Laplacian computation example

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

[@CandidDate]

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!

[@shakennotstired8392]

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!

[@z00ey]

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

[@yuxiangwu4573]

Easy to understand. Nice video!

[@photon7777777]

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

[@ExperimentLife]

I have never heard of this! Neat

[@djalmasimoes8442]

great job.

[@moozzzmann]

Loved this video and the previous one

[@ralstonrobertson6644]

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.

[@citrarizqin]

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

[@kim15742]

Wow, I understand this!

[@gloriacastaneda114]

Thanks!!!

[@henrimartialmeke556]

Merci

[@robertwilsoniii2048]

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?

[@yonghuiliew8066]

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

[@pritam_sadhukhan]

You've actually got 2 types of fields:
1. A vector field (a vector as a function of space x,y,z)
2. A scaler field (a scaler as a function of space)
Now the gradient of a scaler field is a vector field.
And divergence of a vector field is a scaler field
So the Laplacian of a scaler field turns out to be a scaler field

[@med-9official876]

Which software are you using to draw the graphs?

[@michaelmacdonald2907]

easy pezy. Thanks

[@skandys9847]

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

[@tomlowe6382]

Correct. This is a type of mathematics used in the physics of gravitational fields.

[@SohamChakraborty42069]

@@tomlowe6382 Could you explain how?

[@davehumphreys1725]

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?

[@JeaneAdix]

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.

[@tsraikage]

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