Lecture
Introduction and Theoretical Results
Related lectures (31)
Harmonic Forms and Riemann Surfaces
Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.
Cauchy-Euler Equations
Covers the definition and solution of Cauchy-Euler equations, which are second-order differential equations with specific form and solutions.
Differential EquationsMOOC: Numerical Analysis for Engineers
Covers the numerical resolution of differential equations, focusing on first-order equations and Euler diagrams.
Existence of y: Proofs and EDO Resolution
Covers the proof of the existence of y and the resolution of EDOs with practical examples.
Cauchy-Lipschitz Theorem: Local Existence and Uniqueness
Explores the Cauchy-Lipschitz theorem for local existence and uniqueness of solutions to differential equations.
Cauchy Problem: Initial Conditions
Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.
Existence and Uniqueness of Solutions
Explores the existence and uniqueness of solutions for differential equations through local Lipschitz continuity and the Cauchy-Lipschitz theorem.
Differential Equations: Solutions and Periodicity
Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.
Harmonic Forms: Main Theorem
Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.
Ordinary Differential Equations: Non-linear Analysis
Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.