Lectures related to Submanifolds: Locally Deformable into Linear Patches

Explores basic functions and criteria in quadrangular finite elements using the finite element method.

Explores comparing tangent vectors and parallel transport on manifolds.

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Explores the dynamics of singular Riemann surface foliations, focusing on vector fields, linear parts, and coordinate changes.

Covers the basics of linear mapping and coordinate systems.