MATH 401 Midterm: MATH 401 2010 Winter Test 2
Document Summary
Math 401 final exam april 18, 2011. Total: 50 pts: consider the ode problem for u(x): (cid:26) lu := (p(x)u ) + q(x)u = f (x), u(1) = 2, u(2) = 5. 1 < x < 2 (1) (p(x), q(x), and f (x) are given functions). (a) (2 pts. ) Write down the problem satis ed by the green"s function gx(y) = G(x; y) for problem (1). (b) (2 pts. ) Express the solution u(x) of (1) in terms of the green"s function gx(y). (c) (3 pts. ) If p(x) = 1/x2 and q(x) = 2/x4, nd the green"s function g(x; y) for (1). (d) (3 pts. ) Again with p(x) = 1/x2 and q(x) = 2/x4, nd the solvability condition on f (x) for (1) if the boundary conditions are changed to u (1) = 2, u(2) = 5. 2: the free-space green"s function for in the plane r2 is gr2 x (y) = a ln |y x|. (a) (3 pts. )
