Laplacian computation example

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worked example of computing the laplacian of a two-variable function.

Khan Academy

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I've got a book on electromagnetics, but had trouble with the gradient, curl, divergence and Laplacian. I just binged these videos and now am ready to tackle these concepts. Thanks!

CandidDate

This series of videos are so unbelievably helpful in developing an intuition of the concepts involved and whys and hows; a sort of an real understanding in the sense that you can see it the your mind because you just know it. Thanks a million!

shakennotstired

Nice, this pair of videos really helped me visualize the scalar laplacian :) Thanks.

photon

really well described and narrated - the visualisations were spot on! thx so much

zey

You should consider employing the complete definition of gradient where a scalar function is converted to a vector function via the gradient process. This approach insures the extension to a 3-D vector situation. The application of the Divergence then takes you back to the scalar answer.

ralstonrobertson

Thank you very much! This video helps me a lot!

citrarizqin

Hi, is gradient of scalar function a vector function? For that, is Laplacian vector function as well?

yonghuiliew

Which software are you using to draw the graphs?

med-official

This is how you do it without infinite series’. Still not sure how you get boundary values though. I guess you would parametrize the boundary?

robertwilsoniii

I think this is the graphics program grant has been making for a while now. If you look at :12 you can see he's using Photoshop, whats going on with that?

edit: nvm I see whats happening, he switched programs to Photoshop to write. I thought his program was in Photoshop and somehow he was manipulating 3d graph in Photoshop.

JeaneAdix

oh. so thats how easy it should be. why my teacher loves to complicate everything?...

tsraikage

Given the chicken scratches, I can just about follow the maths. But, what on earth is the physical interpretation of the Lapacian of a gradient field? For that matter, what is the physical interpretation of the Lapacian of ANY vector field?

davehumphreys

Could a 4d version of this be used to explain gravity?

skandys

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