Gaussian Quadrature | Lecture 40 | Numerical Methods for Engineers

An explanation of Gaussian quadrature. An example of how to calculate the weights and nodes for two-point Legendre-Gauss quadrature.
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[@pristonluc]

Thank you Professor, it was an excellent introductory lesson.

[@ajayrathore4665]

Really this the best lecture I ever face... You used very unique way of teaching... Wonderful

[@Fallkhar]

Thank you so much! This is such concise and clear explanation of what is going on under the hood

[@lounesbenali4889]

Finally I understand what's going on, a HUGE thanks !

[@sudandevkota7268]

Thank you dear professor. Lots of respect to you.

[@Eloss69]

This serie of videos is enormously helpful, many thanks.
Q: How does one choose the right formula to integrate a discrete function ? (In the video there are four "flavors" but we can find as many weight function as we want !)
What kind of information on the function to be integrated should we have in order to perform such a choice ?

[@ProfJeffreyChasnov]

Difficult question. Sometimes the weight function is already inside the integral you need, when you are using special functions to solve pde's for example. For simple integration tasks, I would just use the MATLAB integrate function and not worry about it.

[@ANJA-mj1to]

Predicting instantaneous hourly and integrated daily direct and diffuse solar flux we can use Gaussian quadrature form. Valuable topic where we can see how to imply fast Gaussian quadrature based estimate for water vapor pathlenghts. So we can give hydrostatic equilibrium form of Gaussian quadrature which will represent the atmospheric density.

[@eddiechen6389]

Hi professor Jeffrey, why do we assume that w1 = w2 = 1, and why do they have to be in symmetry?

[@ProfJeffreyChasnov]

I just made the algebra easier. You don't need to assume anything and just solve the equations.

[@juiteko8375]

Q: Do we have a numerical approach for integrals involving generalized functions like Green's or Dirac delta?
can orthogonal polynomials take the form of generalized function?

[@bhagyarajuakepogu]

Nice explanation professor.

[@ShulamitMorjossef]

How do you get that the integral is found with W(x) by which method?

[@TheCsePower]

Very good presentation

[@shihanjanith1804]

nicely explained.

[@abhimanusingh1284]

Thanks a lot. Excellent presentation.

[@eluz7903]

So 3 points requires f(x) goes to polynomial 5, right?

[@mohammadanadani7898]

Exactly what I needed! much appreciated

[@shashankpandey8346]

I think if you wore a black gloves with coloured finger tips, then we would still get it when you point on something or put your hand on some part

[@AJ-et3vf]

Great video. Thank you

[@vwcanter]

This guy’s got mad flavor.

[@SuheybBecerek]

Thank you professor, this is really helpful explanation

[@ritobanbasak9204]

Very useful video. Thank you sir.

[@erikasoares25]

thank you so so much for helping me !!!!!!! ❤

[@ijyoyo]

So helpful! Thank you for putting it into words

[@andrewnicholas2221]

did he just write things backward from his pov

[@freepointsgals609]

I think he's right handed

[@Oscar-gv1si]

Yo I had the same question I think he his which is nuts

[@blibilb]

the video is mirrored after recording

[@estebanrequena2694]

Great video !

[@beinspired3408]

where does w1=w2=1 ? please explain clearly

[@ktk.1201]

this board setup is making me trip xO

[@lukunil]

Thanks. You're a bit like a nice version of the teacher in whiplash 😅

[@jacobblack2544]

Why does prof looks like a character from sopranos

[@nami1540]

I dont understand how this compares to ua-cam.com/video/nQZYBWB6q_k/v-deo.html and ua-cam.com/video/cKKrGr93f6c/v-deo.html . There the weights only need to solve up to degreen n and the locations xi result from the polynomial division of f(x) by the order n polynomial.

[@davidkos5326]

kid named finger

[@jeanniez8981]

internet college UA-cam institute

[@SushmaDevi-jg7il]

😂👍

[@greed5891]

Waltuh