Re: Multi-variable first-order perturbation analysis?

• To: mathgroup at smc.vnet.net
• Subject: [mg104572] Re: Multi-variable first-order perturbation analysis?
• From: dh <dh at metrohm.com>
• Date: Wed, 4 Nov 2009 01:34:56 -0500 (EST)
• References: <hcl3i9\$blv\$1@smc.vnet.net>

```
Hi,

what you are looking for is called the Jacobian and may be obtained by "D":

funs = {f1[x1, x2], f2[x1, x2]};

D[funs, {{x1, x2}}] /. {x1 -> x10, x2 -> x20}

Daniel

AES wrote:

> 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.]

>

```

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