Lectures related to Finite Difference Methods: Linear Systems and Band Matrices

Explores finite differences for solving linear systems from PDEs iteratively, emphasizing convergence criteria and exercises on singularities.

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

Covers the solution of linear systems using direct methods and the evolution of matrices.

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

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

Covers the numerical approximation of PDEs and examples of nonlinear behavior.

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

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

Explores linear systems, Gaussian elimination, LU decomposition, and matrix types.

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

Explores the evolution of PDEs, focusing on heat and wave equations in 1D, uniqueness of solutions, and the d'Alembert formula.

Covers the basics of the Finite Element Method (FEM) for linear and nonlinear partial differential equations.

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

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

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

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

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

Explores direct methods for solving linear equations, LU factorization, Gass elimination, and computational complexity.

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

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