Harmonic Functions

[@TheAwesomoe]

I really am glad that Khan Academy was built, and especially expanding. It truly is a great tool.

[@GabrielConstantinides]

Chanson it has positive divergence!! 😅😅

[@halbarad7932]

8 years later the teacher in this video is an absolute masterclass of youtube math content.

[@KydroxHD]

3BLUE1BROWN?!?!?!? I am so excited right now

[@MrMarkgyuro]

this is the Origin. this was before he became the One. :)

[@YoYo-nt7yf]

@@MrMarkgyuro that's why I felt like know the voice.

[@ayushsaraf8421]

SAME. I was looking for his video and found this!

[@howmathematicianscreatemat9226]

Yeah. He is one of a kind and the same man 😎

[@scoutgaming737]

He does the entire series

[@ziadyoussef9157]

can't express how happy I am seeing people like khan and his team just trying to teach people in a great way without willing to get money but instead of taking money they give time and knowledge, thank you .....

[@jagandwarampudi]

Man, Why are you still here? You should be a professor at Stanford may be. You deserve that. You're the best teacher ever...

[@markykid8760]

Well I'm glad 3B1B is making content available to the masses instead of some privileged people in one University!

[@kellywshere]

3BLUE1BROWN!!! Best math explantions on the web! You provide TRUE insight that I have not seen anywhere else.

[@monisha7007]

Suggestion: 5:57 it would be good to say that the `magnitude` of the neighbours is less than the magnitude of the point, instead of `less than` since we are also dealing with negative numbers here.

[@joeyquiet4020]

I know his voice, this guy is my hero, learned a lot from this guy

[@SomeOfOthers]

the computation is: partialf/partialx = e^x*sin(y) partial^2f/partialx^2 = e^*sin(y) (e^x is it's own derivative, y is a constant) partialf/partialy =(e^x*cos(y)) partial^2f/partialy^2 = -(e^x*sin(y) ) (e^x is a constant, sin(y) --> cos(y) --> -sin(y)) e^*sin(y) - e^*sin(y) = 0

[@AshirwadPradhan007]

This guy is X-GOD of Mathematics! Keep up your insanely good work, 3B1B!!!

[@rahulmukherjee3638]

In the book called introduction to electrodynamic by D.J. Griffiths the same intuitive explanation of laplacian is given. I want to know why the term 'Harmonic' is used for such kind of functions which follow that rule of averages. Can anyone share some views why the term harmonic is used

[@OrdenJust]

The Wikipedia article for "harmonic function" gives a good etymology of the term. Basically, what started as a study of sine and cosine properties generalized to other functions, and the term harmonic continued to be associated with all such functions. I am trying to think of an example of another term that got generalized this way. Maybe "mechanics", which nowadays refers to more than just the study of machines.

[@danielchoi3440]

Best explanation on harmonic functions... very intuitive. thank you for the video

[@laurahoughton1289]

I wonder whether you could imagine the surface as consisting of an infinite set of equally spaced strings emanating out from the central point. Some go up, some go down, but any one that goes up must be matched in height from the centre by one going down. That would yield an average height equivalent to the height of the centre.

[@joluju2375]

This great video was too short. Still wondering what "landscapes" of harmonic functions have in common (when it's not a plane). I understand there must be no "top of hills", nor "bottom of depressions", but does it mean the landscape is full of saddles ? Since this guy loves geometric interpretations, I wished he had gone further. Also, why is the word "harmonic" used ? I feel there is much more to understand here.

[@PedroTricking]

wth This guy sounds like 3B1B, is it him?

[@aSeaofTroubles]

Yes it is :)

[@synchronicitystudios8217]

👍

[@halbarad7932]

Roots and beginnings

[@dominicellis1867]

Does the harmonic series have anything to do with harmonic functions?

[@MechanicalEI]

3B1B, Great video. Its's always cool to find you here! Thanks Khan Academy for doing this and uploading!

[@theomommsen6875]

Thank you so much! This video is absolutely brilliant and has made me understand the Laplacian so much better!

[@beppenonantola216]

He is too good.. Such a great way of explaining math!

[@bhavyagarg1871]

Khan Academy always surprises me with there explanation 😀

[@brajagopaldas12345]

Which software is used for this type of graphing?

