Problem 1 (10pt). Let f(z,t) be a function defined on (x,t) R? and (x) be a function defined on = R. Let u(z,t) be the solution to the equation u't(m?t) - um(m't) = f(ma t)s for (mat) Rza (1) u(z,0) = p(x), for z R. Let f(p,t), (p) and @(p, t) be the Fourier transform of f(z,t), p(x) and u(z, t) respectively. Find the explicit form of #i(p,t) in terms of f(p,t) and @(p). Problem 2 (10pt). For fixed a R, the delta function centered at a, d,(z), has the following properties. First, 30,(19) = e WP, Second, for all function g(z), (0a * g)(z) = g(z a). Use those two properties and Problem 1 to solve the equation (1)