Diffusion Equations: Green's Function Approach

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Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

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Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

Covers the analysis of incompressible fluid flow and numerical solutions in fluid dynamics.

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

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

Covers the basics of continuum mechanics, including forces transmission, energy conservation, and body motion geometry.

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

Explores diffusion in incompressible fluid mechanics, covering continuum description, Fick's law, and steady-state solutions.