A COURSE IN COMPLEX ANALYSIS FROM BASIC RESULTS TO ADVANCED TOPICS

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A Course In Complex Analysis

Author : Wolfgang Fischer
ISBN : 9783834886613
Genre : Mathematics
File Size : 77.5 MB
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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.
Category: Mathematics

Introductory Complex Analysis

Author : Richard A. Silverman
ISBN : 0486646866
Genre : Mathematics
File Size : 58.69 MB
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A shorter version of A. I. Markushevich's masterly three-volume Theory of Functions of a Complex Variable, this edition is appropriate for advanced undergraduate and graduate courses in complex analysis. Numerous worked-out examples and more than 300 problems, some with hints and answers, make it suitable for independent study. 1967 edition.
Category: Mathematics

Complex Analysis

Author : Rubí E. Rodríguez
ISBN : 9781441973238
Genre : Mathematics
File Size : 62.12 MB
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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.
Category: Mathematics

An Introduction To Complex Analysis

Author : Ravi P. Agarwal
ISBN : 146140195X
Genre : Mathematics
File Size : 84.40 MB
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This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
Category: Mathematics

Function Theory Of Several Complex Variables

Author : Steven George Krantz
ISBN : 9780821827246
Genre : Mathematics
File Size : 80.95 MB
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The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.
Category: Mathematics

Visual Complex Analysis

Author : Tristan Needham
ISBN : 0198534469
Genre : Mathematics
File Size : 42.17 MB
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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.
Category: Mathematics

An Introduction To Complex Analysis

Author : O. Carruth McGehee
ISBN : 047133233X
Genre : Mathematics
File Size : 37.28 MB
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* Contains over 100 sophisticated graphics to provide helpful examples and reinforce important concepts
Category: Mathematics

Function Theory Of One Complex Variable

Author : Robert Everist Greene
ISBN : 0821839624
Genre : Mathematics
File Size : 60.74 MB
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This book is a text for a first-year graduate course in complex analysis. It is a modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors."--BOOK JACKET.
Category: Mathematics

A Comprehensive Course In Analysis

Author : Barry Simon
ISBN : 1470410982
Genre : Mathematical analysis
File Size : 66.70 MB
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A Comprehensive Course in Analysis by Poincar 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.
Category: Mathematical analysis

Complex Analysis

Author : Joseph Bak
ISBN : 1441972889
Genre : Mathematics
File Size : 85.78 MB
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This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.
Category: Mathematics