Green-Riemann Formula: Curvilinear Integrals

This lecture introduces the Green-Riemann formula, starting with definitions of connectedness by arcs in R and then focusing on R². It covers the concepts of simply connected sets, homotopy, and smooth arcs in the Oxy plane, emphasizing the parametrization of curves and the formation of closed simple curves. The instructor explains the construction of smooth closed curves and open simply connected domains in the Oxy plane, illustrating the boundary of such domains. The lecture concludes with the application of these concepts to define a smooth closed piecewise arc in the Oxy plane within an open simply connected domain.