Відео

How did you do the animations?

Very helpful

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牛而逼之

After this video, I was sure that everything could be simplified enough to be explained to a child.

Thanks! I had to watch a few times, but it makes sense now

The animation at 2:50 was incredible, definitley ignited a light bulb moment in my head.

Fantastic

literally awesome

You like this video ? Wait to watch it while listening to Brahms : gavotte in A major

Man I love you great video thank you

this video is low key the best math lesson even made, congrat s

single-handedly saving my vector calc grade!

Almost perfect video but Jacobi matrix and Jacobian determinant came out of nowhere and that don't help to understand the essence

Please come back!

You got me in 2:49. I was so easily going with your flow. Haha

What I do not think is explained is why the determinant of this is precisely what you need to make the conversion. Maybe it is based on top of a prior video where this meaning is explained. Anyway, good video and well explained. I also like the comment about how this can be understood without Jacobians. I always have used that way of thinking, but thinking about the same topic in multiple ways is helpful

Nothing less than amazing!

Is this morphoculer??

This is high quality 👌

In order to actually find the extremum of a function subject to constraints, it's typically necessary to determine the actual values of the Lagrange multipliers. One of the better behaved algorithms is to replace the scalar Lagrange multiplier by a convex curve which can be adjusted by means of an iterative solution process. This method, known as the Generalized Lagrange Multiplier Method is mathematically related to another important branch of mathematics called Duality Theory. Such Primal-Dual Methods were explored by myself and Professor Dimitri Bertsekas in the early 1970s, when we were both at Stanford University. The resultant algorithm is spelled out in one of Dimitri's textbooks on the subject of Optimization Methods.

This was so great… but how about when constraints are inequalities?

Clear and succint!

Idea for finding the extrema on a boundary: use that boundary's parametric equation and plug it into the function which will result in a 1d function. From that it's as trivial to fund the extrema as it would be on a 1d function!

I suck at maths, i picked extended maths for highschool because i couldnt force myself to learn it on my own I wasnt satisfied to i went on for engineering and i must say i hate it even more but now i can do anything I do triple integrals daily but man this visualisation was cool, the only thing it lacked is showing what the values of the function are as the function 'swipes' to visually prove that it moves too and set one at constant rate of change and integrate it to the constant rate, then the other as a constant rate and integrate it that way so that it doesnt matter whether you integrate x, y or whatever in whatever order but it would still work.

Worse explanation I have seen in ages :-) All the rhetorical questions that distract the concentration and then, "guess what? This isn't the surface I have been talking about, it is this different one. Surprise!" and more than once. I'm bookmarking it as a very good example of pedagogy gone wild.

What does it mean that the gradient of g at a point (a,b) is perpendicular to the constraint (level) set (curve) g^{-1}(k)? It means that the g-surface gradient is perpendicular to the level curve tangent vector, meaning (grad g)(a,b)•(x’(t),y’(t)) = 0, where t is such that (a,b)=(x(t),y(t)). That is, the directional derivative (rate of change of g) in the direction of the tangent vector of the level curve is 0. That is intuitive, as the g-surface gradient points in the direction the value of g grows fastest, while moving on the level curve in its tangent vector direction the value of g does NOT change (‘cause the curve is, well, level!)!

Thank you❤🌹🙏

This is awesome

you could also say that the unit/normalised gradient vector f is equal to the unit/normalised gradient vector g

This is legit the best video on this topic. Awesome work.

How to prove that the Jacobian determine is true?

In my opinion, good mathematical education should strive to develop your mathematical intuition, which in turn you would be able to turn into formality. This video is literally perfect.

best explanation ever without killing some of my brain cells

I can’t thank you enough 🙂🥲🥲

I guarantee that 99% of the comments claiming this video finally made them understand are still utterly incapable of solving a problem involving Lagrange multipliers. That is to say, such youtube videos only provide an illusion of understanding. This is the flaw of the educational sector of youtube; they peddle understanding but the people never learn anything. But hey, as long as they feel they learned something, that is all that matters. Also, places like Brilliant do not help you learn either; it is curated to allow you to progress on easy problems

nnnDope af my dude

Suppose is 9r-r cube to be integrated. Not 9-r square

Wtf

Jacobian conjecture tru or Rong? I think wrong 🤔 ⚠️⚠️⚠️

Best explanation ever on the Jacobian. Amazing. I graduated almost a decade ago, but this was fun to revisit.

Read the Wikipedia article and then came back here. While there it was fairly understandable, here the explanation was absolutely brilliant.

Thank you so much

Cannot thank you enough for this explanation

@11:04 but aren't all tangents to g(x,y) is parrallel to all tangents of the boundary curve f(x,y). So won't we consider every point on f(x,y) a maxima or minima?

That explanation was stellar! You broke down a tough concept without frying anyone's brain cells.

Great video!

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I love you so much. This genuinely help me a ton.

so the gradient of f at the max has no z component?