Lectures related to Polygonal chain

Covers the definition and properties of Laurent series, including convergence and function expansion.

Explores Catalan numbers in cutting polygons, parenthesis structures, and Dyck paths.

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

Explains the definitions of cones and cylinders as ruled surfaces and how to find tangent planes to them.

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.