Very good video ! Why is it that the Jacobian is the matrix of these partial derivatives ?

A true masterpiece

The video was phenomenal and truly amazing; thank you for providing such valuable content!

since you're taking the absolute value of the determinant, the order of the rows and columns doesn't matter. All that matters is that the old coordinates are in the "numerators" and the new coordinates are in the "denominators", and that the variables line up.

Canyou please explain me what will happens if integrate an integral infinit times ????

Wonderful

Very clearly explained, thank you!

why the g surface is not a cylinder surface? Did it make sth wrong?

I mean, wow...

自殺😊

自殺

love it <333

Excellent video and explanation of the Jacobian - thank you for creating !!!

<3

Merci!

Wonderful presentation man... please post more, you are realy great at it...

Really initiatives explanation

For someone who just started learning integral techniques, this video was surprisingly well explained

I wish I could rewire my mind to the point I understood this, I wish for the me that was once in love with math

Very good

Excellent explanation of the Jacobian! If I'd been able to watch this 40 years ago when I first learned this, I could have learned in 15 minutes what took me a month or so to learn!

10:41: but why does the gradient of f have to be perpendicular if the boundery line is flat at that point?

This is god damn clear. Amazing!

this is the best video I've seen on this topic and it still doesn't clear all the doubts about it. Why does it when the tangent line at the 3d curve of g is parallel to the plane xy we can say the gradient at f is perpendicular to the "level curve" of g? Also, given that there are infinite lines perpendicular to a given line, how does it guarantees grad f // grad g?

How did you do the animations?

Very helpful

I get the best education on KZbin. KZbin university the melting pot of universities and independent educators.

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.