Surface Integrals: Change of Variables

This lecture covers the last chapter on vector calculus, focusing on surface integrals and the divergence theorem. The instructor explains how to compute integrals with several variables and introduces the concept of a change of variables, using examples such as transforming integrals from Cartesian to spherical coordinates. The lecture also delves into regular surfaces, defining them as bounded open domains with continuous partial derivatives. The instructor discusses regular parameterization, injectivity, and the unit normal vector of a surface, emphasizing the importance of these properties in surface analysis.