L1-Part2of3 - Euler's Method of Finite Differences - M1_Fix y_k - Brachistochrone Sol. (Audio Fixed)
This lecture is part 2 of 3 lectures introducing Euler's Method of Finite Differences as an approach of dealing with optimization of integral functionals.
In this lecture, I solve the Brachistochrone problem using Euler's Method of Finite Differences. There are actully two approaches of solving the problem this way. In this lecture, we will focus on the first method, which is to approximate the integral for total time of traversal using a Riemann Sum where we fix the y-coordinates and treat the x-coordinates as variables. The resulting approximation function can be minimized using traditional methods from multivariable calculus.