Using the Linear Algebra Package to do some Operations connected with the Equations in Chapters 3 & 10

>  restart;
>  with(linalg);
>  s:=[x1,x2,x3];
>  grad(T,s);
>  grad(T(x1,x2,x3),s);

>  v:=(x1,x2,x3)->vector([v1(x1,x2,x3),v2(x1,x2,x3),v3(x1,x2,x3)]);
>  ?diverge  Note this only works on vectors
>  diverge(v(x1,x2,x3),s);

>  q:=(x1,x2,x3)->vector([q1(x1,x2,x3),q2(x1,x2,x3),q3(x1,x2,x3)]);
>  ?dotprod  Note that this only works with vectors!
>  g:=(x1,x2,x3)->vector([g1(x1,x2,x3),g2(x1,x2,x3),g3(x1,x2,x3)]);
>  rho*dotprod(v(x1,x2,x3),g(x1,x2,x3));
>  rho*dotprod(v(x1,x2,x3),g(x1,x2,x3),'orthogonal');

>  tau:=(x1,x2,x3)->matrix([[t11(x1,x2,x3),t12(x1,x2,x3),t13(x1,x2,x3)],[t21(x1,x2,x3),t22(x1,x2,x3),t23(x1,x2,x3)],[t31(x1,x2,x3),t32(x1,x2,x3),t33(x1,x2,x3)]]);
>  taudotv:=multiply(tau(x1,x2,x3),v(x1,x2,x3)); See eq. A.4-19



>  deldottaudotv:=diverge(taudotv,s); Compare to A.4-33 but note that the derivatives of the products are expanded by Maple.
>  divv:=diverge(v(x1,x2,x3),s);
>  ?row
>  tau1:=(x1,x2,x3)->col(tau(x1,x2,x3),1);
>  tau1(x1,x2,x3);
>  dt1:=(x1,x2,x3)->diverge(tau1(x1,x2,x3),s); This is the first component of deldottau as seen in A.4-26
>  dt2:=(x1,x2,x3)->diverge(col(tau(x1,x2,x3),2),s);
>  dt3:=(x1,x2,x3)->diverge(col(tau(x1,x2,x3),3),s);
>  deldottau:=(x1,x2,x3)->vector([dt1(x1,x2,x3),dt2(x1,x2,x3),dt3(x1,x2,x3)]);
>  deldottau(x1,x2,x3);



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