Nine Introductions in Complex Analysis PDF Download

Author: Sanford L. Segal
Publisher: Elsevier
ISBN: 9780080871646
Category : Mathematics
Languages : en
Pages : 714

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Book Description
Nine Introductions in Complex Analysis

Author: Sanford L. Segal
Publisher: Elsevier
ISBN: 0080550762
Category : Mathematics
Languages : en
Pages : 501

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Book Description
The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. - Proof of Bieberbach conjecture (after DeBranges) - Material on asymptotic values - Material on Natural Boundaries - First four chapters are comprehensive introduction to entire and metomorphic functions - First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off

Author: Kalyan Chakraborty
Publisher: World Scientific Publishing Company
ISBN: 9813108533
Category : Mathematics
Languages : en
Pages : 208

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Book Description
The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels. If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples. This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.

Author: Mario Gonzalez
Publisher: Routledge
ISBN: 1351459384
Category : Mathematics
Languages : en
Pages : 544

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Book Description
A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

Author: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 1470411008
Category : Mathematical analysis
Languages : en
Pages : 641

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Book Description
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3319421816
Category : Mathematics
Languages : en
Pages : 592

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Book Description
This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

Author: Charles H. C. Little
Publisher: Springer Nature
ISBN: 3030906469
Category : Mathematics
Languages : en
Pages : 258

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Book Description
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

Author: Adrian Constantin
Publisher: Cambridge University Press
ISBN: 1107044103
Category : Mathematics
Languages : en
Pages : 368

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Book Description
A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.

Author: Hilary A. Priestley
Publisher: Oxford University Press, USA
ISBN: 9780198532477
Category : Functions of complex variables
Languages : en
Pages : 0

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Book Description
Straightforward in concise, this introductory volume treats the theory rigorously but uses a minimum of sophisticated machinery and assumes no prior knowledge of topology. Priestley presents the major theorems as early as possible, so that those meeting complex analysis for the first time can appreciate the power and elegance of the subject by seeing applications of results, both practical and theoretical. A valuable resource for pure and applied mathematicians, this book is also suitable for graduate students and, as a reference, for engineers.

Author: Rolf Nevanlinna
Publisher: American Mathematical Society
ISBN: 0821843990
Category : Mathematics
Languages : en
Pages : 366

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Book Description
This textbook, based on lectures given by the authors, presents the elements of the theory of functions in a precise fashion. This introduction is ideal for the third or fourth year of undergraduate study and for graduate students learning complex analysis. Over 300 exercises offer important insight into the subject.