Laplacian intuition
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- เผยแพร่เมื่อ 30 พ.ค. 2016
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A visual understanding for how the Laplace operator is an extension of the second derivative to multivariable functions. - แนวปฏิบัติและการใช้ชีวิต
That voice... makes me feel safe with math
Adalberto Rojas you just spoke my mind sir!
Again voiced my mind!!!
same
Go check out 3blue1brown on TH-cam, this guy's awesome!
lmfao!! Same dude!
3blue one brown????
yup .....100% sure
Yes
ya dude. he is awesome. love his videos. he uses right brain thinking.
Yes that’s him 😂👌🏻❤️
He did say in an interview that he taught in khan academy or something before youtube
Welcome, all you travelers, coming from Partial Differential Equations! Praised be 3B1B!
I'm from the video "Divergence and Curl" ( also from 3b1b )
Literally got more intuition from a 5 min video than scouring through a myriad of textbooks back in my college days. It's interesting to note that the Physicists' notation for the Laplacian is nabla^2, which maybe makes it a bit more confusing because it implies it's the second order gradient or could imply the curl of gradient, etc.
you do know that multiplication can be rendered in English as 'of', right?
3 * 4 apples = 12 apples -> three groups of 4 apples is 12 apples
and thus a second order derivative, which is the derivative of a derivative is validly derivative * derivative, or derivative^2. and the only difference between a generic derivative and the differential is that a nabla indicates is that it's the sum of all n partial derivatives over an n-space. so the second order differential is nabla of nabla, or nabla * nabla, or nabla^2.
the reason it appears to be the same as the second order gradient is because it is. it's the sum of the partial derivatives... which is the second order gradient, and the laplacian, they're two names for the same thing, and thus it's actually not confusing. and curl is notated differently, since it's the cross product. if you separate it out as nabla dot nabla, then it might be ambiguous as divergence of the gradient, but with very little effort you can see for yourself that it's actually the same thing anyway, so again... what are you confused about, exactly?
see @0:52
he literally shows you that the laplacian is the divergence of the gradient and it remains on screen for the entire rest of the video.
how in the world are you confused, and how did anybody like your comment that you're confused? it's not remotely confusing.
@@sumdumbmick 1) Chill out. Just because something isn't confusing to you doesn't mean everyone needs to agree.
2) The Laplacian is not the same as a second-order gradient. The Laplacian is the *divergence* of a gradient, which gives a scalar. The gradient is a vector, so you would expect a second-order gradient to also be a vector / matrix. Ryan is right that the notation obscures the meaning of the term. Leaving it as del dot del would be a lot more clear.
3) The eye-rolling-ness of appealing to English grammar to criticize a benign internet comment aside, multiplication and "of" are not always the same thing in this context. Let's say f(x) = x^3. The derivative of the derivative of f(x) is 6x. The derivative of f(x) times the derivative of f(x) is 9x^4. This line of reasoning is only going to get us into trouble.
I agree definitely.
This is heaven on Earth for someone like me that learned this 24 years ago and just now understand!
You guys are amazing, thank you for publishing these! Multivariable calc is so much more understandable now!
I swear to god, I've been reading various pages for days to understand what this operator does. You made it cristal clear in a few minutes
The intuition for the laplacian is exquisite I am very glad that you’re getting a ton of recognition.
with your young face you risk getting some detractors here. Check some neighboring comments for Dunning or Obama. Hilarious. I agree with the intuition part. First time in my life I understand that stuff! :)
I could never understand Laplace operators at school. I hated them. Today, my 7 year old kid looks at this video and says: "it is simple, why did you not understand?". Yes! This is a new wave of learning. Thank you Sal and thank you Blue Brown. You redefine learning!
as a 10 yr old, he makes everything hyper - simple.
My son just got out of my wife's womb guys and he also said it's so easy,...thanks Obama.
@@suveermanj1001are you mocking? the statement? And Obama at the same time? Kids have a knack to find their own interpretation of stuff presented in visual form. Perhaps they forget in a day, but they comprehend more than adults think
Dunning Kruger effect go crazy
@@DaBestNub Dunning Kruger effect MYTH go crazy
Thank you soooo much for amazing illustration and for making it so easy to understand.
superb ... finally, I understand the concept of gradient, divergence and Laplace's equation.
I was saying today why doesn’t 3blue have a video on laplace… one trip to the search bar later and I found this hidden gem.
3blue1brown should voice all math videos on the internet
Awesome, this helps with my electrical prospecting class.
What a great explanation. Thank you
Brilliant explanation !
Well explained, so far! Even for a german, thanks!
please make a vedio on LAPLACE TRANSFORM
Omg god, this video is sublime. I am currently taking an Electromagnetism class so we constantly use this concepto of the Laplace equation but I never really understood what it meant.
Thank you, great intuitive explanation
this man is getting me through grad school
Great lesson!!!
Revisiting all of this cause its beena while I didnt touch Multivariable Calc and its still so fascinating and I realised how much I discovred more even if I watched this already time ago
Nice explanation...it will help us get a picture of what we are doing when we solve laplacians...
this is awesome, thank you :D
Please do a video on spectral clustering or graph theory!
