problems in real and complex analysis

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Problems In Real And Complex Analysis

Author : Bernard R. Gelbaum
ISBN : 9781461209256
Genre : Mathematics
File Size : 65. 39 MB
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This text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces. In complex analysis, they include polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.

Modern Real And Complex Analysis

Author : Bernard R. Gelbaum
ISBN : 9781118030806
Genre : Mathematics
File Size : 44. 51 MB
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Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.

A Collection Of Problems On Complex Analysis

Author : Lev Izrailevich Volkovyski?
ISBN : 9780486669137
Genre : Mathematics
File Size : 56. 28 MB
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Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition.

Complex Analysis Through Examples And Exercises

Author : Endre Pap
ISBN : 0792357876
Genre : Mathematics
File Size : 62. 91 MB
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This volume on complex analysis offers an exposition of the theory of complex analysis via a comprehensive set of examples and exercises. The book is self-contained and the exposition of new notions and methods is introduced step by step. A minimal amount of expository theory is included at the beginning of each section in the Preliminaries, with maximum effort placed on well-selected examples and exercises capturing the essence of the material. The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercises; the answers, and occasionally, some hints, are given. Special sections contain so-called Composite Examples which consist of combinations of different types of examples explaining some problems completely and giving the reader an opportunity to check all his previously accepted knowledge. Audience: This volume is intended for undergraduate and graduate students in mathematics, physics, technology and economics interested in complex analysis.

A Complex Analysis Problem Book

Author : Daniel Alpay
ISBN : 9783034800785
Genre : Mathematics
File Size : 40. 46 MB
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This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises we wish to show to the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

Problems And Solutions For Complex Analysis

Author : Rami Shakarchi
ISBN : 0387988319
Genre : Mathematics
File Size : 50. 92 MB
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This book is an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. The problems cover such topics as: power series, Cauchys theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and Jensens formula. All the exercises from this volume were derived from Serge Lang's fourth edition of Complex Analysis and can also serve as a companion guide to it.

Real And Complex Analysis

Author : Christopher Apelian
ISBN : 1584888075
Genre : Mathematics
File Size : 83. 40 MB
Format : PDF
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Presents Real & Complex Analysis Together Using a Unified Approach A two-semester course in analysis at the advanced undergraduate or first-year graduate level Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide. By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website. This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.

Some Problems In Real And Complex Analysis

Author : John Edensor Littlewood
ISBN : STANFORD:36105031257871
Genre : Mathematics
File Size : 51. 50 MB
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Some Problems In Real And Complex Analysis

Author : John Edensor Littlewood (Mathematician, Great Britain)
ISBN : OCLC:637056441
Genre :
File Size : 56. 44 MB
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Problems In Analysis

Author : B. Gelbaum
ISBN : 9781461576792
Genre : Mathematics
File Size : 58. 21 MB
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These problems and solutions are offered to students of mathematics who have learned real analysis, measure theory, elementary topology and some theory of topological vector spaces. The current widely used texts in these subjects provide the background for the understanding of the problems and the finding of their solutions. In the bibliography the reader will find listed a number of books from which the necessary working vocabulary and techniques can be acquired. Thus it is assumed that terms such as topological space, u-ring, metric, measurable, homeomorphism, etc., and groups of symbols such as AnB, x EX, f: IR 3 X 1-+ X 2 - 1, etc., are familiar to the reader. They are used without introductory definition or explanation. Nevertheless, the index provides definitions of some terms and symbols that might prove puzzling. Most terms and symbols peculiar to the book are explained in the various introductory paragraphs titled Conventions. Occasionally definitions and symbols are introduced and explained within statements of problems or solutions. Although some solutions are complete, others are designed to be sketchy and thereby to give their readers an opportunity to exercise their skill and imagination. Numbers written in boldface inside square brackets refer to the bib liography. I should like to thank Professor P. R. Halmos for the opportunity to discuss with him a variety of technical, stylistic, and mathematical questions that arose in the writing of this book. Buffalo, NY B.R.G.

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