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Textbook of Functional Analysis

Textbook of Functional Analysis Author V. K. Krishnan
ISBN-10 8120316274
Release 2001-01-01
Pages 404
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Textbook of Functional Analysis has been writing in one form or another for most of life. You can find so many inspiration from Textbook of Functional Analysis also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Textbook of Functional Analysis book for free.


ISBN-10 9788120348912
Release 2014-01-01
Pages 416
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This unique, comprehensive and student-friendly book, now in its second edition, continues to hold the purpose of explaining and illustrating the use of the basic theorems in functional analysis through solved numerical problems. The text has been revised on the basis of the readers’ feedback. The book now covers ample worked-out numerical problems related to the spectral properties of compact operators on Banach spaces as well as on Hilbert spaces. Inclusion of a few problems based on the square root of a positive operator also contributes to the major highlights of this edition. Such a practical approach will greatly facilitate students to have a thorough grasp of the subject. This stands in stark contrast to the method followed in most of the books where a great amount of theory is given with a smattering of problems to elucidate the topics discussed. Intended as a text for the students pursuing postgraduate courses in mathematics, this book with its systematic and precise presentation and provision of a large number of exercises should prove to be a trendsetter in its approach to the subject. This novelty of approach appeals the students in particular.

Essential Results of Functional Analysis

Essential Results of Functional Analysis Author Robert J. Zimmer
ISBN-10 0226983382
Release 1990-01-15
Pages 157
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Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.

Functional Analysis Calculus of Variations and Optimal Control

Functional Analysis  Calculus of Variations and Optimal Control Author Francis Clarke
ISBN-10 9781447148203
Release 2013-02-06
Pages 591
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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Functional Analysis

Functional Analysis Author Balmohan Vishnu Limaye
ISBN-10 8122408494
Release 1996
Pages 612
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This Book Is An Introductory Text Written With Minimal Prerequisites. The Plan Is To Impose A Distance Structure On A Linear Space, Exploit It Fully And Then Introduce Additional Features Only When One Cannot Get Any Further Without Them. The Book Naturally Falls Into Two Parts And Each Of Them Is Developed Independently Of The Other The First Part Deals With Normed Spaces, Their Completeness And Continuous Linear Maps On Them, Including The Theory Of Compact Operators. The Much Shorter Second Part Treats Hilbert Spaces And Leads Upto The Spectral Theorem For Compact Self-Adjoint Operators. Four Appendices Point Out Areas Of Further Development.Emphasis Is On Giving A Number Of Examples To Illustrate Abstract Concepts And On Citing Varirous Applications Of Results Proved In The Text. In Addition To Proving Existence And Uniqueness Of A Solution, Its Apprroximate Construction Is Indicated. Problems Of Varying Degrees Of Difficulty Are Given At The End Of Each Section. Their Statements Contain The Answers As Well.

A Companion to Analysis

A Companion to Analysis Author Thomas William Körner
ISBN-10 9780821834473
Release 2004
Pages 590
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This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.

Quantitative Finance

Quantitative Finance Author Erik Schlogl
ISBN-10 9781498785549
Release 2016-04-07
Pages 354
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Quantitative Finance: An Object-Oriented Approach in C++ provides readers with a foundation in the key methods and models of quantitative finance. Keeping the material as self-contained as possible, the author introduces computational finance with a focus on practical implementation in C++. Through an approach based on C++ classes and templates, the text highlights the basic principles common to various methods and models while the algorithmic implementation guides readers to a more thorough, hands-on understanding. By moving beyond a purely theoretical treatment to the actual implementation of the models using C++, readers greatly enhance their career opportunities in the field. The book also helps readers implement models in a trading or research environment. It presents recipes and extensible code building blocks for some of the most widespread methods in risk management and option pricing. Web Resource The author’s website provides fully functional C++ code, including additional C++ source files and examples. Although the code is used to illustrate concepts (not as a finished software product), it nevertheless compiles, runs, and deals with full, rather than toy, problems. The website also includes a suite of practical exercises for each chapter covering a range of difficulty levels and problem complexity.

Functional Analysis

Functional Analysis Author V.S. Sunder
ISBN-10 3764358920
Release 1998-08-25
Pages 241
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In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutative C*-algebras. A discussion of representations of C*-algebras follows, and the final section of this chapter is devoted to the Hahn-Hellinger classification of separable representations of commutative C*-algebras. After this detour into operator algebras, the fourth chapter reverts to more standard operator theory in Hilbert space, dwelling on topics such as the spectral theorem for normal operators, the polar decomposition theorem, and the Fredholm theory for compact operators. A brief introduction to the theory of unbounded operators on Hilbert space is given in the fifth and final chapter. There is a voluminous appendix whose purpose is to fill in possible gaps in the reader's background in various areas such as linear algebra, topology, set theory and measure theory. The book is interspersed with many exercises, and hints are provided for the solutions to the more challenging of these.

