Lecture1 - Part 3of3 - Finite Differences - Intro. to Euler-Lagrange Eq. and Variational Derivative
This lecture is part 3 of 3. It introduces an alternative (more general) finite-difference scheme for solving the simplest variational problem introduced in parts 1 and 2. In this lecture, we consider what happens when we fix x_k and treat y_k as variable (Finite Difference Method #.2). In the limit as n tends towards infinity, we arrive at the famous Euler-Lagrange equation. I show how this equation reduces to the equation arrived at in the previous part (part 2of3) of this lecture.
This lecture is part 3 of 3. It introduces an alternative (more general) finite-difference scheme for solving the simplest variational problem introduced in parts 1 and 2. In this lecture, we consider what happens when we fix x_k and treat y_k as variable (Finite Difference Method #.2). In the limit as n tends towards infinity, we arrive at the famous Euler-Lagrange equation. I show how this equation reduces to the equation arrived at in the previous part (part 2of3) of this lecture.