Ordinary Differential Equations: Basics

This lecture covers the basics of ordinary differential equations (ODEs), focusing on equations of the form y' = f(t, y) with initial conditions. It explores the existence and uniqueness of solutions, both globally and locally, and extends to higher dimensions and orders. The lecture also discusses the connection between different generalizations of ODEs and introduces the concept of Lipschitz functions. Through examples and proofs, the instructor demonstrates how to find solutions to ODEs and emphasizes the importance of understanding the behavior of the functions involved.