I'm trying to understand Stokes' Thm better (Not just how to apply it, but when to apply it, and why it is so important). If someone could help me clear this up, that would be cool: Lets say we have a surface integral: [tex] \int \int_S \vec F \cdot d\vec S [/tex] and for some reason we can easily formulate a path around the surface. (I guess this next portion is the part I'm confused, or curious about) We would then be able to use Stokes' Theorem if: [tex] \oint \vec U \cdot d\vec r = \int \int_S \nabla \times \vec U \cdot d\vec S [/tex] IF we can come up with a vector that satisfies: [tex] \nabla \times \vec U = \vec F [/tex] right? Any insight on this would be awesome... I don't know why it's so hard for me to get a feel for the theorem. Thanks in advance.