Green's Theorem: Boundary and Normal Vectors

This lecture covers the concepts of boundaries, normal vectors, and the application of Green's theorem in transforming integrals from surfaces to curves. The instructor clarifies the importance of positively oriented boundaries and explains how to define the normal vector to the boundary. By using a regular domain with positively oriented boundaries and a continuous vector field, the theorem allows for the transformation of surface integrals into line integrals, providing a powerful tool for computations. The lecture also hints at the extension of these concepts to 3D scenarios, showcasing the versatility and efficiency of Green's theorem in various applications.