Complex Analysis - Joseph Bak

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Résumé :
This unusually lively textbook introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. The book offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. For the second edition, the authors have revised some of the existing material and have provided new exercises and solutions. The third edition contains a new section on Schwarz-Christoffel mappings, an improved treatment of the Schwarz Reflection Principle, and an expanded section on applications to number theory. TOC:- Preface.- The Complex Numbers.- Functions of the Complex Variable z.- Analytic Functions.- Line Integrals and Entire Functions.- Properties of Entire Functions.- Properties of Analytic Functions.- Further Properties of Analytic Functions; 8. Simply Connected Domains.- Isolated Sigularities of an Analytic Function.- The Residue Theorem.- Applications of The Residue Theorem to the Evaluation of Integrals Sums.- Further Contour Integral Techniques.- Introduction to Conformal Mapping.- The Riemann Mapping Theorem.- Maximum-Modulus Theorems for Unbounded Domains.- Harmonic Functions.- Different Forms of Analytic Functions.- Analytic Continuation; The Gamma and Zeta Functions.- Applications to Other Areas of Mathematics.- Appendices.- Answers.- Bibliography.- Index.

Biographie:
Dr. Joseph Bak is the Assistant Chair of the Mathematics department at The City College of New York. Joseph Bak's primary area of research is approximation theory. Dr. Donald J. Newman (July 27, 1930 - March 28, 2007) was a champion problem solver. His mathematical specialties included complex analysis, approximation theory and number theory. His career included posts as a Professor of Mathematics at MIT, Brown University, Yeshiva University, Temple University and a distinguished chair at Bar Ilan University in Israel. His publications include 150 papers and five books.

Sommaire:
Preface.- The Complex Numbers.- Functions of the Complex Variable z.- Analytic Functions.- Line Integrals and Entire Functions.- Properties of Entire Functions.- Properties of Analytic Functions.- Further Properties of Analytic Functions; 8. Simply Connected Domains.- Isolated Sigularities of an Analytic Function.- The Residue Theorem.- Applications of The Residue Theorem to the Evaluation of Integrals Sums.- Further Contour Integral Techniques.- Introduction to Conformal Mapping.- The Riemann Mapping Theorem.- Maximum-Modulus Theorems for Unbounded Domains.- Harmonic Functions.- Different Forms of Analytic Functions.- Analytic Continuation; The Gamma and Zeta Functions.- Applications to Other Areas of Mathematics.- Appendices.- Answers.- Bibliography.- Index.-

From the reviews of the third edition: The book of the known mathematicians J. Bak and D. Newman is an excellent introduction into the theory of analytic functions of one complex variable. The book is written on an elementary level and so it supports students in the early stages of their mathematical studies. ... The book also contains many illustrations, examples and exercises, which give additional information and explanations. (Konstantin Malyutin, Zentralblatt MATH, Vol. 1205, 2011)