This authoritative text presents the classical theory of functions of a
single complex variable in complete mathematical and historical detail.
Requiring only minimal, undergraduate-level prerequisites, it covers the
fundamental areas of the subject with depth, precision, and rigor.
Standard and novel proofs are explored in unusual detail, and
exercises - many with helpful hints - provide ample opportunities for
practice and a deeper understanding of the material.
In addition to the mathematical theory, the author also explores how key
ideas in complex analysis have evolved over many centuries, allowing
readers to acquire an extensive view of the subject's development.
Historical notes are incorporated throughout, and a bibliography
containing more than 2,000 entries provides an exhaustive list of both
important and overlooked works.
Classical Analysis in the Complex Plane will be a definitive reference
for both graduate students and experienced mathematicians alike, as well
as an exemplary resource for anyone doing scholarly work in complex
analysis. The author's expansive knowledge of and passion for the
material is evident on every page, as is his desire to impart a lasting
appreciation for the subject.
"I can honestly say that Robert Burckel's book has profoundly
influenced my view of the subject of complex analysis. It has given me a
sense of the historical flow of ideas, and has acquainted me with byways
and ancillary results that I never would have encountered in the
ordinary course of my work. The care exercised in each of his proofs is
a model of clarity in mathematical writing...Anyone in the field should
have this book on [their bookshelves] as a resource and an
inspiration."- From the Foreword by Steven G. Krantz
