In article <1124303215.77c7216acb8341860620356fb2e914ee@teranews>,
Matt <mmmabos@comcast.net> wrote:
> Is there a way to do a Taylor expansion for a function f(x) where x is a
> p dimensional vector around some vector p0? (not just around one
> component of x)
Its known as a multivariate Taylor series. You can expand
a function of multiple variables around some point p0 in
a vector space. Assuming that x and x0 are row vectors,
f(x) = f(p0) + grad(x0)*(xx0)' + (xx0)*H(x)*(xx0)'/2 + ...
Here grad(x0) is the gradient of f at the point x0, and H(x0)
is the nxn Hessian matrix of second partial derivatives.
You can see that for scalar x, it reduces to the standard
boring old Taylor series.
HTH,
John D'Errico

The best material model of a cat is another, or
preferably the same, cat.
A. Rosenblueth, Philosophy of Science, 1945
