Lectures related to Fourier Series: Extension and Periodicity

Explores differentiating under the integral sign and continuity of functions in integrals.

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Covers the properties of harmonic functions and the concept of mollification.

Covers the isomorphism of coverings and the lifting theory.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores the Cauchy-Schwarz inequality in integrals and functions, offering a comprehensive understanding of its applications.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

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

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Explores real functions, covering parity, periodicity, and polynomial functions.

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Covers functions, including even and odd functions, periodicity, and function operations.

Covers Fourier series, periodic functions, and Fourier transforms.

Covers the analysis of functions, composition, and mathematical induction.

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

Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.

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

Explores differentiability, propositions evaluation, and solutions to equations using derivatives.