Introduction To The Analysis Of Normed Linear Spaces
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Introduction To The Analysis Of Normed Linear Spaces
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Author : J. R. Giles
language : en
Publisher: Cambridge University Press
Release Date : 2000-03-13
Introduction To The Analysis Of Normed Linear Spaces written by J. R. Giles 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 2000-03-13 with Mathematics categories.
This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.
Introduction To The Analysis Of Metric Spaces
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Author : John R. Giles
language : en
Publisher: Cambridge University Press
Release Date : 1987-09-03
Introduction To The Analysis Of Metric Spaces written by John R. Giles 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 1987-09-03 with Mathematics categories.
This is an introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. Assuming a basic knowledge of real analysis and linear algebra, the student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. An example is the link between normed linear spaces and linear algebra; finite dimensional spaces are discussed early. The treatment progresses from the concrete to the abstract: thus metric spaces are studied in some detail before general topology is begun, though topological properties of metric spaces are explored in the book. Graded exercises are provided at the end of each section; in each set the earlier exercises are designed to assist in the detection of the structural properties in concrete examples while the later ones are more conceptually sophisticated.
Classical Analysis On Normed Spaces
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Author : Tsoy-Wo Ma
language : en
Publisher: World Scientific
Release Date : 1995
Classical Analysis On Normed Spaces written by Tsoy-Wo Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis.
Normed Linear Spaces
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Author : Mahlon Marsh Day
language : en
Publisher: Springer
Release Date : 2013-06-29
Normed Linear Spaces written by Mahlon Marsh Day and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book contains a compressed introduction to the study of normed linear spaces and to that part of the theory of linear topological spaces without which the main discussion could not well proceed. Definitions of many terms which are required in passing can be found in the alphabetical index, page 134. Symbols which are used throughout all, or a significant part, of this book are indexed on page 132. Each reference to the bibliography, page 124, is made by means of the author's name, supplemented when necessary by a number in square brackets. The bibliography does not completely cover the available literature, even the most recent; each paper in it is the subject of a specific reference at some point in the text. The writer takes this opportunity to express thanks to the University of Illinois, the National Science Foundation, and the University of Washington, each of which has contributed in some degree to the cultural, financial, or physical support of the writer, and to Mr. R. R. PHELPS, who eradicated many of the errors with which the manuscript was infested.
Introduction To Functional Analysis
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Author : Angus Ellis Taylor
language : en
Publisher: Krieger Publishing Company
Release Date : 1986
Introduction To Functional Analysis written by Angus Ellis Taylor and has been published by Krieger Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Functional analysis categories.
Spaces An Introduction To Real Analysis
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Author : Tom L. Lindstrøm
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-28
Spaces An Introduction To Real Analysis written by Tom L. Lindstrøm 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 2017-11-28 with Functional analysis categories.
Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.
Analysis In Vector Spaces
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Author : Mustafa A. Akcoglu
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
Analysis In Vector Spaces written by Mustafa A. Akcoglu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined withrelated computational methods are essential to understanding nearlyall areas of quantitative science. Analysis in Vector Spacespresents the central results of this classic subject throughrigorous arguments, discussions, and examples. The book aims tocultivate not only knowledge of the major theoretical results, butalso the geometric intuition needed for both mathematicalproblem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology,and notation and also provide a basic introduction to set theory,the properties of real numbers, and a review of linear algebra. Anelegant approach to eigenvector problems and the spectral theoremsets the stage for later results on volume and integration.Subsequent chapters present the major results of differential andintegral calculus of several variables as well as the theory ofmanifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter toreinforce new concepts and to illustrate how results can be appliedto additional problems. Furthermore, proofs and examples arepresented in a clear style that emphasizes the underlying intuitiveideas. Counterexamples are provided throughout the book to warnagainst possible mistakes, and extensive appendices outline theconstruction of real numbers, include a fundamental result aboutdimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra andsingle variable calculus, Analysis in Vector Spaces is anexcellent book for a second course in analysis for mathematics,physics, computer science, and engineering majors at theundergraduate and graduate levels. It also serves as a valuablereference for further study in any discipline that requires a firmunderstanding of mathematical techniques and concepts.
Functional Analysis
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Author : Terry J. Morrison
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
Functional Analysis written by Terry J. Morrison and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.
Analysis Of Normed Linear Spaces
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Author : John Robilliard Giles
language : en
Publisher:
Release Date : 1976
Analysis Of Normed Linear Spaces written by John Robilliard Giles and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Normed linear spaces categories.
Calculus On Normed Vector Spaces
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Author : Rodney Coleman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-25
Calculus On Normed Vector Spaces written by Rodney Coleman 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 2012-07-25 with Mathematics categories.
This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.