Fields from Potential: Derivation and Curvilinear Integral

This lecture covers the derivation of fields from a potential, including the conditions for a function to derive from a potential and the concept of symmetric Jacobian matrix. It also explores the curvilinear integral and its application in the fundamental theorem of integral calculus, as well as the extension of results to continuous functions. The lecture concludes with the necessary conditions for a domain and the equivalence between deriving from a potential and the integral over closed curves being zero.