A Second Course In Complex Analysis
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| Author | : William A. Veech |
| Publisher | : Courier Corporation |
| Total Pages | : 257 |
| Release | : 2014-08-04 |
| Genre | : Mathematics |
| ISBN | : 048615193X |
A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.
| Author | : Saeed Zakeri |
| Publisher | : Princeton University Press |
| Total Pages | : 442 |
| Release | : 2021-11-02 |
| Genre | : Mathematics |
| ISBN | : 0691207585 |
"This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--
| Author | : Stephen D. Fisher |
| Publisher | : Courier Corporation |
| Total Pages | : 292 |
| Release | : 2014-06-10 |
| Genre | : Mathematics |
| ISBN | : 0486151107 |
A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
| Author | : John W. Dettman |
| Publisher | : Courier Corporation |
| Total Pages | : 514 |
| Release | : 2012-05-07 |
| Genre | : Mathematics |
| ISBN | : 0486158284 |
Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.
| Author | : Wolfgang Fischer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2011-10-21 |
| Genre | : Mathematics |
| ISBN | : 3834886610 |
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.
| Author | : Theodore W. Gamelin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2013-11-01 |
| Genre | : Mathematics |
| ISBN | : 0387216073 |
An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.
| Author | : Rubí E. Rodríguez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 319 |
| Release | : 2012-11-28 |
| Genre | : Mathematics |
| ISBN | : 1441973230 |
The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.
| Author | : Dennis Zill |
| Publisher | : Jones & Bartlett Learning |
| Total Pages | : 471 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0763757721 |
The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.
| Author | : John D. Paliouras |
| Publisher | : Courier Corporation |
| Total Pages | : 612 |
| Release | : 2014-02-20 |
| Genre | : Mathematics |
| ISBN | : 0486493474 |
Outstanding undergraduate text provides a thorough understanding of fundamentals and creates the basis for higher-level courses. Numerous examples and extensive exercise sections of varying difficulty, plus answers to selected exercises. 1990 edition.
| Author | : Junjiro Noguchi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 268 |
| Release | : 2008-04-09 |
| Genre | : Mathematics |
| ISBN | : 9780821889602 |
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.
