The Lagrangian

Рет қаралды 478,318

7 жыл бұрын

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How a special function, called the "Lagrangian", can be used to package together all the steps needed to solve a constrained optimization problem.

Пікірлер: 192

@Rubikorigami 7 жыл бұрын

Wait... Could it be... 3Blue1Brown?!

@Birdman12468 7 жыл бұрын

Kappy Engi Kappington that's what I was wondering as well!

@SoumilSahu 7 жыл бұрын

it is

@FlorinToader 5 жыл бұрын

it is

@keithwatkins6465 4 жыл бұрын

3Blue 1Brown Wave

@anirudhkotiyal2640 3 жыл бұрын

Yes ...he used to work there ....

@flomoose7315 Жыл бұрын

This man is bringing me single handedly through my economics undergraduate degree!!! Keep it up and thank you!

@Vaibhav101 6 жыл бұрын

Perhaps the best explanation on the Internet. Thanks 3B1B !

@andeslam7370 3 жыл бұрын

can't agree more....

@sjoerd7512 Жыл бұрын

Is this actually 3Blue1Brown??

@universal69 Жыл бұрын

@@sjoerd7512 yes he worked with khan academy

@WigglyHedgehog 7 жыл бұрын

The usefulness of the Lagrangian equation is not only because it's easier to program into a computer. The lambda can also be interpreted as the amount that R(x,y) would increase if the constant b in the constraint function could be relaxed by one unit. That can also be explained given only the geometric setup, but it's a little easier to calculate it given the Lagrangian.

@rokarus7658 4 жыл бұрын

This also justifies its usage in economics - marginal propensity to save and to consune are the bedrock for Keynesian (read: modern) economics.

@vambire02 2 жыл бұрын

Very clear and concise explanation. Thanks a lot. I had the lagrange function in many courses at college but this is the first time I fully understand the concept behind it.

@NoahTopper 3 жыл бұрын

I just...can't believe that I took a whole course in Optimization and nobody ever told me this is where the Lagrangian comes from. It's so clear.

@borninthenorthMi 3 жыл бұрын

Well, I guess they had to take this part out to make room for the course in deconstructionist critical-race mathematics. Universities have become a straight-up scam.

@98danielray 2 жыл бұрын

@@borninthenorthMi it is ok, michalina. you will go to a decent university someday

@borninthenorthMi 2 жыл бұрын

@@98danielray name one

@jasonports8517 2 жыл бұрын

@@borninthenorthMi CRT in maths? nice meme

@RaviShankar-jm1qw Жыл бұрын

Arguably the best explanation of Lagrangian on the internet! Thanks @Khan Academy!

@eughyuck 2 жыл бұрын

Thank you! I have this issue in lectures where I frequently zone-out/forget to turn up so I appreciate your thorough clear explanation which leaves no knowledge gaps :)

@moussatouhami7567 7 жыл бұрын

hi khan family ,i'm very happy to find your videos on the internet free and very comfortable to watch your videos it's help me so much and we need more video about electromagnetism circuits magnetic (hyper circuits&circuits composite..& Coils ...)

@danielc4267 7 жыл бұрын

3:06 "why is lambda so hard to draw?" lol

@dangiscongrataway2365 7 жыл бұрын

Is this 3blue1brown talking?

@mr.mirror1213 4 жыл бұрын

yes

@erikhicks6184 Жыл бұрын

@@mr.mirror1213 no

@principaljpnce9802 4 жыл бұрын

Simplest way of explaining the most complicated looking concept. Hats off to you Sir 👌👌👌

@luiskraker807 10 ай бұрын

I was struggeling a bit with understanding the concept of Lagrangian, but this videos of you helped me a lot. Thanks!

@joezhang2633 7 жыл бұрын

Awesome explanations! I've been struggling to figure this out for 3 years in my Ph.D. and this is the best one!

@hichamboukharsa1639 4 жыл бұрын

Could you explain me why lambda not equal to 1? Is shouldn't be 1 because the gradient is calculated for the same point (tangent) Thnx

@anmol.sharma010 4 жыл бұрын

@@hichamboukharsa1639 lambda could be 1 and it could not be. But there is no guarantee. And yes the gradient is being calculated at the same point, but we are calculating the gradient with respect to two separate functions and then equating the two. The two gradients will be proportional and in order to remove the proportionality, we add lambda(a constant). If It is still unclear, see the previous video on lagrangian multipliers. Hope this helps!

@harisrashid0773 2 жыл бұрын

And our mad processor is teaching us this in bachelors electronics and communication engineering here in India.

