Lectures related to Approximation in Sobolev Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores the effective version of the explicit formula in Number Theory, focusing on smooth functions and integral calculations.

Covers the proof and identification of isomorphisms in the Seifert van Kampen theorem.

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Covers Hilbert's theorem, direct methods, and Sobolev spaces, including classical and modern methods.

Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.