Understanding Positive and Negative Orientation in Curves

This lecture delves into the concept of positive and negative orientation in curves, explaining how the orientation of a curve impacts the direction of the tangent and normal vectors. The instructor clarifies the importance of orientation in computing the normal vector to a curve and demonstrates how to determine positive and negative orientation in closed curves. Additionally, the lecture covers the verification of Green's Theorem through the computation of curvilinear integrals and the application of the divergence theorem in the context of vector fields. The instructor also introduces corollaries related to Green's Theorem, such as the Divergence Theorem and the computation of areas using vector fields.