Surface integrals, orientation, Stokes' Theorem, Divergence Theorem

NOTES ON STOKES' THEOREM: The orientation of the surface S must agree with the orientation (direction of travel) of the boundary C when applying Stokes' Theorem. S must have a boundary, thus it won't enclose a three-dimensional region. Also note, "curl" appears on the surface integral side. NOTES ON DIVERGENCE THEOREM: The orientable surface S must enclose a three-dimensional region D. Thus, S is the boundary of D, and S itself has no boundary. Also note that no differential operator of any kind (whether curl or something else) appears in the integrand on the surface integral side.

Видео Surface integrals, orientation, Stokes' Theorem, Divergence Theorem автора Графические гаджеты