(A) Consider the wave equation with c=1, l=1, u(0,t)=0, and u(l,t)=0. The initial data are: f(x)=x(1-x)2, g(x)=sin2(pi x). Find the value of the solution at x=0, t=10, and at x=1/3, t=0. Find the value of the solution at x=1/2, t=2.

Question

(A) Consider the wave equation with c=1, l=1, u(0,t)=0, and u(l,t)=0. The initial data are: f(x)=x(1-x)2, g(x)=sin2(pi x). Find the value of the solution at x=0, t=10, and at x=1/3, t=0. Find the value of the solution at x=1/2, t=2.
(B) Suppose that l=2, c=1/2. Draw the domain of influence for the point (1/2,0), for values of t between 0 and 6. Find the equations for characteristics for t<6. Find the domain of dependence for point (1,3) (graphically and by writing down equations).