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Cauchy And The Creation Of Complex Function Theory
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Book Synopsis Cauchy and the Creation of Complex Function Theory by : Frank Smithies
Download or read book Cauchy and the Creation of Complex Function Theory written by Frank Smithies and published by Cambridge University Press. This book was released on 1997-11-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr Smithies' analysis of the process whereby Cauchy created the basic structure of complex analysis, begins by describing the 18th century background. He then proceeds to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem. Controversies associated with the the birth of the subject are also considered in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This authoritative book is the first to make use of the whole spectrum of available original sources.
Book Synopsis Complex Function Theory by : Donald Sarason
Download or read book Complex Function Theory written by Donald Sarason and published by American Mathematical Society. This book was released on 2021-02-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
Book Synopsis Theory of Complex Functions by : Reinhold Remmert
Download or read book Theory of Complex Functions written by Reinhold Remmert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.
Book Synopsis Function Theory of One Complex Variable by : Robert Everist Greene
Download or read book Function Theory of One Complex Variable written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.
Book Synopsis Complex Function Theory by : Anthony S. B. Holland
Download or read book Complex Function Theory written by Anthony S. B. Holland and published by North-Holland. This book was released on 1980 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hidden Harmony—Geometric Fantasies by : Umberto Bottazzini
Download or read book Hidden Harmony—Geometric Fantasies written by Umberto Bottazzini and published by Springer Science & Business Media. This book was released on 2013-06-21 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
Book Synopsis Notes on Complex Function Theory by : Donald Sarason
Download or read book Notes on Complex Function Theory written by Donald Sarason and published by . This book was released on 1994 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Analysis by : Jerry R. Muir, Jr.
Download or read book Complex Analysis written by Jerry R. Muir, Jr. and published by John Wiley & Sons. This book was released on 2015-05-26 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.
Download or read book Complex Analysis written by Murali Rao and published by World Scientific. This book was released on 1991 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.
Book Synopsis An Introduction to Complex Function Theory by : Bruce P. Palka
Download or read book An Introduction to Complex Function Theory written by Bruce P. Palka and published by Springer Science & Business Media. This book was released on 1991 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
Book Synopsis Classical Topics in Complex Function Theory by : Reinhold Remmert
Download or read book Classical Topics in Complex Function Theory written by Reinhold Remmert and published by Springer Science & Business Media. This book was released on 1997-11-14 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein's proof of Euler's product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike
Book Synopsis Complex Analysis by : Jerry R. Muir, Jr.
Download or read book Complex Analysis written by Jerry R. Muir, Jr. and published by John Wiley & Sons. This book was released on 2015-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.
Book Synopsis Real and Complex Analysis by : Christopher Apelian
Download or read book Real and Complex Analysis written by Christopher Apelian and published by CRC Press. This book was released on 2009-12-08 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Function Theory written by and published by Academic Press. This book was released on 2014-05-14 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Function Theory
Book Synopsis Theory Of Complex Variable by : R.K. Pandey
Download or read book Theory Of Complex Variable written by R.K. Pandey and published by Discovery Publishing House. This book was released on 2007 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Algebra of Complex Number, Functions of Complex Number, Limit and Continuity, Analytic Functions, Complex Integration, Cauchy Integral Theorem, Contour Integration, Series in Complex Number, Taylor and Laurent Series.
Book Synopsis Elementary Theory of Analytic Functions of One or Several Complex Variables by : Henri Cartan
Download or read book Elementary Theory of Analytic Functions of One or Several Complex Variables written by Henri Cartan and published by Courier Corporation. This book was released on 2013-04-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Book Synopsis The Real and the Complex: A History of Analysis in the 19th Century by : Jeremy Gray
Download or read book The Real and the Complex: A History of Analysis in the 19th Century written by Jeremy Gray and published by Springer. This book was released on 2015-10-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
