Lectures related to Classification of PDEs: Linear, Semi-linear, Quasi-linear

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

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

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

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

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Introduces the basics and classification of partial differential equations, including notation, definitions, and examples.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Covers ODE RK schemes, including explicit RK stages and accuracy computation.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

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

Covers the analysis of speed variation using differential equations and small time intervals.

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Covers the organization of linear algebra course and exercises for civil engineering and environmental sciences students.

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

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

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

Explores characteristic curves and solutions in partial differential equations, emphasizing uniqueness and existence in various scenarios.

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.