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Explores ion crystals, conductors, and Poisson/Laplace equations in electrostatics, including charge behavior and energy calculations.

Uniqueness Results for Poisson Equation

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

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Linear PDEs of Order 2

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

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Green's Functions in Laplace Equations

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

Electrostatics and Green's Functions: Mathematical Methods

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Electrostatics: Charge Distributions and Conductor Properties

Explores charge distributions, conductor properties, and the concept of a Faraday cage in electrostatics.

Elliptic Partial Differential Equations

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

Groundwater Flow: Laplace Equation and Boundary Conditions

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

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.

Partial Differential Equations

Covers the basics of Partial Differential Equations, including the Laplace equation, heat equation, and wave equation.

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.

Electric Fields and Currents

Explores electric fields, energy storage, charge displacement, DC currents, and historical aspects of electricity.

Partial Differential Equations: Laplace Equation

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

Electric Charges and Fields

Covers electrostatics, Coulomb force, electric field calculations, potential, Gauss's law, conductor behavior, and field line representation.

Laplace Poisson Equation

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

Electric Fields and Gauss's Law

Explores charged particles, electric dipoles, Gauss's law applications, conducting spheres, and the circuital law.