Section 10.1 part b. Looking at "del dot" or diverge to get eq. 10.1-9

>  restart;
>  with(linalg):
>  v:=(x,y,z,t)->vector([vx(x,y,z,t),vy(x,y,z,t),vz(x,y,z,t)]);
>  q:=(x,y,z,t)->vector([qx(x,y,z,t),qy(x,y,z,t),qz(x,y,z,t)]);
>  g:=(x,y,z,t)->vector([gx(x,y,z,t),gy(x,y,z,t),gz(x,y,z,t)]);
>  s:=vector([x,y,z]); The position vector
>  IKE:=(x,y,z,t)->rho(x,y,z,t)*(U(x,y,z,t)+Vsq(x,y,z,t)/2);
>  ddq:=(x,y,z,t)->diverge(q(x,y,z,t),s); Note the second argument 
is s. Thus del dot q is an abbreviation for the terms involving conduction 
in eq. 10.1-8. This gives us del dot q.
>  ddvike:=(x,y,z,t)->diverge(scalarmul(v(x,y,z,t),IKE(x,y,z,t)),s); 
This is the del dot v*rho(U+(1/2)v^2) term in 10.1-9
>  ddvike(x,y,z,t);
>  ddvp:=(x,y,z,t)->diverge(scalarmul(v(x,y,z,t),p(x,y,z,t)),s);
>  ddvp(x,y,z,t); Here is del dot v*p. Note tha Maple automatically 
splits up the product.
>  tau:=(x,y,z,t)->matrix([[txx(x,y,z,t),txy(x,y,z,t),txz(x,y,z,t)],
[tyx(x,y,z,t),tyy(x,y,z,t),tyz(x,y,z,t)],[tzx(x,y,z,t),tzy(x,y,z,t),
tzz(x,y,z,t)]]); Note that txy is the y component of the stress acting 
on a plane perpendicular to the x axis.
>  taudv:=multiply(tau(x,y,z,t),v(x,y,z,t)); tau dot v
>  taudv[1]; It has 3 components. Here is the first one.
>  ddtdv:=(x,y,z,t)->diverge(taudv,s); del dot tau dot v. These are 
the same 18 terms that you find in eq. 10.1-8
>  RHS:= (x,y,z,t)->-ddvike(x,y,z,t)-ddq(x,y,z,t)+
rho(x,y,z,t)*multiply(v(x,y,z,t),g(x,y,z,t))-ddvp(x,y,z,t)-
ddtdv(x,y,z,t);
>  RHS(x,y,z,t); The right hand side of eq. 10.1-9
>  Accum:=dV*(IKE(x,y,z,t+dt)-IKE(x,y,z,t));
>  LHS:=(x,y,z,t)->limit(Accum/(dt*dV),dt=0);
>  eq9:=LHS(x,y,z,t)-RHS(x,y,z,t); eq. 10.1-9 in expanded form. 
This is the reason for using the compact notation shown in the text.