@Kentucky_Fried_Man Жыл бұрын

@@harisrashid0773 Same, Economics

@Kentucky_Fried_Man Жыл бұрын

Hope you got your Ph. D

@silverlining6824 3 жыл бұрын

Turning some calculus into geometry is helpful to those who visualize. Thank you!

@cesaaargm 2 жыл бұрын

thanks. I am studying the mechanical aspect of the lagrangian, applied to a mechanical system that is conservative. This approach is useful to widen my view of the probelam!

@ull893 6 жыл бұрын

Welcome Blue and Brown guy! You are such a great teacher !

@lewistian7975 4 жыл бұрын

That perfect red curve looks satisfying

@Chalisque 7 жыл бұрын

The art of creatively adding zero: B(x,y)=4 means B(x,y)-4 = 0 means lambda(B(x,y)-4) = 0 means R(x,y) - lambda(B(x,y)-4) = R(x,y) provided the constraint holds. So lambda only has an effect when the constraint does not hold. Minimising the magnitude of influence of lambda (i.e. how much effect changing lambda has) is equivalent to making that influence zero (since influence=0 can be attained when the constraint is), and making that influence zero for nonzero lambda means obeying the constraint. I always enjoy cleverness like this in mathematics. Zero is a creature with many disguises.

@gavtriple9 3 жыл бұрын

Very similar to a Perturbation

@aeroscience9834 7 жыл бұрын

Dang it. I was hoping for Lagrangian mechanics.

@zairaner1489 7 жыл бұрын

Well that is what is behind the first Lagrange formalism for mechanics ;)

@user-vb4eq4vx1q 7 жыл бұрын

Same :(

@eulefranz944 7 жыл бұрын

we are in 2. semester and learn Lagrange...

@eulefranz944 7 жыл бұрын

We learn both actually^ :/

@Chalisque 7 жыл бұрын

Before you try to get your head around Lagrangian mechanics, it is perhaps useful to understand the Lagrangian itself, and the intuition behind it. When applying it to mechanics, you don't want to still be thinking about what Lagrangians are and how they work.

@shutupimlearning Жыл бұрын

Apparently this is going to be important in my classical mechanics and QM class. Thanks!

@ES-qe1nh Жыл бұрын

I mean yeah classical mechanics is basically just fancy constrained optimization with some cool mathematical theorems behind it (

@tudor6210 3 жыл бұрын

Such a nice presentation of the Lagrangian!

@saurabhsharma7123 6 жыл бұрын

Such an excellent tutorial!

@naviderfani 4 жыл бұрын

Thanks for the great video. Would you please make a video about Lagrange duality.

@juliechoudury6912 7 жыл бұрын

Please do a video explaining the inter-temporal rate of substitution

@peterfisher3161 3 жыл бұрын

I just clicked on this video, because I trust Khan Academy as a knowledge source. But Grant was a welcome surprise.

@sarahmushroomkiller9233 6 жыл бұрын

omg, 3Blue1Brown never fail you. Always can find the best explanation from him! BRAVO!

@sigeeky 4 жыл бұрын

Great video, now it's clear and easy to understand! THANK YOU!

@ClosiusBeg 2 жыл бұрын

Could anybody explain: What the difference between Lagrangian multipliers and sequential quadratic programming (SQP)?

@zachmiles3433 Жыл бұрын

Khan academy is the GOAT of mathematical/physics topics!

@johnphillips4887 Жыл бұрын

Very helpful - as always! Didn't ZZ top write a song about La Grange?

@liabraga4641 6 жыл бұрын

3Blue1Brown ❤❤❤ thank you!!

@1722mayur 2 жыл бұрын

Imagine this guy being your university professor for every course you take.

@edwinyangtw 3 жыл бұрын

Could you please put the link of the next course blow for convenience.

@sleeepymoe 3 жыл бұрын

12:25 he mentioned modeling the revenue or the budget as functions, any idea how to calculate such functions?

@Stardoll0tutorials 3 жыл бұрын

i won`t for sure need this in life , but i will for sure need this to pass my maths exam .

@g3452sgp 6 жыл бұрын

Which playlist does this video belong to? I want to see more.

@The_Chowmein_Papi 4 жыл бұрын

kzfaq.info/get/bejne/rN2FiZV6qbK0aIU.html

@MaxwellsWitch 6 жыл бұрын

Wait... 3Blue1Brown? Awesome!

@hardikgupta4038 5 жыл бұрын

usually we have many constraints and not just one. suppose there was another constraint, how will the equation change?

@momolesumo201 4 жыл бұрын

I think you can add a variable and have '

@franciscorivas4036 4 жыл бұрын

Can I suggest adding the link to the full playlist so one can find more videos related to the current video?

