Introduction to ODEs: System of 1st Order ODEs

This lecture introduces Ordinary Differential Equations (ODEs) as essential tools in physics for describing continuous dynamics. It covers the basics of ODEs, including the distinction between ODEs and Partial Differential Equations (PDEs), initial value problems, and linear, second-order ODEs. The instructor emphasizes the importance of ODEs in physics, illustrating their application in classical mechanics, fluid dynamics, electrodynamics, and quantum mechanics. The lecture also discusses the formulation of general systems of first-order ODEs, autonomous systems, and linear ODEs. Additionally, it explores the existence and uniqueness of solutions to initial value problems, providing examples to enhance understanding.