Numerical Integration: Euler Method

This lecture introduces the progressive Euler method for numerically approximating solutions of ordinary differential equations. Starting with the exact solution of a physics problem, the instructor guides through the implementation of the method in Python. The lecture covers the basics of Euler method, its application to first-order ODEs, and the graphical representation of approximate and exact solutions. It also delves into the concept of Cauchy problems, convergence of numerical methods, and the use of Runge-Kutta methods. The presentation includes detailed explanations, examples, and diagrams to aid in understanding the numerical integration process.