An Introduction To Functional Analysis In Computational Mathematics

Author : V.I. Lebedev
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241287

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An Introduction to Functional Analysis in Computational Mathematics by V.I. Lebedev Pdf

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand ing from a general viewpoint of ideas and methods of computational mathematics and of optimization problems for numerical algorithms. Functional analysis in mathematics is now just the small visible part of the iceberg. Its relief and summit were formed under the influence of this author's personal experience and tastes. This edition in English contains some additions and changes as compared to the second edition in Russian; discovered errors and misprints had been corrected again here; to the author's distress, they jump incomprehensibly from one edition to another as fleas. The list of literature is far from being complete; just a number of textbooks and monographs published in Russian have been included. The author is grateful to S. Gerasimova for her help and patience in the complex process of typing the mathematical manuscript while the author corrected, rearranged, supplemented, simplified, general ized, and improved as it seemed to him the book's contents. The author thanks G. Kontarev for the difficult job of translation and V. Klyachin for the excellent figures.

Author : L. V. Kantorovich,G. P. Akilov
Publisher : Elsevier
Page : 604 pages
File Size : 43,7 Mb
Release : 2014-05-18
Category : Mathematics
ISBN : 9781483147741

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Functional Analysis by L. V. Kantorovich,G. P. Akilov Pdf

Functional Analysis examines trends in functional analysis as a mathematical discipline and the ever-increasing role played by its techniques in applications. The theory of topological vector spaces is emphasized, along with the applications of functional analysis to applied analysis. Some topics of functional analysis connected with applications to mathematical economics and control theory are also discussed. Comprised of 18 chapters, this book begins with an introduction to the elements of the theory of topological spaces, the theory of metric spaces, and the theory of abstract measure spaces. Many results are stated without proofs. The discussion then turns to vector spaces, normed spaces, and linear operators and functionals. Subsequent chapters deal with the analytic representation of functionals; sequences of linear operators; the weak topology in a Banach space; and compact and adjoint operators. The last section focuses on functional equations, including the adjoint equation and functional equations of the second kind. This monograph is intended for students specializing in mathematical analysis and computational mathematics.

Author : Ramon E Moore,Michael J Cloud
Publisher : Elsevier
Page : 212 pages
File Size : 54,8 Mb
Release : 2007-06-01
Category : Technology & Engineering
ISBN : 9780857099433

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Computational Functional Analysis by Ramon E Moore,Michael J Cloud Pdf

This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ‘‘hybrid’’ method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ‘‘We learn by doing’’ is reflected throughout the book. Contains 100 problem-exercises, answers and tutorial hints for students reading applied functional analysis Introduces interval analysis into the mainstream of computational functional analysis

Author : Charles Swartz
Publisher : CRC Press
Page : 624 pages
File Size : 47,5 Mb
Release : 1992-01-28
Category : Mathematics
ISBN : 0824786432

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An Introduction to Functional Analysis by Charles Swartz Pdf

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

Author : Alfredo Lorenzi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 256 pages
File Size : 44,6 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940923

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An Introduction to Identification Problems via Functional Analysis by Alfredo Lorenzi Pdf

this monograph is based on two courses in computational mathematics and operative research, which were given by the author in recent years to doctorate and PhD students. The text focuses on an aspect of the theory of inverse problems, which is usually referred to as identification of parameters (numbers, vectors, matrices, functions) appearing in differential – or integrodifferential – equations. The parameters of such equations are either quite unknown or partially unknown, however knowledge about these is usually essential as they describe the intrinsic properties of the material or substance under consideration.

Author : J. Tinsley Oden,Leszek Demkowicz
Publisher : CRC Press
Page : 695 pages
File Size : 52,6 Mb
Release : 2017-12-01
Category : Mathematics
ISBN : 9781498761154

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Applied Functional Analysis by J. Tinsley Oden,Leszek Demkowicz Pdf

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Author : Abul Hasan Siddiqi
Publisher : Springer
Page : 566 pages
File Size : 52,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9789811037252

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Functional Analysis and Applications by Abul Hasan Siddiqi Pdf

This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.

Author : J. Tinsley Oden,Leszek Demkowicz
Publisher : CRC Press
Page : 589 pages
File Size : 54,6 Mb
Release : 2010-03-02
Category : Mathematics
ISBN : 9781420091953

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Applied Functional Analysis, Second Edition by J. Tinsley Oden,Leszek Demkowicz Pdf

Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods. While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources. New to the Second Edition Completely revised section on lim sup and lim inf New discussions of connected sets, probability, Bayesian statistical inference, and the generalized (integral) Minkowski inequality New sections on elements of multilinear algebra and determinants, the singular value decomposition theorem, the Cauchy principal value, and Hadamard finite part integrals New example of a Lebesgue non-measurable set Ideal for a two-semester course, this proven textbook teaches students how to prove theorems and prepares them for further study of more advanced mathematical topics. It helps them succeed in formulating research questions in a mathematically rigorous way.

Author : Jean-Pierre Aubin
Publisher : John Wiley & Sons
Page : 520 pages
File Size : 51,5 Mb
Release : 2011-09-30
Category : Mathematics
ISBN : 9781118030974

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Applied Functional Analysis by Jean-Pierre Aubin Pdf

A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition. Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveries-adding three new chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations. He presents, for the first time at an introductory level, the extension of differential calculus in the framework of both the theory of distributions and set-valued analysis, and discusses their application for studying boundary-value problems for elliptic and parabolic partial differential equations and for systems of first-order partial differential equations. To keep the presentation concise and accessible, Jean-Pierre Aubin introduces functional analysis through the simple Hilbertian structure. He seamlessly blends pure mathematics with applied areas that illustrate the theory, incorporating a broad range of examples from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and nonsmooth analysis, and more. Finally, a summary of the essential theorems as well as exercises reinforcing key concepts are provided. Applied Functional Analysis, Second Edition is an excellent and timely resource for both pure and applied mathematicians.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 631 pages
File Size : 51,9 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9781441904584

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added. Review of earlier edition: "...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references." R. Glowinski, SIAM Review, 2003

Author : Yuli Eidelman,Vitali D. Milman,Antonis Tsolomitis
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 48,9 Mb
Release : 2004
Category : Functional analysis
ISBN : 9780821836460

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Functional Analysis by Yuli Eidelman,Vitali D. Milman,Antonis Tsolomitis Pdf

This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The amount of mathematics presented in the book can well be absorbed in a year's study and will provide a sound basis for future reading. It is suitable for graduate students and researchers interested in operator theory and functional analysis.

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 421 pages
File Size : 54,9 Mb
Release : 2020-03-12
Category : Mathematics
ISBN : 9780521899642

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An Introduction to Functional Analysis by James C. Robinson Pdf

Accessible text covering core functional analysis topics in Hilbert and Banach spaces, with detailed proofs and 200 fully-worked exercises.

Author : Erwin Kreyszig
Publisher : John Wiley & Sons
Page : 706 pages
File Size : 54,8 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : 9780471504597

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Introductory Functional Analysis with Applications by Erwin Kreyszig Pdf

KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry

Author : Mischa Cotlar,Roberto Cignoli
Publisher : Unknown
Page : 585 pages
File Size : 46,8 Mb
Release : 1974
Category : Espaces linéaires normés
ISBN : 0720420660

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An Introduction to Functional Analysis by Mischa Cotlar,Roberto Cignoli Pdf

Author : Terry J. Morrison
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 47,8 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118031247

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Functional Analysis by Terry J. Morrison Pdf

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.