Twenty One Lectures On Complex Analysis
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Twenty One Lectures On Complex Analysis
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Author : Alexander Isaev
language : en
Publisher: Springer
Release Date : 2017-11-29
Twenty One Lectures On Complex Analysis written by Alexander Isaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.
At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.
Proceedings Of The Conference On Complex Analysis
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Author : A. Aeppli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Proceedings Of The Conference On Complex Analysis written by A. Aeppli 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.
This volume contains the articles contributed to the Minnesota Con ference on Complex Analysis (COCA). The Conference was held March 16-21, 1964, at the University of Minnesota, under the sponsorship of the U. S. Air Force Office of Scientific Research with thirty-one invited participants attending. Of these, nineteen presented their papers in person in the form of one-hour lectures. In addition, this volume con tains papers contributed by other attending participants as well as by participants who, after having planned to attend, were unable to do so. The list of particip ants, as well as the contributions to these Proceed ings, clearly do not represent a complete coverage of the activities in all fields of complex analysis. It is hoped, however, that these limitations stemming from the partly deliberate selections will allow a fairly com prehensive account of the current research in some of those areas of complex analysis that, in the editors' belief, have rapidly developed during the past decade and may remain as active in the foreseeable future as they are at the present time. In conclusion, the editors wish to thank, first of all, the participants and contributors to these Proceedings for their enthusiastic cooperation and encouragement. Our thanks are due also to the University of Min nesota, for offering the physical facilities for the Conference, and to Springer-Verlag for publishing these proceedings.
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.
Five Lectures In Complex Analysis
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Author : Manuel D. Contreras
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Five Lectures In Complex Analysis written by Manuel D. Contreras 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 2010 with Functions of complex variables categories.
This volume contains state-of-art survey papers in complex analysis based on lectures given at the second Winter School on Complex Analysis and Operator Theory held in February 2008 at the University of Sevilla, Sevilla, Spain. --
Complex Analysis
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Complex Analysis written by Serge Lang 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 2013-06-29 with Mathematics categories.
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.
Foundations Of Group Analysis For The Twenty First Century
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Author : Jason Maratos
language : en
Publisher: Routledge
Release Date : 2018-05-15
Foundations Of Group Analysis For The Twenty First Century written by Jason Maratos and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-15 with Psychology categories.
The Institute of Group Analysis (IGA) celebrates forty years from its foundation with the publication of two new volumes tracing the foundations and applications of Group Analysis. The first volume ('Foundations') aims to publicise the foundations of group analysis (with the earliest papers of Foulkes) as well as the most influential theoretical contributions by pillars of modern group analysis, such as Pines, Brown, and Hopper. The reader will be able to see the development of Group Analysis, form an opinion about the trajectory that it follows, and judge which way the tradition of openness and creative integration of diverse theoretical contributions will lead in the twenty-first century. The second volume ('Applications') focuses on the numerous fields of work that use group analytic principles. Workers in the field of forensic psychotherapy would now consider it a great omission if they did not use some form of group analytic intervention, as would professionals dealing with those who manifest personality disorders, or those who work with different age groups, such as adolescents.
Operation Of Complex Water Systems
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Author : E. Guggino
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Operation Of Complex Water Systems written by E. Guggino 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 Science categories.
Most water systems in the industrial regions of the world are already developed. At the same time they are highly complex. This is true with respect to physical configuration, managment, operation, political goals, environmental interactions, etc. Thus the basic systems are already in place. This realization is the starting point for any new water developments and for operation. From this we conclude that whatever we do to meet new exigencies requires an understanding of the presently in-place complex water systems. Their operation is the important thing. And how can we adjust their operation to meet the new demands upon the system? This book deals with complex water systems and their operation. Some chapters are highly theoretical while others are rooted in practical applications. How can we an~lyze the operation of a complex water system and determine how its performance can be improved? Several chapters on mathematical analysis give approaches involving different aspects of this problem. But operation also has political, management, and physical aspects. These problems are addressed in chapters by managers who operate such systems. The main theme of all chapters is how to deal with the different aspects of a complex water system, already in place. We feel the book, in dealing with this question could be a start for new theoretical premises in water planning.
A Course In Complex Analysis
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Author : Saeed Zakeri
language : en
Publisher: Princeton University Press
Release Date : 2021-11-02
A Course In Complex Analysis written by Saeed Zakeri 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 2021-11-02 with Mathematics categories.
"This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry
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Author : Roger Penrose
language : en
Publisher: Cambridge University Press
Release Date : 1984
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry written by Roger Penrose and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
Complex Analyses In Engineering Science And Technology
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Author : S. G. Ahmed
language : en
Publisher: Bentham Science Publishers
Release Date : 2015-04-27
Complex Analyses In Engineering Science And Technology written by S. G. Ahmed and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-27 with Mathematics categories.
Complex Analysis for Science and Technology is a textbook for undergraduate and postgraduate students undertaking science, technology, engineering and mathematics (STEM) courses. The book begins with an introduction to basic complex numbers, followed by chapters covering complex functions, integrals, transformations and conformal mapping. Topics such as complex series and residue theory are also covered. Key features of this textbook include: -simple, easy-to-understand explanations of relevant concepts -a wide range of simple and complex examples -several figures where appropriate