1. Find the extremal of the functional
subject to the boundary conditions y(0) = 1,y(1) = 0,z(0) = 0,z(1) = e.
2. Find the extremal of the functional
subject to the boundary conditions
3. Find the extremal of the functional
How many boundary conditions do you need to specify at the two endpoints to determine the extremal uniquely?
4. Find the extremal of the functional
subject to the conditions y(0) = 0,y(1) = 0 and the constraint
5. Find the extremal of the functional
subject to the conditions y(0) = 0,y(1) = 1 and the constraint = 1. For this problem you may stop after expressing y(x) in terms of the multiplier λ but this should be the only unknown constant. For a challenge, determine λ to finish solving the problem.
