]

thank you for the detailed explanation. I really appreciate it

[@thomasfranzstockhammer7846]

Thank you so much ! Best regards

[@chimetimepaprika]

Did you discover the Lambert W function? Tee hee hee. Great video, mate! Neat and tidy explanations!

[@AuroraClair]

Waw, thanks for the detailed explanation. I was just wondering, maybe a silly question but still, how come we are only using odd-order polynomials for determining weights and locations for evaluating functions? Is there an explanation for this? Thanks again Is it because the number of unknowns is always even?

[@PaulJ_81]

exactly

[@AJ-et3vf]

Awesome video! Thank you!

[@Fundamental_Islam.]

How did u find w1 2 x1 etc

[@kavehsiah4021]

So, what happens if your polynomial is of an even order or a non-integer order?

[@starkillre]

So one point I'm wanting to get perfectly straight, if you could help me understand. Doesn't this mean that, for intergration of finite intergrals of valid f(x), the weighs and values of x are effectivly always known? and that the actual issue is figuring out which point you specifically want?

[@protyush18]

What kind of quadrature can be used for double integrals and functions with singularities?

[@김승환-g3c]

Thank you!! I can understand it!!!

[@JacekKarwowski]

After calculating the Lagrange polynomial, why not just use its integral as the approximation of the integral of f? I get that the answer is probably "because Gaussian quadrature is better", but why is it better? In the simulaton showed in the video, it seemed that the integral of polynomial had a much smaller error than the value you got from sampling.

[@mariovelez578]

It's the same thing. As he said in the video, gaussian quadrature for polynomials is an exact approximation, but is a lot faster since it uses less calculations.

[@cfcalle]

Amazing explanation. Thank you very much!

[@ismaelerroussi9704]

masterclass 👏

[@1827641]

4:38 you meant \hat{f} instead of f, didn't you?

[@finite_elements]

Thank you

[@tag_of_frank]

Where can I find this legendre table

[@chickenkorma3163]

Just google it. It is on wikipedia.

[@ajeetgary9707]

For your example you did something that happens to work out exactly - it's a linear approximation, manufacturing a serendipitous example is misleading to how good the first step of the algorithm actually is.

[@glaswasser]

would be nice if your lectures would include more intuition and less math to understand the concept

[@alfredanderson238]

good explanation

[@malharjajoo7393]

This was terrible explanation, I got lost in first 8 min. :/