Let $n(x,y,z)$ be the unit outward normal of the surface $S$ of the cylinder $x^2 + y^2 \leq 1 , 0 \leq z \leq 3$. We have to compute $\int_{S} v.n dS = ?$ where $v = xz \hat{i} + 2yz\hat{j} + 3xy\hat{k}$. the unit normal vector is given by the gradient of $S$, But how to find the gradient I th...