Complex Analysis

 
 
Springer (Verlag)
  • 3. Auflage
  • |
  • erschienen am 13. Oktober 2012
 
  • Buch
  • |
  • Softcover
  • |
  • 340 Seiten
978-1-4614-2636-3 (ISBN)
 
This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.
Paperback
Softcover reprint of hardcover 3rd ed. 2010
  • Englisch
  • NY
  • |
  • USA
  • Für Beruf und Forschung
  • |
  • Lower undergraduate
  • Überarbeitete Ausgabe
  • 77 s/w Abbildungen
  • |
  • 77 Illustrations, black and white; XII, 328 p. 77 illus.
  • Höhe: 235 mm
  • |
  • Breite: 155 mm
  • |
  • Dicke: 18 mm
  • 517 gr
978-1-4614-2636-3 (9781461426363)
10.1007/978-1-4419-7288-0
weitere Ausgaben werden ermittelt
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.
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.- Simply Connected Domains.- Isolated Singularities of an Analytic Function.- The Residue Theorem.- Applications of the Residue Theorem to the Evaluation of Integrals and Sums.- Further Contour Integral Techniques.- 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.
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)
This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques.

Notable additions to "Complex Analysis, Third Edition," include:

The solution of the cubic equation and Newton's method for approximating the zeroes of any polynomial;
Expanded treatments of the Schwarz reflection principle and of the mapping properties of analytic functions on closed domains;
An introduction to Schwarz-Christoffel transformations and to Dirichlet series;
A streamlined proof of the prime number theorem, and more.

Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

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