Example 1

Consider the curvilinear coordinate system x=u-v, y=u+v, w=z^2 for z>=0 (we need this to have an inverse!).


  Clear[x,y,z,u,v,w]


  x[u_,v_,w_]:=u-v
  y[u_,v_,w_]:=u+v
  z[u_,v_,w_]:=w^2


  scalefactors[x,y,z][u,v,w]

Answer:


  {a,b,c}=scalefactors[x,y,z][u,v,w]


  Clear[F]
  F[u_,v_,w_]:={u w,v w, u v}


  newdiv[F][u,v,w]


  newcurl[F][u,v,w]


  Simplify[%]