15 сент. 2021 г. · 1)I meant that we are warping a 2D space ,but we are considering a 3D function(with 2 inputs and 1 output). 2)We are transforming the basis ...

17 дек. 2015 г. · In our case, we have a 2 variable function (or actually two 2 variable functions: r and θ) instead of a 1 variable function, but it's the same ...

6 авг. 2023 г. · Derivatives are a way of taking a linear approximation of a function at a point. Their interpretation as rates of change is a special case of ...

26 янв. 2016 г. · The gist of it is that up to a good approximation the coordinate transformation is given by just multiplying by the Jacobian, J (and some ...

19 нояб. 2017 г. · Small insight that helped me understand change of variables. I'm talking specifically about the jacobian. I've already learned all my calculus ...

14 апр. 2014 г. · I read somewhere that the matrix approximates a point in space and the derivatives are the directions of the local basis vectors, so is it used ...

26 окт. 2013 г. · In terms of coordinate system transformations, it tells us how a tangent vector expressed in one basis can be expressed in another basis.

28 авг. 2020 г. · I have a question regarding using the jacobian when changing variables in double integrals yet I think the answer is above me at the moment ...

3 мая 2021 г. · The determinant of the jacobian is then the volume of the parallelepiped spanned by these new basis vectors. So the jacobian measures how ...

23 сент. 2021 г. · The transformation law for a vector coordinates is v' = J v (that you have done) and for a vector basis a' = J-1 a, where J is the jacobian.