Видео: https://youtu.be/qlX8Nz5u_os
What do you know about types of derivatives?
Derivatives of order pi in calculus there may be.
But we will start from simple and will now introduce
The mapping from R^n to the space R^m.
Construct Jacobian, write it down now if you can.
Give definition here, and new theory will appear.
We choose a point at which we calculate derivative,
And from this point we now begin our dance.
Delta x is change of our argument,
Multiply it by our function’s gradient.
Also add infinitely small o...
Oppa nabla style! These are gradients. Oppa nabla style!
Let us then suppose that our function will be complex.
At this time we’re repeating our previous definitions.
But now multiplication is for complex numbers,
Then we will repeat this crazy song again.
(Repeat)
It is not all, it is far from all.
We have not considered functional spaces at all.
It may be Frechet, and it may be Gateaux,
And the weak derivatives play an important role.
This is Sobolev!
These are integrals. These are limits.
Let’s repeat again.