(1) Let w(x,t) = (1/sqrt(t)) times exp[-(x^2)/(4kt)] for t > 0. Show that w satisfies w_t = k times u_{xx}

By interpreting this second series as a Fourier series on [-pi,pi], use the integration theorem to derive the Fourier series of |x| on [-pi,pi]. No coefficients should be left as infinite series.