1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

11.4 • TwO-DI MENSJONAL MATHEMATICAL MODELS 445

For convenience, we introduce the term complex potential for the analytic func-
tion

F (z) = tfa (x, y) +it/I (x, y).

We use Theorem 11 .4, regarding the orthogonality of the families of level curves
(Equations ( 11 -16) and (11-17)), to develop ideas concerning the physical appli-
cations that we will consider.

The complex potential F(z) = tfa(x,y) + itfi(x,y) has many physical inter-

pretations. Suppose, for example, that we have solved a problem in steady state

temperatures. Then we can obtain the solution to a similar problem with the

same boundary conditions in electrostatics by interpreting the isothermals as