Lectures related to Sub/Super Harmonic Functions

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

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

Covers the approximation of functions in Sobolev spaces using smooth functions.

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

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

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

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

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

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

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Explores the properties and transformations of theta functions, including modular forms and lattice levels.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

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

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

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

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

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

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

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.