Stokes' Theorem Example // Verifying both Sides // Vector Calculus

In this video we verify Stokes' Theorem by computing out both sides for an explicit example of a hemisphere together with a particular vector field. Stokes Theorem was introduced in the previous video in the vector calculus playlist (see below) and equated the line integral giving the circulation around the boundary curve with the surface integral of the proportion of the curl of the vector field in the normal direction. We finish with a really cool trick, where the old surface can be replaced with an entirely new one that is actually easier to computer.

0:00 Recalling Stoke's Theorem
2:40 Computing Circulation
5:02 Computing Surface Integral
10:40 Replacing the old surface with a new one
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Видео Stokes' Theorem Example // Verifying both Sides // Vector Calculus канала Dr. Trefor Bazett