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Re: Partial derviatives in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg95771] Re: [mg95753] Partial derviatives in mathematica
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Tue, 27 Jan 2009 06:56:15 -0500 (EST)
• Reply-to: hanlonr at cox.net

Partial derivatives are done with D

D[f[x, y], x]

Derivative[1, 0][f][x, y]

For further info, execute:

?D


Bob Hanlon

---- xareon at gmail.com wrote: 

=============
Hi all, i got thi Newton-Raphson mathematica code:



Code:

F[{x_, y_}] = {f1[{x, y}], f2[{x, y}]};

jacobian[{x_, y_}] = Transpose[{\[PartialD]x F[{x, y}], \[PartialD]y F
[{x, y}]}];

MatrixForm[jacobian[{x, y}]];

NewtonSystem[X0_, max_] := Module[{},
         n = 2;
         k = 0;
         Dp = {0, 0};
         P0 = X0;
         F0 = F[P0];
         Print["F[", P0, "]=", N[F0, 3]];
         P1 = P0;
         F1 = F0;
         While[k < max,
                k = k + 1;
                 P0 = P1;
               F0 = F1;
                J0 = jacobian[P0];
                det = Det[J0];
                If[det == 0, Dp = {0, 0}, Dp = Inverse[J0].F0];
                P1 = P0 - Dp;
               F1 = F[P1];
         Print["F[", P1, "]=", N[F1, 3]];];];



where f1[x, y] and f2[x, y] are defined in this way



Code:

f1[{x_, y_}] = n/x - Sum[y*Exp[-y*A*t[i]]*T[i+1], {i, 0, n-1}];

f2[{x_, y_}] = n/y - Sum[A*t[i], {i, 0, n-1}] - Sum[x*Exp[-y*A*t[i]]*T
[i+1], {i, 0, n-1}] + Sum[y*x*A*t[i]*Exp[-y*A*t[i]]*T[i+1], {i, 0,
n-1}];




T[i] e t[i] are functions defined point-by-point  (from T[1] to T[50]
and from t[0] to t[49]) with this syntax:


Code:

t[0] = *un certo numero*; t[1] = *un altro numero*; t[2] = *ancora un
altro numero*; ... T[1] = *numero*; T[2] = *altro numero* ...



I got an error on the second line



Code:

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}]}];".




This line should define a 2-variables function named jacobian, that is
a jacobian matrix. I'm not a Mathematica-guru, but the code should
work anyway.

What's wrong there? f1 and f2 seem well defined (i.e., when i write
them Mathematica doesn't say nothing bad):



Thank you all ;)