[@tomaszgruszka3845]

It might be an incredibly dumb question, but it just got me thinking. Since on average, every point in the neighborhood-circle has exactly the same „height”, no matter where, can we actually calculate this average height for the entire function?

[@uzferry5524]

Tomasz Gruszka boneless

[@theomommsen6875]

The average height depends on around which point you start drawing neighborhood circles. You always get the 'height' (value of the function) at the point you draw the circle around and take the average of the function over. This result has a mathematical formula and is called the 'mean value property' of harmonic functions.

[@avichein2702]

I understand the explanation, but still don't understand why it's called "harmonic"? What does harmonic have to with anything ? Can someone please explain..

[@luck3949]

Seems that any harmonic function is a good roof.

[@jesussanchezherrero5262]

Hey that was a great video! I was wondering what you meant by the harmonic functions giving the notion of stability. I think you meant something like what you explain in the Heat Equation video (on 3blue1brown) that an average of higher or lower temperatures to the actual point excites the transfer of heat. Do you mean that? And by stability, you mean a state non changing in time or is it more general? Thanks for the content

[@kisho2679]

What's the physical meaning/interpretation (usage)?

[@dannis5165]

THANK YOU FOR THE INTUITION!!

[@shubhanjalitiwari381]

My god the...voice 😭💘

[@jeanphilippepuyravaud439]

Great explanation.

[@emlmm88]

Is it messed up that my first exposure to this was in complex analysis?

[@laurahoughton1289]

Yes, my first exposure as well!!

[@giorgioyoung102]

No and you should notice where this harmonic function came from, e^xsin(y)=Im(e^z)

[@1MstAkey]

Thank You

[@walikhantutorial9715]

Which software used to deliver lecture please tell me

[@SuperPomax]

Good video, yet I don't get Spherical harmonics. I don't get why a sphere is harmonic

[@YourMakingMeNervous]

Spherical harmonics is a term that refers to harmonic functions that are defined using the basis coordinates of a sphere instead of the cartesian x,y,z space!

[@mrx42]

What is your software to draw graph please ?

[@zairaner1489]

Can this "on average they are on the same height" by formalized via integration, maybe line integration?

[@jackozeehakkjuz]

Yes. Actually it is the integral of the function on a circle of radius r arround a point, then you divide by 2*pi*r in order to take the average and finally you make the limit so that r -> 0.

[@mattikemppinen6750]

Very helpful conceptually, thank you! =)

[@vinbo2232]

Thanks

[@TheMASTERshadows]

Thank you very much

[@volkerblock]

Very good Video.I like it. But , please use another mikrophon (I am a little bit deaf and, worse, german)

[@firstnamelastname3106]

thank you !

[@pinandhito.dharma]

at this point, I agree that math can be fun

[@bismarcklaplace2460]

Thanks !!!

[@alanwolf313]

Video: starts Me, hearing the teacher's voice: *real s*** 3B1B*

[@elementsofphysicalreality]

I was hoping this was about tonics, dominants and subdominants lol

[@variancewithin]

the way this guys talks reminds me a lot of how JB Strabul speaks. NOt a bad thing

[@287MdSahil]

this was great

[@EdwinCloud]

is this analytic geometry?

[@The112Windows]

Isn't it multivariable calc?

[@makehumanitygreatagain8128]

Couldn't it be both?

[@sagnikmondal4058]

No.

[@aydenmartinez9142]

Music really is math

[@tianlilee14]

brilliant

[@shaambhukhari7720]

Give two examples of harmonic function

[@ryand391]

So is this complex analysis

[@finaltheorygames1781]

I don't get the whole meaning of what it means when a function is harmonic.

[@Gandalfbaws]

spasiba

[@organiccaveman]

can you guys found the next video he mentioned at last ??????

[@aSeaofTroubles]

What series is this a part of?

[@nathanielsaxe3049]

Khan Academy Multivariable Calc kzbin.info/www/bejne/gIK2dGOieLV6aJY

[@DeusExAstra]

I recognize that voice...

[@yli5531]

The person behind the scene changed in this video compared to the last few, right?

[@chenlecong9938]

有三个人一起创作视频的。主要是khan

[@MayankGoel447]

No

[@y0n1n1x]

Last

[@mightyparry]

Well there is a familiar voice...

[@accountman9082]

Lord 3b1b