1. (a) Solve the following boundary value problem using Fourier integrals and interpret physically. du equations...

 

Transcribed Image Text:

1. (a) Solve the following boundary value problem using Fourier integrals and interpret physically. du equations r 01 2 K Ox u(x,0) = f(x), u (0,1)= 0, u(x, t) <M, where, -∞0<x<∞,t> 0. 2 (b) By letting u-RO, where R depends only on and only on 0, in Laplace's equation v¹u0 expressed in spherical coordinates, show that R and satisfy the d'R dR do + 2r + ³R = 0 and -)-2² (sin 0) 0 = 0. dr² dr do do -(sin 8 1. (a) Solve the following boundary value problem using Fourier integrals and interpret physically. du equations r 01 2 K Ox u(x,0) = f(x), u (0,1)= 0, u(x, t) <M, where, -∞0<x<∞,t> 0. 2 (b) By letting u-RO, where R depends only on and only on 0, in Laplace's equation v¹u0 expressed in spherical coordinates, show that R and satisfy the d'R dR do + 2r + ³R = 0 and -)-2² (sin 0) 0 = 0. dr² dr do do -(sin 8