Classical Analysis In The Complex Plane
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| Author | : Robert B. Burckel |
| Publisher | : Springer Nature |
| Total Pages | : 1123 |
| Release | : 2021-10-11 |
| Genre | : Mathematics |
| ISBN | : 1071619659 |
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 | : Mario Gonzalez |
| Publisher | : CRC Press |
| Total Pages | : 796 |
| Release | : 1991-09-24 |
| Genre | : Mathematics |
| ISBN | : 9780824784157 |
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
| Author | : Wolfgang Tutschke |
| Publisher | : CRC Press |
| Total Pages | : 476 |
| Release | : 2004-06-25 |
| Genre | : Mathematics |
| ISBN | : 1420057219 |
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
| Author | : Thomas McCullough |
| Publisher | : Ardent Media |
| Total Pages | : 306 |
| Release | : 1973 |
| Genre | : Mathematics |
| ISBN | : 9780030863707 |
| Author | : R.B. Burckel |
| Publisher | : Birkhäuser |
| Total Pages | : 572 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034893744 |
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 |
| Total Pages | : 1085 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 981426122X |
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 | : Eberhard Freitag |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 553 |
| Release | : 2006-01-17 |
| Genre | : Mathematics |
| ISBN | : 3540308237 |
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 | : I-hsiung Lin |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 713 |
| Release | : 2010-09-09 |
| Genre | : Mathematics |
| ISBN | : 9813101075 |
Classical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 2 begins with analytic continuation. The Riemann mapping theorem is proved and used in solving Dirichlet's problem for an open disk and, hence, a class of general domains via Perron's method. Finally, proof of the uniformization theorem of Riemann surfaces is given.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.
| Author | : John Stalker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2009-10-03 |
| Genre | : Mathematics |
| ISBN | : 0817649190 |
All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.
| Author | : Tristan Needham |
| Publisher | : Oxford University Press |
| Total Pages | : 620 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780198534464 |
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.
