Multi-variable first-order perturbation analysis?

*To*: mathgroup at smc.vnet.net*Subject*: [mg104481] Multi-variable first-order perturbation analysis?*From*: AES <siegman at stanford.edu>*Date*: Sun, 1 Nov 2009 17:53:58 -0500 (EST)*Organization*: Stanford University

I have a half dozen functions f1, f2, ?, each of which depends on some or all of half a dozen variables x1, x2, ?, all of these functions pretty vanilla in character. Objective is to obtain the same number of first-order perturbation expansions df1, df2, ?, where df1 means all the relevant derivatives (df1/dx1) * dx1 + (df2/dx2) * dx2 + . . . evaluated at initial values x1=x10, x2=x20, ? and so on -- all of this totally symbolic in character, and with *no* cross-products dx1 dx2 or similar. I know I can code this various ways -- but what's the "cleanest" way to accomplish this? [Notes: The results for df1, df2, ? don't have to be neatly readable, e.g., the terms multiplying dx1 for a given dfi don't all have to be neatly collected inside a single set of brackets; the resulting expressions just have to be correct. And, by "cleanest" I don't necessarily mean the tersest, most arcane way of coding this.]