Lectures related to Curvilinear Integrals and Conservative Fields

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Covers surface integrals, divergence theorem, and regular domains in 2D and 3D.

Explores notational meaning in Analyse III through examples of shear flow and rotational equations, emphasizing the significance of vector fields and line integrals.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Green's Theorem: Surface Integrals

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Divergence and Stokes' Theorems

Introduces the divergence and Stokes' theorems, comparing surface and volume integrals, and explains parameterization of surfaces and boundaries.