I'm glad to see the dot operator and I'm trying to get around some limitations since it doesn't understand general matrices and vectors. Consider the expression T(g(a)).h(a). In my case, T is a transpose operation and a is a vector. I'm trying to differentiate it with respect to a. The general derivative is of the form, T(h(a)).diff(g(a),a) + T(g(a)).diff(h(a),a). My question is how to get Maple to understand how to apply this particular derivative rule. If I just blindly apply the derivative, I get the second term fine, but the first term is not in a useful form. Basically, I need to tell diff how to carry out the product rule for these non-commutative terms.

I've been trying figure out how to code up arbitrary volume and surface integrals in Maple. I know that Maple has the VectorCalculus package but there doesn't appear to be a way to specify a volume integral (where the infinitesimal is dV). Also, there doesn't seem to be a way to specify a surface integral without defining the surface in advance (i.e., integrate over S with an infinitesimal of dS). In both cases, I'd like to have general integrals where I can specify the bounds at a later time (e.g., inert integrals). I know that there is the triple integrals in the student package but they aren't the same as a volume integral.

Does anybody know of a way to extract derivatives of a specified function from an expression? For example, if I have the expression, int(D[6](F)(x,t,y(x,t),diff(y(x,t),x),diff(y(x,t),t),diff(diff(y(x,t),t),x))*diff(diff(yv(x,t),t),x),t = t1 .. t2); I'd like to be able to get the derivatives of yv(x,t) which in this case would be, diff(diff(yv(x,t),t),x). I ask because I'm trying to systematically integrate a set of expressions by parts where I know that the dv term always contains a certain function's derivatives and I can stop integrating by parts once I have just the function.