Distribution theory

Related lectures (31)

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

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.

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

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

Covers Laplace transforms in chemistry and engineering, exploring their applications and properties.

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.

Covers harmonic functions, Laplacian operator, Dirichlet and Robin problems, and sub-harmonic functions in Partial Differential Equations.

Explores the parabolic heat equation evolution and numerical solution methods.

Covers the theoretical study of Elliptic Partial Differential Equations, including classical and weak solutions.

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 basics of Partial Differential Equations, including the Laplace equation, heat equation, and wave equation.

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Covers the basics of Partial Differential Equations, including well-posedness, operators, and classification of physical PDEs.

Explores the application of Fourier transform to PDEs and boundary conditions.

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

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

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

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