Homework #5
Assigned: Feb. 14, 2012
Due: Feb. 21, 2012
Points: 60
Additional points for work that is beyond instructor's expectation!

1. 40 points
   Write down the Euler-Lagrange equations and boundary conditions for the variable end conditions for single, two, and three independent variables for n function and up to two derivatives.
2. 20 points
   Given two points in the xy-plane, namely (x1,y1) and (x2,y2), and a curve given by f(x,y) = 0 passing through those points, find a second curve of length L passing through the same two points and enclosing maximum area. Pose the problem first and the write the differential equation and boundary conditions. Solve it numerically by taking a particular f(x,y) = 0 and some values for x1, y1, x2, and y2.