Lectures related to Dynamics of Singular Riemann Surface Foliations

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Covers the basics of linear mapping and coordinate systems.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Explores linear dependence and independence of vectors in geometric spaces.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers linear systems, vector subspaces, and the kernel and image of linear applications.

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Covers the extraction of bases from families of vectors and the concept of coordinate application in vector spaces.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers linear independence, bases, change of basis, and vector representation.

Explores vector spaces, linear independence, and spanning sets in linear algebra.

Explores comparing tangent vectors and parallel transport on manifolds.