Linear And Complex Analysis
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Linear And Complex Analysis For Applications
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Author : John P. D'Angelo
language : en
Publisher: CRC Press
Release Date : 2017-08-02
Linear And Complex Analysis For Applications written by John P. D'Angelo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-02 with Mathematics categories.
Linear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author’s teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work, to unify many distinct and seemingly isolated topics, to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems. The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III. As the topics are being reviewed, new material is inserted to help the student develop skill in both computation and theory. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Connections among the topics and applications appear throughout the book. The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, whose unifying theme is linear systems. It includes many unusual examples and contains more than 450 exercises.
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.
Linear Functional Analysis
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Author :
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2005
Linear Functional Analysis written by and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Functional analysis categories.
Linear And Complex Analysis Problem Book 3
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Author : Victor P. Havin
language : en
Publisher: Springer
Release Date : 2006-12-08
Linear And Complex Analysis Problem Book 3 written by Victor P. Havin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and metho- dological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
Complex Analysis
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Author : D.H. Luecking
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analysis written by D.H. Luecking 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.
The main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely identifies the dual of H(G) with the space of germs of holomorphic functions on the complement of G. From this result, for example, Runge's approximation theorem and the global Cauchy integral theorem follow in a few short steps. Other consequences of this duality theorem are the Germay interpolation theorem and the Mittag-Leffler Theorem. The approach via duality is entirely consistent with Cauchy's approach to complex variables, since curvilinear integrals are typical examples of linear functionals. The prerequisite for the book is a one-semester course in com plex variables at the undergraduate-graduate level, so that the elements of the local theory are supposed known. In particular, the Cauchy Theorem for the square and the circle are assumed, but not the global Cauchy Theorem in any of its forms. The second author has three times taught a graduate course based on this material at the University of Illinois, with good results.
Introductory Complex Analysis
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Author : Richard A. Silverman
language : en
Publisher: Courier Corporation
Release Date : 1984-05-01
Introductory Complex Analysis written by Richard A. Silverman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-05-01 with Mathematics categories.
A shorter version of A. I. Markushevich's masterly three-volume Theory of Functions of a Complex Variable, this edition is appropriate for advanced undergraduate and graduate courses in complex analysis. Numerous worked-out examples and more than 300 problems, some with hints and answers, make it suitable for independent study. 1967 edition.
Linear Und Complex Analysis Problem Book
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Author : V. P. Havin
language : en
Publisher: Springer
Release Date : 2006-11-14
Linear Und Complex Analysis Problem Book written by V. P. Havin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Linear And Complex Analysis Problem Book 3
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Author : Victor P. Havin
language : en
Publisher: Springer
Release Date : 2006-12-08
Linear And Complex Analysis Problem Book 3 written by Victor P. Havin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
A Complex Analysis Problem Book
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2016-10-26
A Complex Analysis Problem Book written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-26 with Mathematics categories.
This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.
Complex Analysis
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Author : Theodore W. Gamelin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-01
Complex Analysis written by Theodore W. Gamelin 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 2013-11-01 with Mathematics categories.
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.