@benjaminrichards4709 3 жыл бұрын

You'll be able to find it on the Khan Academy website in the Multivariable Calculus section

@tiberium87 11 ай бұрын

Why does Sal sound like Grant when he explains math?

@MrCobraTraders 3 жыл бұрын

Best best best best explaination ever!!!

@user-iv9nj9nx8q Ай бұрын

I think the constraint equation should actually be x^2 + y^2 =16 to match the red circle because when y=0 and x=4 (where the red circle intersects the x-axis on the right), x^2 would be 16. Or else the red circle should be made smaller to have a radius of 2 units.

@thinkanddo2352 6 жыл бұрын

Thank you!

@SuperDeadparrot Жыл бұрын

Is it really necessary to include the b in R - lambda B? When you take the derivatives in later steps that will just go to 0 because it is constant. Is it really necessary to take dL/dlambda? You get information that was given in the first place.

@SergioLopezSoriano 2 жыл бұрын

still the best explanation in youtube

@jordia.2970 6 ай бұрын

Seems crazy that, given how simple the explanation of where the Lagrangian comes from, that equation is commonly given without further justification... Makes one wonder if some teachers even know what they are doing beyond following a recipe...

@hakeemnaa 8 ай бұрын

Tring to find the maximum when L does not change when x change, that when it reaches maximum( or minimum) same as y also, lima since at that point, it does not change, because of changing in direction ( increase to decrease)

@ugursoydan8187 4 жыл бұрын

why we define the action integral of lagrangian times dt? has we got a proof for it?

@uvenga 2 жыл бұрын

When can see the function is less difficult to understand. Thank you

@TLumVids 6 жыл бұрын

There is a big mistake in this video. Optimizing with constraints is not the same as Optimizing the Lagrangian without constraints unless the function we are optimizing is convex and the constraint is affine!

@mariabardas2568 6 жыл бұрын

thanks

@sachin_suthar 5 жыл бұрын

Nice explanation

@johnmelon45 2 жыл бұрын

God I wish you were my teacher for advanced diff eq!

@waiitwhaat 2 жыл бұрын

Ah the sweet voice of Grant. What a pleasure

@Saptarshi.Sarkar 4 жыл бұрын

We can get both the maximum and minimum using this. Right?

@mariofelipequevedolozano3659 3 жыл бұрын

I have a question, in some textbooks the Lagrangian is written as ''L(x,y,lamda)=F(x,y)+Lamda*G(x,y)'' where G(x,y) is the constriction, and yours is L=GradF-Lamda*GradG, in the end the systems of equations that must be solved are different by a minus sign and it changes quite a bit the results. Why are this equations different? I mean, I understood your explanation and it's pretty cool, but i couldn't use your equation because it was different from the one I saw in cass.

@_nttai 3 жыл бұрын

I had the same question too. After some googling I found out that you'll get different values of λ (positive or negative) but the same solutions in terms of x, y, and your objective function. Using the Lagrangian you want to find the point (x,y) so that ∇f+λ∇g=0 which means the points such that ∇f and ∇g are linearly dependent so it is irrelevant the condition ±λ. In other words, you only care about x and y

@hbbh 3 жыл бұрын

@@_nttai thanks

@Adrian124 3 жыл бұрын

"You'd never have a budget that looks like a circle" Huh, didn't think so

@shibaneethakur5035 3 жыл бұрын

Sir which book you have preferred for this

@imbarron5015 Жыл бұрын

What are the prequisite of langrangian?

@Urias_Velasquez 6 жыл бұрын

This vídeo has an huge error! The graphic o Gradient is not what they paint. The Gradient is the parallel plane to the vector they said.

@pengzhou8926 3 жыл бұрын

非常的透彻

@sherifffruitfly 2 жыл бұрын

"lagrangian is nothing more than repackaging what we already knew". this seems false, and towards the end you finally mentioned why. the transform to lagrangian reduces the constrained optimization problem to an UNconstrained optimization problem by embedding the problem into "lambda space". and that's SUPER significant.

@baruahsarthak_ 10 ай бұрын

Superb!

@kamitube1059 4 жыл бұрын

why do we substract the b ?

@tashitashi9997 2 жыл бұрын

Can somebody explain to me how the gradient of R is promotional of B...please

@johndwolynetz6495 5 жыл бұрын

The Lagrangian function is now my god.

@iamjisiah3065 7 жыл бұрын

What drawing thing is that

@vitorbraga28 6 жыл бұрын

what is the program that he uses for the graph?

@legendariersgaming 5 жыл бұрын

I am pretty sure it is a custom program, probably adapted from his Python library that he uses to animate his videos on 3Blue1Brown

@BKAM78 3 жыл бұрын

where is the next video??!!

