Curvilinear Integrals: Tangent Vectors and Oriented Arcs

This lecture covers the definition of a smooth oriented arc and the tangent vector at a point on the arc, as well as the concept of curvilinear integrals along the arc. It explains how to calculate the tangent vector, the unit tangent vector, and how to perform integrals along a curve. The lecture also discusses the importance of the orientation of the arc in these calculations.