Complex Variables

Take care of the sense, and the sounds will take care of themselves. Alice in
Wonderland
After having lectured for several decades on complex variables to pro-
spective engineers and physicists, I have definite and, I hope, not unrealistic
ideas about their requirements and preferences.
Students are students. Since they are required to take several courses, they
may study some subjects just for the examination, with the intention of
forgetting what they have learned after the examination. Yet they may (and
the more intelligent and purposeful students do) ask pertinent questions
about the subject: Is it interesting? Can I use it?
These questions are fully justified. The instructor of a more advanced
branch of mathematics-such as the theory of complex variables-who is a
mathematician should try to put himself into the position of his students
who are prospective physicists or engineers. Before going into heavy definitions
and lengthy proofs, the student wants to satisfy himself that the subject is
interesting and useful enough to expend his time and effort on definitions
and proofs.