Elements of Abstract Analysis
Elements of Abstract Analysis

Author: Mícheál O'Searcoid

Publisher: Springer Science & Business Media

Published: 2001-11-09

Total Pages: 318

ISBN-13: 9781852334246

DOWNLOAD EBOOK

While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.

Elements of Abstract Analysis
Elements of Abstract Analysis

Author: Mícheál O'Searcoid

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 311

ISBN-13: 1447101790

DOWNLOAD EBOOK

While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.

A Course in Abstract Analysis
A Course in Abstract Analysis

Author: John B. Conway

Publisher: American Mathematical Soc.

Published: 2012-10-03

Total Pages: 385

ISBN-13: 0821890832

DOWNLOAD EBOOK

This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.

Foundations of Abstract Analysis
Foundations of Abstract Analysis

Author: Jewgeni H. Dshalalow

Publisher: Springer Science & Business Media

Published: 2012-11-09

Total Pages: 756

ISBN-13: 1461459621

DOWNLOAD EBOOK

Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.

Real and Abstract Analysis
Real and Abstract Analysis

Author: E. Hewitt

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 485

ISBN-13: 3642880444

DOWNLOAD EBOOK

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], or WALTER RUDIN'S Principles of M athe nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].

Elements of Real Analysis
Elements of Real Analysis

Author: M.A. Al-Gwaiz

Publisher: CRC Press

Published: 2006-08-21

Total Pages: 448

ISBN-13: 142001160X

DOWNLOAD EBOOK

Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.

Elements of Functional Analysis
Elements of Functional Analysis

Author: I. J. Maddox

Publisher: CUP Archive

Published: 1988

Total Pages: 258

ISBN-13: 9780521358682

DOWNLOAD EBOOK

An advanced textbook for an introductory course in functional analysis. Includes revision of the work on metric and topological linear spaces and reflexivity and weak convergence. New material on the Wiener algebra of absolutely convergent Fourier series and on weak topologies has been added. A new final chapter includes elementary applications of functional analysis to differential and integral equations. Annotation copyrighted by Book News, Inc., Portland, OR

Elements of Nonlinear Analysis
Elements of Nonlinear Analysis

Author: Michel Chipot

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 258

ISBN-13: 3034884281

DOWNLOAD EBOOK

"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones...it encompass[es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications." --MATHEMATICAL REVIEWS

Introductory Functional Analysis
Introductory Functional Analysis

Author: B.D. Reddy

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 472

ISBN-13: 1461205751

DOWNLOAD EBOOK

Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.