Approximations (Taylor Expansions) as a function of the point of expansion

Getting Mathematica to represent a general change in a function--multidimensional versions of Taylor expansions

This is  symbolic representation of a first order expansion (keeping all terms) of a function near x,y,z

Using normal converts the approximation into an expression, but higher order terms are still present

The next step eliminates second- and third-order terms… (remember, dx, dy, and dz are small)

Created by Wolfram Mathematica 6.0  (20 September 2007)