Lectures related to Dirichlet problem

Partial Differential Equations: Laplace Equation

Explains the Laplace equation in 2D with mixed boundary conditions.

Covers the general existence result for the Laplace-Dirichlet problem and the properties of the Newtonian potential.

Covers general elliptic equations, including Dirichlet problems and boundary conditions.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Variational Formulation: Weak Formulations & Galerkin

Explores weak formulations, Galerkin method, and variational formulations in finite element methods.

Poisson Problem: Periodic Boundary Conditions

Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

Discrete Pressure Modes in Lecture 4

Explores discrete pressure modes and their impact on system analysis.

Fourier Series and PDE Solving

Covers the solving of PDEs using Fourier series and boundary conditions of Neumann and Dirichlet type.

Correlation Functions of Harmonic Oscillator

Explores correlation functions, Gaussian integrals, and perturbation theory in quantum field theory.

Introduction to PDES

Covers harmonic functions, Laplacian operator, Dirichlet and Robin problems, and sub-harmonic functions in Partial Differential Equations.

Elastic Membrane Boundary Problem 2D

Covers the elastic membrane boundary problem in 2D, exploring mathematical formulation and solution methods.

Green Functions: Methods and Applications

Explores methods to compute Green functions and the behavior of conductors in classical electrodynamics.

Dirichlet Problem on the Ball

Covers the Dirichlet problem on the ball and the solution to the Dirichlet problem on the half plane.

Stability and Convergence in Numerical Methods

Explores stability, consistency, and convergence in numerical methods, emphasizing the importance of order consistency and boundary conditions.

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Laplace Equation in Polar Coordinates

Explores the Laplace equation in polar coordinates and its solution process through separation of variables.

Laplace Equation: Uniqueness and Fundamental Solution

Explores uniqueness results and the fundamental solution of the Laplace equation.

Boundary Conditions in Harmonic Functions

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Dirichlet Problem for Laplace Equation

Explores the Dirichlet problem for the Laplace equation and Green's function.

Green Functions in Electrostatics

Explores methods to construct Green functions in electrostatics, including image charge and eigenfunction expansion, under different boundary conditions.