Lectures related to Carathéodory's existence theorem

Covers the numerical resolution of differential equations, focusing on first-order equations and Euler diagrams.

Covers ordinary differential equations with separable variables and the conditions for unique solutions in EDOs.

Explores energy conservation in wave equations, emphasizing uniqueness, existence of solutions, and stability.

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Explores Lipschitz conditions in differential equations and their implications on solutions and properties.

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

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Explores the Cauchy problem, focusing on the existence and uniqueness of solutions.

Explores the general framework of ordinary differential equations and their significance in various fields.

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

Discusses global solutions in differential equations and the conditions for their existence and uniqueness.

Explores the system of linear first order ODEs and scalar linear ODEs with examples and solutions.

Explores asymptotic solutions of differential equations and their behavior in different scenarios.

Covers the existence and uniqueness theorem for Cauchy problems and explores global solutions of differential equations.

Explores the existence of global or maximal solutions for a specific differential equation.

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

Summarizes the method for solving homogeneous systems of linear equations and discusses their properties and solutions.

Covers the solution of ODEs using Picard's iteration and Riccati equations.

Explores first-order linear equations, existence theorems, and integral solutions in differential equations.