Search results for: real-and-complex-analysis

Real and Complex Analysis

Author : Walter Rudin
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Presents the basic techniques and theorems of analysis. This work includes a chapter on differentiation. It presents proofs of theorems and many exercises appear at the end of each chapter. It is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.

Real and Complex Analysis

Author : Rajnikant Sinha
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This is the second volume of the two-volume book on real and complex analysis. This volume is an introduction to the theory of holomorphic functions. Multivalued functions and branches have been dealt carefully with the application of the machinery of complex measures and power series. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into four chapters, it discusses holomorphic functions and harmonic functions, Schwarz reflection principle, infinite product and the Riemann mapping theorem, analytic continuation, monodromy theorem, prime number theorem, and Picard’s little theorem. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.

Problems in Real and Complex Analysis

Author : Bernard R. Gelbaum
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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.

Real and Complex Analysis

Author : Christopher Apelian
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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.

Elementary Real and Complex Analysis

Author : Georgi E. Shilov
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Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition.

Modern Real and Complex Analysis

Author : Bernard R. Gelbaum
File Size : 79.3 MB
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Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis. While maintaining the strictest standards ofrigor, Professor Gelbaum's approach is designed to appeal tointuition whenever possible. Modern Real and Complex Analysisprovides up-to-date treatment of such subjects as the Daniellintegration, differentiation, functional analysis and Banachalgebras, conformal mapping and Bergman's kernels, defectivefunctions, Riemann surfaces and uniformization, and the role ofconvexity in analysis. The text supplies an abundance of exercisesand illustrative examples to reinforce learning, and extensivenotes and remarks to help clarify important points.

From Real to Complex Analysis

Author : R. H. Dyer
File Size : 45.61 MB
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The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon. Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.

A Complete Solution Guide to Real and Complex Analysis

Author : Kit-Wing Yu
File Size : 41.85 MB
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This is a complete solution guide to all exercises from Chapters 1 to 20 in Rudin's Real and Complex Analysis. The features of this book are as follows: It covers all the 397 exercises from Chapters 1 to 20 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied. There are 40 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems. Sections in each chapter are added so as to increase the readability of the exercises. Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only) Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin. Many useful or relevant references are provided to some questions for your future research.

Studies in Real and Complex Analysis

Author : Isidore Isaac Hirschman
File Size : 28.31 MB
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A Complete Solution Guide to Real and Complex Analysis II

Author : Kit-Wing Yu
File Size : 84.62 MB
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This is a complete solution guide to all exercises from Chapters 10 to 20 in Rudin's Real and Complex Analysis. The features of this book are as follows: It covers all the 221 exercises from Chapters 10 to 20 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied. There are 29 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems. Sections in each chapter are added so as to increase the readability of the exercises. Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only) Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin. Many useful or relevant references are provided to some questions for your future research.

Interactions Between Real and Complex Analysis

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Real and Complex Analysis Real Complex Analysis

Author : Walter Rudin
File Size : 48.81 MB
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The Real and the Complex A History of Analysis in the 19th Century

Author : Jeremy Gray
File Size : 84.57 MB
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This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.

The Higher Calculus A History of Real and Complex Analysis from Euler to Weierstrass

Author : Umberto Bottazini
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"The true method of foreseeing the future of mathematics is to study its history and its actual state." With these words Henri Poincare began his presentation to the Fourth International Congress of Mathematicians at Rome in 1908. Although Poincare himself never actively pursued the history of mathematics, his remarks have given both historians of mathematics and working mathematicians a valuable methodological guideline, not so much for indulging in improbable prophecies about the future state of mathematics, as for finding in history the origins and moti va tions of contemporary theories, and for finding in the present the most fruitful statements of these theories. At the time Poincare spoke, at the beginning of this century, historical research in the various branches of rna thema tics was emerging with distinctive autonomy. In Germany the last volume of Cantor's monumental Vorlesungell iiber die Gesehiehte der Mathematik had just appeared, and many new specialized journals were appearing to complement those already in existence, from Enestrom's Bibliotheea mathematiea to Loria's Bollettino di bibliogra/ia e di storia delle seienze matematiehe. The annual Jahresberiehte of the German Mathematical Society included noteworthy papers of a historical nature, as did the Enzyklopadie der mathematisehen Wissenseha/ten, an imposing work constructed according to the plan of Felix Klein.

Analytical Geometry And Real And Complex Analysis

Author : T. Veerarajan
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Fundamentals Of Complex Analysis Theory And Applications

Author : K K Dube
File Size : 76.46 MB
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The book divided in ten chapters deals with: " Algebra of complex numbers and its various geometrical properties, properties of polar form of complex numbers and regions in the complex plane. " Limit, continuity, differentiability. " Different kinds of complex valued functions. " Different types of transformations. " Conformal mappings of different functions. " Properties of bilinear and special bilinear transformation. " Line integrals, their properties and different theorems. " Sequences and series, Power series, Zero s of functions, residues and residue theorem, meromorphic functions, different kinds of singularities. " Evaluation of real integrals. " Analytic continuation, construction of harmonic functions, infinite product, their properties and Gamma function. " Schwarz-Christoffel transformations, mapping by multi valued functions, entire functions. " Jenson s theorem and Poisson-Jenson theorem. The book is designed as a textbook for UG and PG students of science as well as engineering

Complex Analysis

Author : V. Karunakaran
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Effective for undergraduate and postgraduate students, the single-volume Complex Analysis functions as both a textbook and a reference, depending on the conducted course's structure. The only prerequisites are rudiments of real analysis and linear algebra. Special features include an integrated approach to the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, complex versions of real intermediate value theorem, and exhaustive treatment of contour integration. The book also offers an introduction to the theory of univalent functions on the unit disc, including a brief history of the Bieberbach's conjecture and its solutions.

From Real to Complex Analysis

Author : R. H. Dyer
File Size : 89.88 MB
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The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon. Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.

Complex Analysis with Applications

Author : Richard A. Silverman
File Size : 66.65 MB
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The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

Advances in Real and Complex Analysis with Applications

Author : Michael Ruzhansky
File Size : 52.51 MB
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This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them with a number of solved examples. The topics include real and complex analysis, special functions and analytic number theory, q-series, Ramanujan’s mathematics, fractional calculus, Clifford and harmonic analysis, graph theory, complex analysis, complex dynamical systems, complex function spaces and operator theory, geometric analysis of complex manifolds, geometric function theory, Riemannian surfaces, Teichmüller spaces and Kleinian groups, engineering applications of complex analytic methods, nonlinear analysis, inequality theory, potential theory, partial differential equations, numerical analysis , fixed-point theory, variational inequality, equilibrium problems, optimization problems, stability of functional equations, and mathematical physics. It includes papers presented at the 24th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (24ICFIDCAA), held at the Anand International College of Engineering, Jaipur, 22–26 August 2016. The book is a valuable resource for researchers in real and complex analysis.