Lectures related to Cauchy Problem: Existence and Uniqueness of Solutions

Covers separable differential equations of order 1, defining separable equations and providing examples.

Advanced Analysis II: Cauchy Problem Resolution

Covers the numerical resolution of a Cauchy problem using separation of variables and discusses the conditions for the solution's definition interval.

Semi-groups of Contractions

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

Cauchy Problem Resolution: General Solution Approach

Covers the resolution of a Cauchy problem using a general solution approach for differential equations.

Cauchy Problem: Initial Conditions

Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Linear Differential Equations: Second Order Solutions

Covers second-order linear differential equations, focusing on their solutions and the concept of linear independence among them.

Laplace Transforms: Applications and Convergence Properties

Introduces Laplace transforms, their properties, and applications in solving differential equations.