Applied Functional Analysis

Applications to Mathematical Physics

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Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 9780387944425

Category: Mathematics

Page: 481

View: 4236

The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.

Applied functional analysis

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Author: D. H. Griffel

Publisher: Halsted Press

ISBN: N.A

Category: Mathematics

Page: 386

View: 2986

This introductory text examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Discusses distribution theory, Green's functions, Banach spaces, Hilbert space, spectral theory, and variational techniques. Also outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 1985 ed. Includes 25 Figures and 9 Appendices. Supplementary Problems. Indexes.

Applied Functional Analysis and Partial Differential Equations

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Author: Milan Miklav?i?

Publisher: World Scientific

ISBN: 9789810235352

Category: Mathematics

Page: 294

View: 4798

This book is an introduction to partial differential equations (PDEs) and the relevant functional analysis tools which they require. It is based on a course which has been taught at Michigan State University for a number of years. The purpose of the course, and of the book, is to give students a rapid and solid research-oriented foundation in areas of PDEs, such as semilinear parabolic equations, that include studies of the stability of fluid flows and, more generally, of the dynamics generated by dissipative systems, numerical PDEs, elliptic and hyperbolic PDEs, and quantum mechanics.

Applied Functional Analysis

Numerical Methods, Wavelet Methods, and Image Processing

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Author: Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 0824756622

Category: Mathematics

Page: 660

View: 615

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.

Applied Functional Analysis, Second Edition

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Author: J. Tinsley Oden,Leszek Demkowicz

Publisher: CRC Press

ISBN: 1420091956

Category: Mathematics

Page: 596

View: 3634

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.

Applied Functional Analysis

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Author: Jean-Pierre Aubin

Publisher: John Wiley & Sons

ISBN: 1118030974

Category: Mathematics

Page: 520

View: 9562

A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied FunctionalAnalysis was published, there has been an explosion in the numberof books on functional analysis. Yet none of these offers theunique perspective of this new edition. Jean-Pierre Aubin updateshis popular reference on functional analysis with new insights andrecent discoveries-adding three new chapters on set-valued analysisand convex analysis, viability kernels and capture basins, andfirst-order partial differential equations. He presents, for thefirst time at an introductory level, the extension of differentialcalculus in the framework of both the theory of distributions andset-valued analysis, and discusses their application for studyingboundary-value problems for elliptic and parabolic partialdifferential equations and for systems of first-order partialdifferential equations. To keep the presentation concise and accessible, Jean-Pierre Aubinintroduces functional analysis through the simple Hilbertianstructure. He seamlessly blends pure mathematics with applied areasthat illustrate the theory, incorporating a broad range of examplesfrom numerical analysis, systems theory, calculus of variations,control and optimization theory, convex and nonsmooth analysis, andmore. Finally, a summary of the essential theorems as well asexercises reinforcing key concepts are provided. Applied FunctionalAnalysis, Second Edition is an excellent and timely resource forboth pure and applied mathematicians.

Applications of Functional Analysis and Operator Theory

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

Publisher: Elsevier

ISBN: 9780080527314

Category: Mathematics

Page: 432

View: 4181

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.