Exercise 17. Use
the fact that is
analytic to show that is
a harmonic function.
See text and/or instructor's solution manual.
Answer. Show that is the imaginary part of , and therefore harmonic by Theorem 3.8 in Section 3.3.
Theorem 3.8 in Section
3.3 states that if
is analytic then both and are
Therefore is a harmonic function.
We are done.
Aside. We can let Mathematica double check our work.
Aside. It is always possible to see if Laplace's equation holds.
This solution is complements of the authors.