Hi guys! I need your help! How can i compute the div(grad(cos(wt)))??
Normally "grad" is applied to a function of 2 or 3 variables: if f is a function of x, y, and z, f(x,y,z) then $\displaystyle grad f= \frac{\partial f}{\partial x}i+ \frac{\partial f}{\partial y}j+ \frac{\partial f}\partial z}k$. The div of a vector function $\displaystyle f_xi+ f_yj+ f_zk$ is the scalar function $\displaystyle \frac{\partial f_x}{\partial x}+ \frac{\partial f_y}{\partial y}+ \frac{\partial f_z}{\partial z}$. So div(grad(f)) would be $\displaystyle \frac{\partial^2 f}{\partial x^2}+ \frac{\partial^2 f}{\partial y^2}+ \frac{\partial^2 f}{\partial z^2}$.
With a single variable like t, one way to interpret this is with that single variable replacing one of the x, y, z variables, the others 0. In that case, we would have "div(grad(f))" equal to $\displaystyle \frac{d^2f}{dt^2}$, just the second derivative. Another way to interpret this is as a one component of a two or three component vector. But then I don't know how you would apply "grad" to a vector valued function. Perhaps it would help if you posted the entire problem.