Introduction to Ordinary Differential Equations

This lecture introduces ordinary differential equations (ODEs) as equations involving one unknown function and its derivatives, contrasting them with partial differential equations. The instructor explains the concept of ODEs, their order, and provides examples of first and second-order ODEs. The lecture covers linear and nonlinear ODEs, the Euler method for numerical solutions, and the progressive Euler method for approximate solutions. Practical examples and Python coding for solving ODEs are demonstrated. Additionally, the lecture discusses the significance of initial conditions in determining solutions and the applications of ODEs in various fields like physics, chemistry, and biology.