Understanding Taylor's Theorem w/ Two Variables

[Petrus]

Hello MHB,
I understand taylor series proof with one variable but how does it work with Two variabels? is it pretty much the same? The one I understand is

Taylor's theorem - Wikipedia, the free encyclopedia
Go to proofs Then it's the one under "Derivation for the integral form of the remainder"

Regards,
$$|\pi\rangle$$

 

[I like Serena]

Hello MHB,
I understand taylor series proof with one variable but how does it work with Two variabels? is it pretty much the same? The one I understand is

Taylor's theorem - Wikipedia, the free encyclopedia
Go to proofs Then it's the one under "Derivation for the integral form of the remainder"

Regards,
$$|\pi\rangle$$

Yep. It's pretty much the same.
Note that the symbol $D^\alpha f(\mathbb a)$ is a vector for $\alpha = 1$, a matrix for $\alpha = 2$, a 3-dimensional matrix for $\alpha = 3$, and so on.