Lectures related to Poisson Problem: Periodic Boundary Conditions

Poisson Problem with Neumann Boundary Conditions

Explores the Poisson problem with Neumann boundary conditions and periodic boundary conditions in mathematical modeling and fluid dynamics.

Boundary Conditions and Basis Decomposition

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

Vibrating Strings: Mathematical Analysis and Fourier Series

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Unbounded and Bounded Systems: Fourier Methods

Explores the spectral properties of unbounded and bounded systems using Fourier methods and emphasizes the importance of choosing the correct representation for different boundary conditions.

Green's Function: Theory and Applications

Covers the theory and applications of Green's function in solving differential equations.

Diffusion Equations: Green's Function Approach

Covers the analysis and solution of diffusion equations using Green's function approach and discusses boundary conditions and dimensional analysis.

Poisson Problem: Fourier Transform Approach

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

Fourier Series and PDE Solving

Covers the solving of PDEs using Fourier series and boundary conditions of Neumann and Dirichlet type.

Numerical Flow Simulation: Boundary Conditions

Covers the numerical simulation workflow for fluid dynamics, focusing on boundary conditions and their importance for solution convergence.

Green Functions: Dynamics

Covers the solution of Maxwell equations using advanced and retarded Green functions, focusing on electrostatics with general boundary conditions.

Time-dependent Diffusion: Fourier Trick

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Heat Transfer Applications

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

Fourier Analysis and PDEs

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

Transient Regime: Heat Transfer

Explores the transient regime in heat transfer, solidification, boundary conditions, and heat flux density.

Computational Geomechanics: Unconfined Flow

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

Naturally Curved Hair in 2D

Explores the behavior of naturally curved hair in a 2D space under gravity.

Numerical Flow Simulation: Basics and Boundary Conditions

Covers the basics of numerical flow simulation, including boundary conditions and geometry reduction.

Beam Analysis: Distributed Loads and Internal Forces

Covers beam analysis under distributed loads, focusing on internal forces and moments.

Image Processing I: Filter Design and Boundary Conditions

Explores filter design, boundary conditions, Fourier-domain filtering, and useful smoothing filters for image processing.