Lectures related to Stokes Theorem

Discusses the mathematical concepts of cylinders and their parametrizations, including surface area, volume, and related exercises.

Covers the Green and Gauss theorems, focusing on their applications in vector calculus.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

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

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

Covers the concept of line integrals and their application in vector fields.

Covers the approximation of functions in Sobolev spaces using smooth functions.