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Re: Symbolic tensor analysis in Mathematica 8

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125543] Re: Symbolic tensor analysis in Mathematica 8
  • From: fabrizio <sgrignuoli at science.unitn.it>
  • Date: Sun, 18 Mar 2012 02:43:12 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hy,
first question,
if I understood correctly, your answer is something like this:
Dim = 3;
V = Table[v[i], {i, 1, Dim}]
in this way you creates a vector with v[1],v[2] and v[3] as components.
second question:
In this way you can, for example, also define it with a loop for:
For[i=1,i<=Dim,i++,
V[[i]]= "what you want" 
];
To tell to mathematica that for example v[1] is a function of x,y,z you can use two way.
I suggest to use this one.
v[1]=x^2+y^2+z^2 (for example);

I wrote for you this very simply example:

Dim = 3;
V = Table[v[i], {i, 1, Dim}];
V[[1]] = x^2 + y^2 + z^2;
V[[2]] = x^3 + 4 y^3 - z^2;
V[[3]] = x - y + z;
D[V, x, y, z] 
 
the last line evaluates the total derivative of the vector V .If you want the partial derivative 
D[V, x] respect to x
D[V,y] respect to y
D[V, z] respect to z

Fabrizio



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