Partial derviatives in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg95753] Partial derviatives in mathematica*From*: xareon at gmail.com*Date*: Mon, 26 Jan 2009 05:02:34 -0500 (EST)

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 ;)