Euler-Lagrange Equations

This lecture covers integrals depending on a parameter, the least action principle, and the derivation of Euler-Lagrange equations. The slides discuss the Euler-Lagrange equations for a given function, the necessary conditions for local extremum, and the concept of space-time. The equations are derived step by step, showing the importance of the necessary conditions for extremum. The lecture also explores the application of Euler-Lagrange equations in various scenarios, emphasizing the significance of these equations in mathematical analysis. The examples provided illustrate the practical use of the equations in solving optimization problems.