Several Real Variables
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Functions Of Several Real Variables
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Author : Martin A. Moskowitz
language : en
Publisher: World Scientific
Release Date : 2011
Functions Of Several Real Variables written by Martin A. Moskowitz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one theorem upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify the theory and teach the reader how to apply it to solve problems in mathematics and other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Brouwer's fixed point theorem, Picard's theorem and the Weierstrass approximation theorem are discussed in stared sections.
Several Real Variables
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Author : Shmuel Kantorovitz
language : en
Publisher: Springer
Release Date : 2016-02-09
Several Real Variables written by Shmuel Kantorovitz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-09 with Mathematics categories.
This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: •The p-norms on vector space and their equivalence •The Weierstrass and Stone-Weierstrass approximation theorems •The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables •The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem •Applications to Ordinary Differential Equations •Line integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.
Functions Of Several Real Variables
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Author : J. R. L. Webb
language : en
Publisher: Prentice Hall
Release Date : 1991
Functions Of Several Real Variables written by J. R. L. Webb and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Aimed at second year undergraduates through to postgraduates studying mathematical analysis, this textbook describes the theory of real analysis up to, but excluding, multiple integration. It includes a study of differentiation, culminating in the implicit function theorem.
First Steps In Several Complex Variables
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Author : Marek Jarnicki
language : en
Publisher: European Mathematical Society
Release Date : 2008
First Steps In Several Complex Variables written by Marek Jarnicki and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader may learn much about this area without encountering too many technical difficulties. Chapter 1 describes the fundamental notions and the phenomenon of simultaneous holomorphic extension. Chapter 2 presents a fairly complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter gives a classification of Reinhardt domains of existence for the most important classes of holomorphic functions. The last chapter deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may be useful as seminar topics. The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the only prerequisite is a basic knowledge of analysis.
Introduction To Analysis In Several Variables Advanced Calculus
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Author : Michael E. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-27
Introduction To Analysis In Several Variables Advanced Calculus written by Michael E. Taylor 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 2020-07-27 with Education categories.
This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
Introduction To Complex Analysis In Several Variables
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Author : Volker Scheidemann
language : en
Publisher: Springer Nature
Release Date : 2023-04-26
Introduction To Complex Analysis In Several Variables written by Volker Scheidemann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-26 with Mathematics categories.
This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.
Tasty Bits Of Several Complex Variables
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Author : Jiri Lebl
language : en
Publisher: Lulu.com
Release Date : 2019-05-06
Tasty Bits Of Several Complex Variables written by Jiri Lebl and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-06 with Mathematics categories.
An introduction to the field of Several Complex Variables. A course for graduate students after one semester of standard complex analysis in one variable. This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014, Spring 2016, and Spring 2019 semesters at Oklahoma State University. See https: //www.jirka.org/scv/ for more information.
Theory And Applications Of Differentiable Functions Of Several Variables
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Author : Sergei Mikhailovich Nikol'skii
language : en
Publisher: American Mathematical Soc.
Release Date : 1967
Theory And Applications Of Differentiable Functions Of Several Variables written by Sergei Mikhailovich Nikol'skii 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 1967 with Differentiable functions categories.
Holomorphic Functions And Integral Representations In Several Complex Variables
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Author : R. Michael Range
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-06-26
Holomorphic Functions And Integral Representations In Several Complex Variables written by R. Michael Range 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 1998-06-26 with Mathematics categories.
The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Library Of Congress Subject Headings
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Author : Library of Congress
language : en
Publisher:
Release Date : 2007
Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Subject headings, Library of Congress categories.