Time-dependent Diffusion: Fourier Trick

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Explores linear partial differential equations, elliptic PDEs, Laplace equation, boundary conditions, and classical solutions.

Discusses complex analysis, focusing on Laplace transforms, Fourier series, and the heat equation's solutions and uniqueness.

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

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

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

Covers the fixed energy propagator, including its analytic structure and examples of free particle and barrier penetration.

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Covers the illustration of a stationary wave on a vibrating plate and spatial solution formulas with specific boundary conditions.