Complex Variables

by Francis J. Flanigan

A caution to mathematics Complex Variables does not follow conventional outlines of course material. One reviewer noting its originality "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 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.

Genres: Mathematics, Textbooks, Physics

588 pages, Kindle Edition

First published January 1, 1983

Reviews

[marcel · Rating 4 out of 5]

I never took a class on complex analysis so this book taught me everything I know about the subject. It came in handy a few times during my undergrad research. In the past few months I read it cover to cover and it is one of the most supremely readable math textbooks I've come across. Conversational prose and excellent figures. Flanigan really wants to convince you that complex analysis is really the study of harmonic functions. As with every math book I read I don't remember (even close to) everything but at least I now have pointers (in the computer-science sense) in my mind to where I can find these theorems and their proofs.