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need help learning how to type vector problems into wolfram alpha

Posted 9 years ago
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I am trying to see how i can use wolfram alpha pro to assist me with vector problems from my multivariable calculus class. anyways i have a problem like ... Find a potential function for the vector ?eld ?

F (x, y, z) = {z^3 ? 2xy^2, z^2 ? 2x^2y, 3xz^2 + 2yz}

I do not know Wolfram alpha pro, but the command in Mathematica are

    Clear[x, y, z, g];
     f = {z^3 - 2 x y^2, z^2 - 2 x^2 y, 3 x z^2 + 2 y z};
     Curl[f, {x, y, z}]  (*check first if conservative field*)
     (* {0, 0, 0} *)  (*ok it is*)

     DSolve[{D[g[x, y, z], x]== f[[1]], D[g[x, y, z], y]== f[[2]], D[g[x, y, z], z]== f[[3]]},g[x, y, z],{x, y, z}]

     (*   {{g[x, y, z] -> (-x^2)*y^2 + y*z^2 + x*z^3 + C[1]}}  *)     (*this is the potential function g(x,y,z) *)
POSTED BY: Nasser M. Abbasi
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