The Theory Of Functions Of A Real Variable Second Edition
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Functions Of A Real Variable
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Functions Of A Real Variable written by N. Bourbaki 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 2013-12-01 with Mathematics categories.
This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to thestudy of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
Methods Of The Theory Of Functions Of Many Complex Variables
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Author : Vasiliy Sergeyevich Vladimirov
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Methods Of The Theory Of Functions Of Many Complex Variables written by Vasiliy Sergeyevich Vladimirov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
Real And Abstract Analysis
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Author : Edwin Hewitt
language : en
Publisher: Springer
Release Date : 1975-07-09
Real And Abstract Analysis written by Edwin Hewitt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-07-09 with Mathematics categories.
This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus tomarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we have given elementary avatars of all important theorems, with appro priate suggestions for skipping. We have given complete definitions, ex planations, and proofs throughout, so that the book should be usable for individual study as well as for a course text. Prerequisites for reading the book are the following. The reader is assumed to know elementary analysis as the subject is set forth, for example, in ToM M. APOSTOL's Mathematical Analysis [Addison-Wesley Publ. Co., Reading, Mass., 1957], orWALTERRUDIN's Principles of Mathe matical Analysis [2nd Ed., McGraw-Hill Book Co., New York, 1964].
The Theory Of Functions Of A Real Variable Second Edition
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Author : Ralph Jeffery
language : en
Publisher:
Release Date : 2019
The Theory Of Functions Of A Real Variable Second Edition written by Ralph Jeffery and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Functions of real variables categories.
This textbook leads the reader by easy stages through the essential parts of the theory of sets and theory of measure to the properties of the Lebesgue integral. The first part of the book gives a general introduction to functions of a real variable, measure, and integration, while the second part treats the problem of inverting the derivative of continuous functions, leading to the Denjoy integrals, and studies the derivates and approximate derivates of functions of a real variable on arbitrary linear sets. The author considers the presentation of this second part as the main purpose of his book.
Intermediate Analysis
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Author : John Meigs Hubbell Olmsted
language : en
Publisher:
Release Date : 1956
Intermediate Analysis written by John Meigs Hubbell Olmsted and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Mathematics categories.
Basic Real Analysis
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Author : Houshang H. Sohrab
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-03
Basic Real Analysis written by Houshang H. Sohrab 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 2003-06-03 with Mathematics categories.
Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.
Theory Of Functions Of A Complex Variable
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Author : A. I. Markushevich
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Theory Of Functions Of A Complex Variable written by A. I. Markushevich 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 2013 with Analytic functions categories.
Complex Function Theory
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Author : Donald Sarason
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-12-20
Complex Function Theory written by Donald Sarason 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 2007-12-20 with Mathematics categories.
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.
The Theory Of Functions Of Real Variables Second Edition
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Author : Lawrence Murray GRAVES
language : en
Publisher:
Release Date : 1956
The Theory Of Functions Of Real Variables Second Edition written by Lawrence Murray GRAVES and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with categories.
The Theory Of Functions Of A Real Variable And The Theory Of Fourier S Series
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Author : Ernest William Hobson
language : en
Publisher: CUP Archive
Release Date : 1927
The Theory Of Functions Of A Real Variable And The Theory Of Fourier S Series written by Ernest William Hobson and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Fourier series categories.