Lectures related to Approximation of Functions: Principles and Theorems

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Explores uniform convergence of series of functions and its significance in complex analysis.

Explores limits, convergence, and boundedness of functions and sequences.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores the limit of the quotient for sequences and the periodicity of functions.

Covers the limited development of integration and methods for calculating the limit development of functions and antiderivatives.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Explores the continuity of functions in R² and R³, emphasizing accumulation points and limits.

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Discusses norms, distances, and the classification of open and closed sets in mathematical analysis.

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Explains limits at right and left endpoints, convergence conditions, and function behavior near specific values.

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Explores Riemann integral, convergence, and limit processes, emphasizing continuity and monotonic convergence.

Explores convergence criteria for series and functions, including the squeeze theorem and D'Alembert's criterion.

Explores the pointwise convergence of Fourier series and its applications in optimal transport.