Stokes' theorem (which might well be called the curl theorem if we wanted to be more consistent in our terminology) is equally critical to our future work:
Again, read as ``the open surface bounded by the closed curve , and note that there is an implicit direction in this equation. In particular, you must choose (from the two possible choices) the direction for that corresponds to the right-handed direction around the loop . In words, if you curl the fingers of your right hand around in the direction in which you wish to do the integral, your thumb should point ``through'' the loop in the direction you must select for the normal.
We can once again derive an additional form of the curl theorem/Stokes' theorem:
Note well that the has been moved to the front!