Lectures related to Laplace Equation in Polar Coordinates

Boundary Conditions in Harmonic Functions

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

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

Boundary Conditions and Basis Decomposition

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

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

Groundwater Flow: Laplace Equation and Boundary Conditions

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

Uniqueness Results for Poisson Equation

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

Rayleigh Taylor: Normal Mode Expansion

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

Heat Transfer Applications

Explores the applications of the Fourier equation in heat transfer phenomena.

Symmetry in Finite Element Models

Explores using symmetries in Finite Element models to simplify boundary conditions and reduce rigid-body motions.

Electric Field Between Infinite Planes: Laplace Equation

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

Computational Geomechanics: Unconfined Flow

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

Internal Heat Transfer Effects

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

Laplace Equation in a Rectangle

Explores the Laplace equation in a rectangle using the separation of variables method.

Rectangular Waveguides: TE and TM Modes

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

General Existence Results for PDEs

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

Fourier Analysis and PDEs

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

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Poincaré - Friedrichs: Theorem and Kernel Inequality

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

Computational Geomechanics: Unconfined Flow Analysis

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

Maxwell Equations: Green Functions for Electrostatic Problems

Explores the use of Green functions for solving electrostatic problems with different boundary conditions, emphasizing the importance of choosing the correct function.