Theoretical Study of Elliptic Partial Differential Equations

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Covers the theoretical study of Elliptic Partial Differential Equations, including electrostatics and advection-diffusion-reaction equations.

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.

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

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Covers the application of finite difference methods to solve partial differential equations.

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

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

Covers the Laplace and Poisson equations, the heat equation, and the wave equation in physics.

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