Lectures related to Laplace Equation in a Rectangle

Internal Heat Transfer Effects

Covers internal heat transfer effects in heterogeneous reactions, emphasizing dimensionless numbers and transport effects.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Linear PDEs of Order 2

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

Groundwater Flow: Laplace Equation and Boundary Conditions

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

Laplace Equation in Polar Coordinates

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

Rectangular Waveguides: TE and TM Modes

Covers guided propagation in rectangular waveguides for TE and TM modes.

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Boundary Conditions in Harmonic Functions

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

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Uniqueness Results for Poisson Equation

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

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Poincaré - Friedrichs: Theorem and Kernel Inequality

Explores the Poincaré - Friedrichs theorem and kernel inequality in constant conditions and boundary uniqueness.

Numerical Groundwater Flow Resolution

Explains the numerical resolution of groundwater flows using finite differences and demonstrates the method with Excel.

Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Electric Field Between Infinite Planes: Laplace Equation

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

Analysis IV: Laplace Equation Solutions

Explores Laplace equation solutions through separation of variables and general solution writing for complex problems.

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

Electric Displacement in Dielectrics: Gauss's Law and Boundary Conditions

Introduces the concept of electric displacement vector D and explores boundary conditions in dielectrics.

Recent Advances in the Dimer Model and Its Applications

Covers recent advancements in the dimer model, emphasizing its applications in probability and conformal field theory.

Green Functions: Theory and Applications

Explores the theory and applications of Green functions in classical electrodynamics, emphasizing the importance of choosing the right function based on boundary conditions.