Vector Calculus: Green's Theorem

This lecture covers the demonstration of the divergence theorem in regular R3 by parts, the calculation of the curl of a vector field, and the application of Green's theorem to relate line integrals to surface integrals. The instructor explains the parametrization of surfaces, the concept of circulation of a vector field along a curve, and the modeling of magnetic fields using Ampère's law. The lecture concludes with a practical example of calculating the magnetic field around a current-carrying wire and introduces the upcoming topic of complex analysis. Students are also informed about an upcoming practice exam to prepare for theoretical and computational questions.