The Linear Functions Of A Complex Variable
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The Linear Functions Of A Complex Variable
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Author : Frank Nelson Cole
language : en
Publisher:
Release Date : 1890
The Linear Functions Of A Complex Variable written by Frank Nelson Cole and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1890 with Functions categories.
Functions Of A Complex Variable
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Author : Hemant Kumar Pathak
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2016
Functions Of A Complex Variable written by Hemant Kumar Pathak and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
Functions of a Complex Variable provides all the material for a course on the theory of functions of a complex variable at the senior undergraduate and beginning graduate level. Also suitable for self-study, the book covers every topic essential to training students in complex analysis. It also incorporates special topics to enhance students' understanding of the subject, laying the foundation for future studies in analysis, linear algebra, numerical analysis, geometry, number theory, physics, thermodynamics, or electrical engineering. After introducing the basic concepts of complex numbers and their geometrical representation, the text describes analytic functions, power series and elementary functions, the conformal representation of an analytic function, special transformations, and complex integration. It next discusses zeros of an analytic function, classification of singularities, and singularity at the point of infinity; residue theory, principle of argument, Rouché's theorem, and the location of zeros of complex polynomial equations; and calculus of residues, emphasizing the techniques of definite integrals by contour integration. The authors then explain uniform convergence of sequences and series involving Parseval, Schwarz, and Poisson formulas. They also present harmonic functions and mappings, inverse mappings, and univalent functions as well as analytic continuation.
Entire Functions Of Several Complex Variables
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Author : Pierre Lelong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Entire Functions Of Several Complex Variables written by Pierre Lelong 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.
I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
Theory Of Functions Of A Complex Variable
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Author : Andrew Russell Forsyth
language : en
Publisher:
Release Date : 1893
Theory Of Functions Of A Complex Variable written by Andrew Russell Forsyth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1893 with Functions categories.
Functions Of A Complex Variable
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Author : J.N. Sharma
language : en
Publisher: Krishna Prakashan Media
Release Date : 1991
Functions Of A Complex Variable written by J.N. Sharma and has been published by Krishna Prakashan Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Functions of a complex variable categories.
The Linear Functions Of A Complex Variable
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Author : Jacob Goodman
language : en
Publisher:
Release Date : 1928
The Linear Functions Of A Complex Variable written by Jacob Goodman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1928 with categories.
Elements Of The Theory Of Functions Of A Complex Variable
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Author : Heinrich Durège
language : en
Publisher:
Release Date : 1896
Elements Of The Theory Of Functions Of A Complex Variable written by Heinrich Durège and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with Analytic functions categories.
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 : 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.
The Linear Functions Of A Complex Variable Interpreted As Transformations Of The Plane And Of The Sphere
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Author : Emory Potter Starke
language : en
Publisher:
Release Date : 1917
The Linear Functions Of A Complex Variable Interpreted As Transformations Of The Plane And Of The Sphere written by Emory Potter Starke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1917 with categories.