@DarwinsChihuahua 7 жыл бұрын

Sounds like the name of a Highlander spin-off.

@NatCo-Supremacist 7 жыл бұрын

I wonder if this is related to Lagrangian points in Astrophysics in any way.

@abhayshankar8762 4 жыл бұрын

XORRE yeah. Figured out by same guy.

@hichamboukharsa1639 4 жыл бұрын

Why gradient of R not equal to gradient of B ? Is should be equal because we calculate the gradient in the same point

@yanceq2690 3 жыл бұрын

Can somebody please tell me, what is this all for? I mean, if we can use the Pythagorean Theorem to find lengths in triangles, what can we use this for?

@robertbrandywine 2 жыл бұрын

Solving motion problems in mechanics. Sometimes difficult problems in Newtonian mechanics are much easier using Lagrangian mechanics.

@bxmoreno1988 7 жыл бұрын

Do a video on Bitcoin !!

@raulreyes7125 7 жыл бұрын

DANG THE DRAWING

@DarkCloud7 6 жыл бұрын

Danke

@Jimmy-vy7lk 5 жыл бұрын

I tried to scroll up the video.

@TheAmigodaniel 2 жыл бұрын

What courses in mathematics do I have to have in my body before going inside the famous Lagrangian? Somebody can explain?

@robertbrandywine 2 жыл бұрын

It looks like you just have to know how to take partial derivatives. Those are covered, I believe, in Calculus III (maybe Calculus II).

@minsoe8014 7 жыл бұрын

Could someone please tell me that the reasons to assume the gradient equal to zero?

@McRaylie 7 жыл бұрын

You are not assuming the gradient is zero, you are looking for values, so it equals zero.

@iwtwb8 7 жыл бұрын

There's surely deeper meaning, but he shows from about 6:00 onward that the way L is constructed makes it so that the gradient of R and B are proportional and that the value of B equals the constraint.

@krasnoyarsk512 5 жыл бұрын

I didn't get it :( too complicated or just too much writing I don't know..

@mooloongee9595 4 жыл бұрын

Thats the problem with American videos.

@mithsaradasanayake3211 2 жыл бұрын

I notice that voice from anywhere

@kamitube1059 4 жыл бұрын

why is the gradient equal to 0

@Postermaestro 6 жыл бұрын

Commenting to spread on the tubes!

@faraza5161 7 жыл бұрын

Hi.. I am just curious.. Which software has been used in the making of this video?

@nabzo46 7 жыл бұрын

Microsoft paint

@McRaylie 7 жыл бұрын

I think he said it was Python once, but not sure

@Chalisque 7 жыл бұрын

The pen sketching stuff, I use mypaint, though I don't know what he uses. Set the brush to work like a small pen, and nicely you can paint where you like and mypaint automagically extends the canvas for you. Also, though 3b1b doesn't use this for these videos, geogebra is worth playing with.

@pi17 4 жыл бұрын

Grant Sanderson in the house ladies and gentlemen!

@fahimhossain165 4 жыл бұрын

Yasser Abu Mostafa himself sent me here!

@hello_neighbor0_05 Күн бұрын

Hey, hey , grant?

@nu11y61 6 жыл бұрын

3Blue1Brown!

@ranvirsinha9149 2 жыл бұрын

Can someone pls explain the Standard Model Lagrangian as a 15 year old wld understand it?😅

@vladzyk10 Жыл бұрын

He kills me with... it's just artificial fanciness... "it looks like you'redoing advancedmath but it is just artificial xD"

@bakibalcioglu5871 5 жыл бұрын

Wait... I know you

@zack_120 2 жыл бұрын

Why the term "gradient" is used instead of velocity or slope in this video, any hidden meaning?

@robertbrandywine 2 жыл бұрын

And why is the arrow he drew perpendicular to the slope?

@ES-qe1nh Жыл бұрын

The gradient vector is defined as an n-tuple of partial derivatives of some multivariate function

@craigmalcom6294 3 жыл бұрын

why are the gradients not equal to each other but proportional?

@joluju2375 3 жыл бұрын

Why would they be equal ? R & B are 2 different functions, and we are interrested in contour lines to be tangent. So far, no need for gradients. The trick is that for lines to be tangent, their perpendiculars (gradients) have to be aligned. V1 = λ V2 is merely the way to say the vectors are on the same line. Aligned, or proportional, or colinear are synonyms here.

@ES-qe1nh Жыл бұрын

They are linear combinations of eachother, kind of by definition if you look at the constraint function

@bobbywinston116 Жыл бұрын

"And all these letters make it look like were using some advanced math" Me, a normal guy who looked up a math video to see how stupid it will make me feel: 🤓🤡😶