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...Section stokes theorem objectives use to evaluate line and surface integrals assignments read problems challenge maple commands lecture is really an extension or variant of green s stoke theo rem relates a integral over around the boundary orientation needs induce positive c this means that if you walk in direction region labeled as both your text then always on left want for same reasons might some are easier instead vice versa following let be oriented piecewise smooth bounded by simple closed curve with f vector eld whose components have continuous partial derivatives open ir contains z dr zz ds work two examples using example problem we given yzi xzj xyk rrs see can rewrite cf r t dt part paraboloid x y lies above plane upward circle at so parametric representation cos sin set since xy but coordinate constant thus evaluated class questions check answer what changes lying e i j k where rst octant only would need separate into its before evaluating could case easy represent curl beco...