Study guide and 5 practice problems on:

Determining if a vector field is conservative

If a vector field $\mathbf{F}(x,y)$ is conservative, $\mathbf{F}(x,y) = \nabla \phi(x,y)$ for some function $\phi(x,y)$.
$\mathbf{F}(x,y) = u(x,y) \mathbf{i} + v(x,y) \mathbf{j}$ is conservative if and only if
$$\partial_y u(x,y) = \partial_x v(x,y).$$
To determine if $\mathbf{F}$ is conservative, check if this equality is satisfied.