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
I know I can code this various ways -- but what's the "cleanest" way to
[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.]
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