Complex Analysis

  • Filename: complex-analysis.
  • ISBN: 9781475730838
  • Release Date: 2013-03-14
  • Number of pages: 489
  • Author: Serge Lang
  • Publisher: Springer Science & Business Media



Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than is found in other texts, and the resulting proofs often shed more light on the results than the standard proofs. While the first part is suitable for an introductory course at undergraduate level, the additional topics covered in the second part give the instructor of a gradute course a great deal of flexibility in structuring a more advanced course.

Visual Complex Analysis

  • Filename: visual-complex-analysis.
  • ISBN: 0198534469
  • Release Date: 1998
  • Number of pages: 592
  • Author: Tristan Needham
  • Publisher: Oxford University Press



Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

Complex Analysis

  • Filename: complex-analysis.
  • ISBN: 0521287634
  • Release Date: 1983-03-10
  • Number of pages: 290
  • Author: Ian Stewart
  • Publisher: Cambridge University Press



This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.

Complex Analysis

  • Filename: complex-analysis.
  • ISBN: 9781400831159
  • Release Date: 2010-04-22
  • Number of pages: 400
  • Author: Elias M. Stein
  • Publisher: Princeton University Press



With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Complex Analysis 2

  • Filename: complex-analysis-2.
  • ISBN: 3642205542
  • Release Date: 2011-06-10
  • Number of pages: 506
  • Author: Eberhard Freitag
  • Publisher: Springer Science & Business Media



The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.

Classical Complex Analysis

  • Filename: classical-complex-analysis.
  • ISBN: 0824784154
  • Release Date: 1991-09-24
  • Number of pages: 792
  • Author: Mario Gonzalez
  • Publisher: CRC Press



Text on the theory of functions of one complex variable contains, with many elaborations, the subject of the courses and seminars offered by the author over a period of 40 years, and should be considered a source from which a variety of courses can be drawn. In addition to the basic topics in the cl

Complex Variables

  • Filename: complex-variables.
  • ISBN: 0387973494
  • Release Date: 1991-05-23
  • Number of pages: 650
  • Author: Carlos A. Berenstein
  • Publisher: Springer Science & Business Media



Textbooks, even excellent ones, are a reflection of their times. Form and content of books depend on what the students know already, what they are expected to learn, how the subject matter is regarded in relation to other divisions of mathematics, and even how fashionable the subject matter is. It is thus not surprising that we no longer use such masterpieces as Hurwitz and Courant's Funktionentheorie or Jordan's Cours d'Analyse in our courses. The last two decades have seen a significant change in the techniques used in the theory of functions of one complex variable. The important role played by the inhomogeneous Cauchy-Riemann equation in the current research has led to the reunification, at least in their spirit, of complex analysis in one and in several variables. We say reunification since we think that Weierstrass, Poincare, and others (in contrast to many of our students) did not consider them to be entirely separate subjects. Indeed, not only complex analysis in several variables, but also number theory, harmonic analysis, and other branches of mathematics, both pure and applied, have required a reconsidera tion of analytic continuation, ordinary differential equations in the complex domain, asymptotic analysis, iteration of holomorphic functions, and many other subjects from the classic theory of functions of one complex variable. This ongoing reconsideration led us to think that a textbook incorporating some of these new perspectives and techniques had to be written.

A Complex Analysis Problem Book

  • Filename: a-complex-analysis-problem-book.
  • ISBN: 9783034800785
  • Release Date: 2011-08-20
  • Number of pages: 526
  • Author: Daniel Alpay
  • Publisher: Springer Science & Business Media



This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises we wish to show to the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

Complex analysis

  • Filename: complex-analysis.
  • ISBN: UOM:39015049299038
  • Release Date: 1982
  • Number of pages: 244
  • Author: Joseph Bak
  • Publisher: Springer



This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. "Complex Analysis" offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. Stressing motivation and technique, and complete with exercise sets, this volume may be used both as a basic text and as a reference. For this second edition, the authors have revised some of the existing material and have provided new exercises and solutions.

Complex Analysis

  • Filename: complex-analysis.
  • ISBN: 9810203756
  • Release Date: 1991
  • Number of pages: 240
  • Author: Murali Rao
  • Publisher: World Scientific



This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.

Complex Analysis with Applications

  • Filename: complex-analysis-with-applications.
  • ISBN: 0486647625
  • Release Date: 1973
  • Number of pages: 274
  • Author: Richard A. Silverman
  • Publisher: Courier Corporation



The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

A Course in Complex Analysis

  • Filename: a-course-in-complex-analysis.
  • ISBN: 9783834886613
  • Release Date: 2011-10-21
  • Number of pages: 280
  • Author: Wolfgang Fischer
  • Publisher: Springer Science & Business Media



This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem …) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.

Complex Analysis in Number Theory

  • Filename: complex-analysis-in-number-theory.
  • ISBN: 0849328667
  • Release Date: 1994-11-22
  • Number of pages: 208
  • Author: Anatoly A. Karatsuba
  • Publisher: CRC Press



This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.

Complex Analysis

  • Filename: complex-analysis.
  • ISBN: 0849317088
  • Release Date: 2004-03-01
  • Number of pages: 427
  • Author: V. Karunakaran
  • Publisher: CRC Press



Effective for undergraduate and postgraduate students, the single-volume Complex Analysis functions as both a textbook and a reference, depending on the conducted course's structure. The only prerequisites are rudiments of real analysis and linear algebra. Special features include an integrated approach to the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, complex versions of real intermediate value theorem, and exhaustive treatment of contour integration. The book also offers an introduction to the theory of univalent functions on the unit disc, including a brief history of the Bieberbach's conjecture and its solutions.

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