Lectures related to Finite Elements: Basics and Precision

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Finite Element Method: Weak Formulation and Applications

Explores integral and weak formulations in Finite Element Method applications.

Covers the application of finite element methods to solve boundary value problems in one dimension.

Covers the Heisenberg group representation, including shifts, multiplications, and the Fourier transform, extending to finite fields and metaplectic groups.

Characteristic Polynomials and Similar Matrices

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

Linear Independence and Basis

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

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.