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Author: Liong-shin Hahn Publisher: Jones & Bartlett Publishers ISBN: 9780867204940 Category : Functions of complex variables Languages : en Pages : 0
Book Description
Classic Complex Analysis is a text that has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses on the core material. An early chapter on power series gives the reader concrete examples of analytic functions and a review of calculus. Mobius transformations are presented with emphasis on the geometric aspect, and the Cauchy theorem is covered in the classical manner. The remaining chapters provide an elegant and solid overview of special topics such as Entire and Meromorphic Functions, Analytic Continuation, Normal Families, Conformal Mapping, and Harmonic Functions.
Author: Liong-shin Hahn Publisher: Jones & Bartlett Publishers ISBN: 9780867204940 Category : Functions of complex variables Languages : en Pages : 0
Book Description
Classic Complex Analysis is a text that has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses on the core material. An early chapter on power series gives the reader concrete examples of analytic functions and a review of calculus. Mobius transformations are presented with emphasis on the geometric aspect, and the Cauchy theorem is covered in the classical manner. The remaining chapters provide an elegant and solid overview of special topics such as Entire and Meromorphic Functions, Analytic Continuation, Normal Families, Conformal Mapping, and Harmonic Functions.
Author: I-Hsiung Lin Publisher: World Scientific ISBN: 9814271284 Category : Mathematics Languages : en Pages : 713
Book Description
Classical Complex Analysis provides an introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. This volume begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described In detail, and various applications of residues are Included; analytic continuation is also introduced. --Book Jacket.
Author: Robert B. Burckel Publisher: Springer Nature ISBN: 1071619659 Category : Mathematics Languages : en Pages : 1123
Book Description
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
Author: R.B. Burckel Publisher: Birkhäuser ISBN: 3034893744 Category : Mathematics Languages : en Pages : 572
Book Description
This book is an attempt to cover some of the salient features of classical, one variable complex function theory. The approach is analytic, as opposed to geometric, but the methods of all three of the principal schools (those of Cauchy, Riemann and Weierstrass) are developed and exploited. The book goes deeply into several topics (e.g. convergence theory and plane topology), more than is customary in introductory texts, and extensive chapter notes give the sources of the results, trace lines of subsequent development, make connections with other topics, and offer suggestions for further reading. These are keyed to a bibliography of over 1,300 books and papers, for each of which volume and page numbers of a review in one of the major reviewing journals is cited. These notes and bibliography should be of considerable value to the expert as well as to the novice. For the latter there are many references to such thoroughly accessible journals as the American Mathematical Monthly and L'Enseignement Mathématique. Moreover, the actual prerequisites for reading the book are quite modest; for example, the exposition assumes no prior knowledge of manifold theory, and continuity of the Riemann map on the boundary is treated without measure theory.
Author: I-Hsiung Lin Publisher: World Scientific ISBN: 981426122X Category : Mathematics Languages : en Pages : 1085
Book Description
Classical Complex Analysis provides an introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. This volume begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described In detail, and various applications of residues are Included; analytic continuation is also introduced. --Book Jacket.
Author: Wolfgang Tutschke Publisher: CRC Press ISBN: 1584884789 Category : Mathematics Languages : en Pages : 480
Book Description
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
Author: Eberhard Freitag Publisher: Springer Science & Business Media ISBN: 3540308237 Category : Mathematics Languages : en Pages : 553
Book Description
All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included
Author: Tristan Needham Publisher: Oxford University Press ISBN: 9780198534464 Category : Mathematics Languages : en Pages : 620
Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Author: Junjiro Noguchi Publisher: American Mathematical Soc. ISBN: 9780821889602 Category : Mathematics Languages : en Pages : 268
Book Description
This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.
Author: Liong-shin Hahn
Author: Liong-shin Hahn
Author: I-Hsiung Lin
Author: Robert B. Burckel
Author: R.B. Burckel
Author: I-Hsiung Lin
Author: Wolfgang Tutschke
Author: Eberhard Freitag
Author: Tristan Needham
Author: Luogeng Hua
Author: Junjiro Noguchi