Finite Difference Methods: Linear Systems and Band Matrices

Related lectures (30)

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Explores the parabolic heat equation evolution and numerical solution methods.

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

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

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

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Introduces ordinary differential equations, their order, numerical solutions, and practical applications in various scientific fields.

Covers band matrices, linear systems, stability analysis, and boundary corrections in numerical methods.

Covers implicit schemes in numerical analysis for solving partial differential equations.

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

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