Solution 16.

See text and/or instructor's solution manual.

Solution.  For starters Theorem 3.8 states that both the real and imaginary part of an analytic function is a harmonic function.

As illustrated in Exercise 5, if  v(x,y)  is harmonic in a suitable domain D, then it is possible to construct a harmonic function  u(x,y)  

so that   v(x,y)  is harmonic conjugate of   u(x,y)  and   [Graphics:../Images/HarmonicFunctionModHome_gr_927.gif]  is an analytic function the D.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell