Distributions and Laplace Transform: Key Concepts

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Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Covers the properties and applications of the Laplace transform in solving differential equations.

Explores solutions of differential equations and properties of functions.

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

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

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

Explores exact linearization, determining conditions and transformations using Lie bracket and hook of Lie.

Covers second-order linear homogeneous differential equations and their solutions.

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.