Partial Differential Equations: Basics

Related lectures (28)

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Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

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

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

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

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

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

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

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Explores numerical methods for solving partial differential equations computationally, emphasizing their importance in predicting various phenomena.