Since we are talking about the direction of steepest descent instead of ascent, shouldn't the gradient vectors point the opposite direction? Shouldn't the sources be sinks and vice versa?
finally understood this!
Great explaination
So the laplacian is the divergence of a gradient? It'd be so much easier if they just said *that* instead of slapping someone's name onto it.
When I click on a Khan Academy video I pray it's a 3B 1B. Ghee was born for this.
This is amazing.
Wrt the vectors representing the gradient...are these colored differently to represent magnitude of the vectors? Is it also a convention to use longer vectors to represent vectors with larger magnitudes? I prefer color coding since the smaller and more numerous the vectors are, the better the visualization of what they represent. Changing length of vectors would take up space which could be better used to increase the count of vectors used.
Please make a video on laplacian operator in spherical and cylindrical coordinates
solid concept
lucid explanation 😍😍
thank you so much
is there any relationship between laplacian and laplace transform?
Oh my god! You really exist.
is this difference from the laplace transform because i was trying to understand the spherical harmonic. but instead of searching for Laplacian function i searched the laplace transform and i spend like 2 days learning it is it a waist ?
great video, yhanks :)
I just love talking about the Laplacian. It's such an edgy subject.
Anyone know what software was used to make the graph
Amazing ! Amazing !
Anybody here from 3blue one brown PDE video ?
Me lol
😀
Ty, im going to try to create a 2D gravity / space-time simulation using this
Those who're wondering whether this guy is 3Blue1Brown guy..
Hell yes! He is the same guy left khan academy and doing his own videos
he didn't left khan academy, is still working
@@axelmeramas976 OK
Instead of expecting Khan, this guy sounds like 3blue1brown?
yep, that's 3b1b
In fact, it is the same guy 3blue1brown. He decided to do khan just for a bit outside of his patreon channel
@@biggbuck9535 He worked at khan academy before doing his channel
What this has to do with L(f(t))=integral from 0 to inf of e^-st*f(t)
Link so follow-up video, please?
thank's man!
No copyright issue from 3blues1brown?
what program did you use to make this?
Michael Haggerty He wrote his own software from scratch. If you want to learn the skills to build something like this, you can take Stanford’s cs106ab and cs107 via TH-cam.
Difference between Laplace and Poisson equations? One equals zero, the other does not, right?
Why am I in tears after understanding this
coz u r cutting onions
Where i can get this software ????
Will the learner notice that you would have to flip the blue blanket inside-out for the water droplet analogy to make sense? Water does not flow uphill to pool at the peak of a hill.
but why is the gradient is toward the top of hill? shouldn't it converge to the goalie instead?
Martin Johnsons I believe the gradient points toward the steepest point, or the greatest rate of spacial change
When laplacian of function is zero what it mean???
i kindly request you to arrange the videos order wise .
please make a video on your channel 3b1b of Laplace transform
oh, look who I got, mr grant
Grant you're grand❤
what about f(x,y,z) intuition?
I'll be really greedy this time,
What is the software that u used
Plzz seems like a fun way to learn things (intuitively)
Lawliet L i think he Programms it himself, same with the animations on his channel
In 3B1B, he uses Manim: an open-source code that he created himself.
I recognise Grants voice anywhere!
Yup
Not kind of. It is a minimum if f '' > 0 and maximum if f '' < 0, be it a local or extreme.
Hello, Thank you so much!
How would I intuit the Bi-Laplacian ? What's the gradient(3) of the divergence(2) if the divergence(2) of the gradient(1) characterizes already if a point is on a pedestal or in a gap?
thx alooooottt XD
3Bu1Bn miss you at Khan
I recognize this voice :)
Good
3 blue1 brown , I know the voice ... Happy
heat equation intuition
Does anyone say del anymore, instead of nabla? Or is that from another generation?
why wouldn't the water flow downwards following the gravity (:
Because the water example was just an analogy so that he could explain and make us visualise better, with the help of the blue lines, not an actual example of how gravity works
Blanket of nightmare
3BLUE1BROWN YEAHHHHHH
3b1b army reporting!
Oh my goodness
Is this Grant Sanderson ?
You haven't plot the laplacian too :'(
are u bluebrown?? u sounds similar
Omg is this the 3blue1brown guy!?!??!
3Blue1Brown in da house
So, to conclude,
"At lowest point of any field, laplacian gives maximum value and at highest point of any field, lapacian gives minimum value",
am I right?
As intuitive as expected. Was it on purpose you didn't use the word "concavity" ?
idea: Sal does the audio, another the animations and graphs and prettiness, a third the math
1st?
Voice is same as of 3blue 1brown
I guess.
TEACH ME
3BLUE1BROWN!!!!!!!!!!!!!!!
Wait a minute !! I know you !! And you are no sal khan !!!
Lol 1 year to forget not bad
this sounds like Grant. Is this Grant? aha.
No Pi people? What? 3 Blue 1 Brown....
calligraphy hurts my eyes
what ?
Wait... Who is taking 😂
Differential forms. Come on: Give us the straight dope.
3b1b beta video
You too much rong time probrem