Infinite String: consider the initial/boundary value problem хER, t > 0, dx2' u(х, 0) %3D F(x), x E R ди (x, 0) = g(x), x E R dt where f and g are two given twice differentiable functions. We showed...

Extracted text: Infinite String: consider the initial/boundary value problem хER, t > 0, dx2' u(х, 0) %3D F(x), x E R ди (x, 0) = g(x), x E R dt where f and g are two given twice differentiable functions. We showed in class that this problem is solved by he d'Alembert's solution 1 u(x, t) = [f(x + ct) + f(x – ct)] + [G(x + ct) – G(x – ct)], 2c where G is an antiderivative of g. Sketch the solution for t = 0, 1, 2, 3, where f(x) and g(x) are given below.


Extracted text: b) { |x| < 1="" |x|=""> 1 sin TX f(x) = 0 g(x) =