Question

Let ( u(x,y)=sin(x)sinh(y) ).
(a) Verify that ( u ) is harmonic, i.e. that ( uxx+uyy=0 ).
(b) Use the CR equations to find an analytic function ( f ) whose real part is ( u ).
a) ( uxx+uyy=0 )
b) ( uxy-uyx=0 )
c) ( uxy+uyx=0 )
d) ( uxx-uyy=0 )