Description
This is an open book open notes exam but you are not allowed to access the Internet or ask anyone for help. The answers must be 100% your work. Show your work as unsupported answers may receive no credit.
- (5 points) Find the extremal of the functional
- (5 points) Consider the functional
- (2 points) Find the Euler-Lagrange equation of the above functional.
- (1 point) Find r such that y(x) = xr solves your Euler-Lagrange equation.
- (2 points) Find the extremal of J[y] satisfying the boundary conditions y(1) = 0,
.
- (5 points) Determine the extremal of the functional
where α,β are nonzero constants for each of the following boundary conditions:
- y(0) = 0, y(1) = 1.
- y(0) = 0, y(1) is free.
- y(0) and y(1) are both free.
