Lectures related to Laplace Equation: Decomposition and Solutions

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

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.