Practical Software Testing

Practical Software Testing Author Ilene Burnstein
ISBN-10 9780387216584
Release 2006-04-18
Pages 710
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Based on the needs of the educational community, and the software professional, this book takes a unique approach to teaching software testing. It introduces testing concepts that are managerial, technical, and process oriented, using the Testing Maturity Model (TMM) as a guiding framework. The TMM levels and goals support a structured presentation of fundamental and advanced test-related concepts to the reader. In this context, the interrelationships between theoretical, technical, and managerial concepts become more apparent. In addition, relationships between the testing process, maturity goals, and such key players as managers, testers and client groups are introduced. Topics and features: - Process/engineering-oriented text - Promotes the growth and value of software testing as a profession - Introduces both technical and managerial aspects of testing in a clear and precise style - Uses the TMM framework to introduce testing concepts in a systemmatic, evolutionary way to faciliate understanding - Describes the role of testing tools and measurements, and how to integrate them into the testing process Graduate students and industry professionals will benefit from the book, which is designed for a graduate course in software testing, software quality assurance, or software validation and verification Moreover, the number of universities with graduate courses that cover this material will grow, given the evoluation in software development as an engineering discipline and the creation of degree programs in software engineering.

Foundations of Functional Analysis

Foundations of Functional Analysis Author Saminathan Ponnusamy
ISBN-10 1842650793
Release 2002-01-01
Pages 457
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Foundations of Functional Analysis provides fundamental concepts about the theory, application and various methods involving functional analysis for students, teachers, scientists and engineers. Divided into three parts it covers: Basic facts of linear algebra and real analysis Normed spaces, contraction mappings, linear operators between normed spaces and fundamental results on these topics. Hilbert spaces and the representation of continuous linear function with applications. In this self-contained book, all the concepts, results and their consequences are motivated and illustrated by numerous examples in each chapter with carefully chosen exercises.

Functional Analysis

Functional Analysis Author Joseph Muscat
ISBN-10 9783319067285
Release 2014-07-23
Pages 420
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This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

Lie Groups

Lie Groups Author Claudio Procesi
ISBN-10 9780387289298
Release 2007-10-17
Pages 600
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Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. By covering sufficient background material, the book is made accessible to a reader with a relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. This unique exposition is suitable for a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.

Problem Solving Through Problems

Problem Solving Through Problems Author Loren C. Larson
ISBN-10 9781461254980
Release 2012-12-06
Pages 352
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This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

Functional Analysis Sobolev Spaces and Partial Differential Equations

Functional Analysis  Sobolev Spaces and Partial Differential Equations Author Haim Brezis
ISBN-10 9780387709147
Release 2010-11-02
Pages 600
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This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Metaprogramming in R

Metaprogramming in R Author Thomas Mailund
ISBN-10 9781484228814
Release 2017-06-01
Pages 103
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Learn how to manipulate functions and expressions to modify how the R language interprets itself. This book is an introduction to metaprogramming in the R language, so you will write programs to manipulate other programs. Metaprogramming in R shows you how to treat code as data that you can generate, analyze, or modify. R is a very high-level language where all operations are functions and all functions are data that can be manipulated. This book shows you how to leverage R's natural flexibility in how function calls and expressions are evaluated, to create small domain-specific languages to extend R within the R language itself. What You'll Learn Find out about the anatomy of a function in R Look inside a function call Work with R expressions and environments Manipulate expressions in R Use substitutions Who This Book Is For Those with at least some experience with R and certainly for those with experience in other programming languages.

Orthodontic Diagnosis

Orthodontic Diagnosis Author Thomas Rakosi
ISBN-10 9780865774506
Release 1993-01-01
Pages 272
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An illustrated guide for the complex process of orthodontic diagnostics and indication. The total process of treatment planning including the scientific bases is pictorially described. Beside the conventional methods of examination and model analysis, emphasis is placed on the cranio-facial growth processes, the aetiology of malocclusions and on the importance of functional analysis. The following three aspects are described in detail in this book: Growth of the Facial Skeleton - types of treatment which promote or guide growth. In order to control these natural processes artificially, a precise understanding of them is required. Aetiology of the Malocclusion - the various types of causative therapy and the elimination of the causes. Functional Analysis - many malocclusions are a result of dysfunctions. As a variety of methods are available for treating dysfunctions, functional analysis is taken very seriously.

Stroke Rehabilitation

Stroke Rehabilitation Author Glen Gillen
ISBN-10 9780323172813
Release 2015-08-12
Pages 768
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Gillen's Stroke Rehabilitation: A Function-Based Approach, 3rd Edition is theonly comprehensive, evidence-based stroke rehabilitation resource for occupational therapists. Extensively updated with the latest research in assessment and intervention, this essential text presents a holistic, application-based approach that integrates background medical information, samples of functionally based evaluations, and current treatment techniques and intervention strategies to help you confidently manage the growing number of stroke rehabilitation clients. UNIQUE! Case studies challenge you to apply rehabilitation concepts to realistic scenarios. Evidence-based clinical trials and outcome studies clearly outline the basis for stroke interventions. UNIQUE! Survivor's Perspectives help you understand the stroke rehabilitation process from the client's point-of-view. UNIQUE! A multidisciplinary approach highlights discipline-specific distinctions in stroke rehabilitation among occupation and physical therapists, physicians, and speech-language pathologists. Review questions in each chapter help you assess your understanding of rehabilitation concepts. Key terms and chapter objectives at the beginning of each chapter help you study more efficiently. Three new chapters broaden your understanding of stroke intervention in the areas ofUsing Technology to Improve Limb Function, Managing Speech and Language Deficits after Stroke, andParenting after Stroke. Learning activities and interactive references on a companion Evolve Resources website help you review textbook content and locate additional information.