Lectures related to Harmonic function

Harmonic Forms: Main Theorem

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

Fundamental Solutions of Laplace Equation

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Forced Harmonic Oscillator: Resonance Phenomenon

Covers the forced and damped harmonic oscillator, including the harmonic solution and resonance phenomenon.

Dirichlet Problem on the Ball

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

Harmonic Forms and Riemann Surfaces

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

Boundary Conditions in Harmonic Functions

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

Uniqueness Results for Poisson Equation

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Groundwater Flow: Laplace Equation and Boundary Conditions

Explores the Laplace equation, harmonic potential, and boundary conditions in groundwater flow, with practical examples.

Heat Equation: Stationary Distribution

Explores the heat equation, equilibrium equations, heat flux, and harmonic functions in heat distribution.

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Finite Element Method: Galerkin Method

Covers the Galerkin method in the Finite Element Method for solving non-homogeneous Dirichlet problems.

Poisson & Laplace Equations: Understanding Electrostatics

Explores the derivation of a potential function without knowing the charge distribution and its practical implications in analyzing electrostatic problems.

Harmonic Potential: Schrödinger Equation and Eigenstates

Covers the Schrödinger equation, wave function normalization, and eigenstates.

Harmonic Functions: Properties and Mollification

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

Brownian Motion: Einstein Derivation

Covers the derivation of Brownian motion by Einstein and Langevin equations, including the Chapman Kolmogorov equation.

Maximum Principle in Harmonic Functions

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Partial Differential Equations: Classification and Solutions

Covers the classification and solutions of partial differential equations, including Laplace transform and separation of variables techniques.

Introduction to PDES

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

Convergence and Divergence of Series

Covers the definitions of convergent and divergent series and explores the harmonic series and alternating series.