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. .
- (5 points) Find the extremal of the functional
subject to the boundary conditions
- (5 points) Find the extremal of the functional
How many boundary conditions do you need to specify at the two endpoints to determine the extremal uniquely?
- (5 points)Find the extremal of the functional
subject to the conditions y(0) = 0,y(1) = 0 and the constraint , where A is a given constant. You need to find the Lagrange multiplier as a function of A and cannot leave your answer in terms of the Lagrange multiplier.
