Lectures related to Weak Formulations & Solutions: Elliptic Problems

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

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

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

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers weak solutions in the finite element method, emphasizing continuity and the Cauchy-Schwarz inequality.

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

Covers conditions, loops, functions, and graphics in R programming with practical examples.

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

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

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

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

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Covers the definition and properties of convolution of two functions and explores radioactive material decay rates.

Covers the study of convergence of sequences, integrals, and functions.

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

Provides solutions to an Analysis I exam, covering various topics.

Series covers spherical coordinates, harmonics, Legendre polynomials, and angular momentum.

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

Covers the proof of the existence of y and the resolution of EDOs with practical examples.