A caution to mathematics professors: Complex Variables does not follow
conventional outlines of course material. One reviewer noting its
originality wrote: A standard text is often preferred [to a superior
text like this] because the professor knows the order of topics and the
problems, and doesn't really have to pay attention to the text. He can
go to class without preparation. Not so here -- Dr. Flanigan treats this
most important field of contemporary mathematics in a most unusual way.
While all the material for an advanced undergraduate or first-year
graduate course is covered, discussion of complex algebra is delayed for
100 pages, until harmonic functions have been analyzed from a real
variable viewpoint. Students who have forgotten or never dealt with this
material will find it useful for the subsequent functions. In addition,
analytic functions are defined in a way which simplifies the subsequent
theory. Contents include: Calculus in the Plane, Harmonic Functions in
the Plane, Complex Numbers and Complex Functions, Integrals of Analytic
Functions, Analytic Functions and Power Series, Singular Points and
Laurent Series, The Residue Theorem and the Argument Principle, and
Analytic Functions as Conformal Mappings.
Those familiar with mathematics texts will note the fine illustrations
throughout and large number of problems offered at the chapter ends. An
answer section is provided. Students weary of plodding mathematical
prose will find Professor Flanigan's style as refreshing and stimulating
as his approach.
