From Real To Complex Analysis
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Real And Complex Analysis
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Author : Christopher Apelian
language : en
Publisher: CRC Press
Release Date : 2009-12-08
Real And Complex Analysis written by Christopher Apelian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-08 with Mathematics categories.
Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike 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 Real And The Complex A History Of Analysis In The 19th Century
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Author : Jeremy Gray
language : en
Publisher: Springer
Release Date : 2015-11-05
The Real And The Complex A History Of Analysis In The 19th Century written by Jeremy Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-05 with Mathematics categories.
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.
Advances In Real And Complex Analysis With Applications
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Author : Michael Ruzhansky
language : en
Publisher: Birkhäuser
Release Date : 2017-10-03
Advances In Real And Complex Analysis With Applications written by Michael Ruzhansky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-03 with Mathematics categories.
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.
Real And Complex Analysis
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Author : Rajnikant Sinha
language : en
Publisher: Springer
Release Date : 2018-11-15
Real And Complex Analysis written by Rajnikant Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-15 with Mathematics categories.
This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. 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 three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. 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
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Author : Bernard R. Gelbaum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems In Real And Complex Analysis written by Bernard R. Gelbaum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the pages that follow there are: A. A revised and enlarged version of Problems in analysis (PIA) . (All typographical, stylistic, and mathematical errors in PIA and known to the writer have been corrected.) B. A new section COMPLEX ANALYSIS containing problems distributed among many of the principal topics in the theory of functions of a complex variable. C. A total of 878 problems and their solutions. D. An enlarged Index/Glossary and an enlarged Symbol List. Notational and terminological conventions are to be found for the most part under Conventions at the beginnings of the chapters. Spe cial items not included in Conventions are completely explained in the Index/Glossary. The audience to which the current book is addressed differs little from the audience for PIA. The background of the reader is assumed to include a knowledge of the basic principles and theorems in real and complex analysis as those subjects are currently viewed. The aim of the problems is to sharpen and deepenthe understanding of the mechanisms that underlie modern analysis. I thank Springer-Verlag for its interest in and support of this project. State University of New York at Buffalo B. R. G. v Contents The symbol alb under Pages below indicates that the Problems for the section begin on page a and the corresponding Solutions begin on page b. Thus 3/139 on the line for Set Algebra indicates that the Problems in Set Algebra begin on page 3 and the corresponding Solutions begin on page 139.
Complex Analysis
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2010-04-22
Complex Analysis written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Mathematics categories.
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
A History Of Analysis
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Author : Hans Niels Jahnke
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
A History Of Analysis written by Hans Niels Jahnke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Problems In Analysis
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Author : B. Gelbaum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems In Analysis written by B. Gelbaum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Real And Complex Analysis
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Author : Walter Rudin
language : en
Publisher: McGraw-Hill Science, Engineering & Mathematics
Release Date : 1974
Real And Complex Analysis written by Walter Rudin and has been published by McGraw-Hill Science, Engineering & Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Complex Analysis
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Author : Joseph Bak
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-02
Complex Analysis written by Joseph Bak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-02 with Mathematics categories.
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.