Partial Differential Equations: Characteristics and Solutions

Related lectures (28)

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

Introduces partial differential equations, covering derivatives, special cases, transformations, and the Jacobian matrix.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Explains partial derivatives, Hessienne matrix, and their properties.

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

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

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

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.