Re: Partial derviatives in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg95777] Re: Partial derviatives in mathematica
• From: xareon at gmail.com
• Date: Tue, 27 Jan 2009 06:57:23 -0500 (EST)
• References: <glk1na\$los\$1@smc.vnet.net> <glk80p\$o86\$1@smc.vnet.net>

```On Jan 26, 12:49 pm, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com>
wrote:
> In article <glk1na\$lo... at smc.vnet.net>, xar... at gmail.com wrote:
>
> [snip]
>
> > jacobian[{x_, y_}] = Transpose[{\[PartialD]x F[{x, y}], \[PartialD]y =
F
> > [{x, y}]}];
>
> > Mathematica's kernel warns me with this message when i try to insert
> > it:
>
> > Code:
>
> > Syntax::sntxf: "jacobian[{x_, y_}] = Transpose[{" cannot be followed
> > by
> >     "\[PartialD]x F[{x, y}], \[PartialD]y F[{x, y}]}];".
>
> [snip]
>
> On my system (v6.0), I have got the more meaningful message:
>
> "Derivative::novar:  x cannot be interpreted. A partial derivative \
> requires a subscript differentiation variable. >>"
>
> The variable must passed as a *subscript* (shortcut Ctrl+-, control +
> dash keys) to the symbol partial d.
>
> In[1]:= F[{x_, y_}] = {f1[{x, y}], f2[{x, y}]};
>
> In[2]:= jacobian[{x_,y_}]=Transpose[{\!\(
> \*SubscriptBox[\( \), \(x\)]\ \(F[{x, y}]\)\),\!\(
> \*SubscriptBox[\( \), \(y\)]\ \(F[{x, y}]\)\)}];
>
> (* jacobian[{x_, y_}] = Transpose[{D[F[{x, y}], x], D[F[{x, y}], y]}]; =
*)
>
> In[3]:= MatrixForm[jacobian[{x, y}]]
>
> Out[3]//MatrixForm=
>
>   ({1, 0})             ({0, 1})
> f1        [{x, y}]   f1        [{x, y}]
>
>   ({1, 0})             ({0, 1})
> f2        [{x, y}]   f2        [{x, y}]
>
> Regards,
> --Jean-Marc

thank you for your support, with your hints i've finally managed it to
work. What does it mean that i get this output?

In[46]:= NewtonSystem[{60, 0.0001251648904560967}, 30];
F[{60, 0.000125165}]={-0.0798194, -32172.1}

Inverse::luc: Result for Inverse of badly conditioned matrix
8
{{-0.0138889, -2725.54}, {-2725.54, -9.88747 10 }} may contain
significant numerical errors.
F[{61.3904, 0.0000887939}]={0.0295066, 20324.7}

Inverse::luc: Result for Inverse of badly conditioned matrix
9
{{-0.0132669, -4474.06}, {-4474.06, -2.56154 10 }} may contain
significant numerical errors.
F[{60.2913, 0.0000986483}]={0.00312061, 3127.01}

Inverse::luc: Result for Inverse of badly conditioned matrix
9
{{-0.013755, -3907.89}, {-3907.89, -1.91112 10 }} may contain
significant numerical errors.

General::stop: Further output of Inverse::luc will be suppressed
during this calculation.
F[{59.7233, 0.000101446}]={0.000280961, 135.783}
-7
F[{59.7225, 0.000101523}]={1.55248 10  , 0.153813}
-13            -7
F[{59.7225, 0.000101524}]={7.17371 10   , 3.37372 10  }

I can't understand the error i'm getting: Inverse::luc: Result for