Introductory Functional Analysis

With Applications to Boundary Value Problems and Finite Elements

Author: B.D. Reddy

Publisher: Springer Science & Business Media

ISBN: 1461205751

Category: Mathematics

Page: 472

View: 4901

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.

From Vector Spaces to Function Spaces

Introduction to Functional Analysis with Applications

Author: Yutaka Yamamoto

Publisher: SIAM

ISBN: 1611972302

Category: Mathematics

Page: 260

View: 4769

A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.

Partielle Differentialgleichungen der Geometrie und der Physik 2

Funktionalanalytische Lösungsmethoden

Author: Friedrich Sauvigny

Publisher: Springer-Verlag

ISBN: 3540275401

Category: Mathematics

Page: 350

View: 4484

Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.

Lineare Funktionalanalysis

Eine anwendungsorientierte Einführung

Author: Hans Wilhelm Alt

Publisher: Springer-Verlag

ISBN: 3642222617

Category: Mathematics

Page: 449

View: 8683

Die lineare Funktionalanalysis ist ein Teilgebiet der Mathematik, das Algebra mit Topologie und Analysis verbindet. Das Buch führt in das Fachgebiet ein, dabei bezieht es sich auf Anwendungen in Mathematik und Physik. Neben den vollständigen Beweisen aller mathematischen Sätze enthält der Band zahlreiche Aufgaben, meist mit Lösungen. Für die Neuauflage wurden die Inhalte komplett überarbeitet. Das Standardwerk auf dem Gebiet der Funktionalanalysis richtet sich insbesondere an Leser mit Interesse an Anwendungen auf Differentialgleichungen.

An Introduction to Functional Analysis

Author: Charles Swartz

Publisher: CRC Press

ISBN: 9780824786434

Category: Mathematics

Page: 600

View: 4324

Based on an introductory, graduate-level course given by Swartz at New Mexico State U., this textbook, written for students with a moderate knowledge of point set topology and integration theory, explains the principles and theories of functional analysis and their applications, showing the interpla

Functional Analysis

Author: Balmohan Vishnu Limaye

Publisher: New Age International

ISBN: 9788122408492

Category: Functional analysis

Page: 612

View: 8430

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.

Vorlesungen über Differential- und Integralrechnung

Band 1: Funktionen einer Veränderlichen

Author: Richard Courant

Publisher: Springer-Verlag

ISBN: 3662378000

Category: Technology & Engineering

Page: 410

View: 8725

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author: Haim Brezis

Publisher: Springer Science & Business Media

ISBN: 0387709134

Category: Mathematics

Page: 600

View: 8169

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.

Applied Functional Analysis

Numerical Methods, Wavelet Methods, and Image Processing

Author: Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 9780203913017

Category: Mathematics

Page: 660

View: 2655

The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.

Applications of Functional Analysis and Operator Theory

Author: V. Hutson,J. Pym,M. Cloud

Publisher: Elsevier

ISBN: 9780080527314

Category: Mathematics

Page: 432

View: 6044

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features - Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. - Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. - Introduces each new topic with a clear, concise explanation. - Includes numerous examples linking fundamental principles with applications. - Solidifies the reader’s understanding with numerous end-of-chapter problems. · Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. · Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. · Introduces each new topic with a clear, concise explanation. · Includes numerous examples linking fundamental principles with applications. · Solidifies the reader's understanding with numerous end-of-chapter problems.

Functional Analysis

Theory and Applications

Author: Robert E. Edwards

Publisher: Courier Corporation

ISBN: 9780486681436

Category: Mathematics

Page: 783

View: 4102

Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

Linear Functional Analysis

Author: Joan Cerda

Publisher: American Mathematical Soc.

ISBN: 0821851152

Category: Mathematics

Page: 330

View: 8498

"Functional analysis studies the algebraic, geometric, and topological structures of spaces and operators that underlie many classical problems. Individual functions satisfying specific equations are replaced by classes of functions and transforms that are determined by the particular problems at hand. This book presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. The exposition avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems. The material in the first part of the book can be used for an introductory course on functional analysis, with an emphasis on the role of duality. The second part introduces distributions and Sobolev spaces and their applications. Convolution and the Fourier transform are shown to be useful tools for the study of partial differential equations. Fundamental solutions and Green's functions are considered and the theory is illustrated with several applications. In the last chapters, the Gelfand transform for Banach algebras is used to present the spectral theory of bounded and unbounded operators, which is then used in an introduction to the basic axioms of quantum mechanics. The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology. Almost 240 exercises will help the reader in better understanding the concepts employed."--Publisher's description.

Functional Analysis

An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

Author: Joseph Muscat

Publisher: Springer

ISBN: 3319067281

Category: Mathematics

Page: 420

View: 1430

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.

Linear Functional Analysis

Author: Bryan P. Rynne,Martin A. Youngson

Publisher: Springer Science & Business Media

ISBN: 9781852332570

Category: Mathematics

Page: 273

View: 7875

Providing an introduction to the ideas and methods of linear functional analysis, this book shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. In the initial chapters, the theory of infinite-dimensional normed spaces (in particular Hilbert spaces) is developed, while in later chapters the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapter discusses the two particularly important areas of integral and differential equations. The reader is assumed to have a standard undergraduate knowledge of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration. An introductory chapter summarizes the requisite material. Many exercises are included with solutions provided for each.