Lectures related to Laplace's equation

Fundamental Solutions of Laplace Equation

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

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

Laplace Equation: Decomposition and Solutions

Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.

Properties of Fundamental Solutions: Green's Representation Formula

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

Uniqueness Results for Poisson Equation

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

Fundamental Solutions of Laplace Equation

Explores fundamental solutions of the Laplace equation and their physical interpretation.

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Linear PDEs of Order 2

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Dirichlet Problem for Laplace Equation

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

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.

Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including electrostatics and advection-diffusion-reaction equations.

Notion of Transfer Function

Introduces the concept of transfer function in dynamic systems analysis.

Laplace Poisson Equation

Covers the Laplace and Poisson equations, the heat equation, and the wave equation in physics.

Theoretical Study of Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including classical and weak solutions.

Laplace Equation: Uniqueness and Fundamental Solution

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

Basic Potential Flows: Sources, Sinks, and Vortices

Covers the concept of basic potential flows, including sources, sinks, and vortices.

Partial Differential Equations: Laplace Equation

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

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Electric Field Between Infinite Planes: Laplace Equation

Focuses on finding the electric field between infinite planes in electrostatics.