Green s Functions and Boundary Value Problems

Author: Ivar Stakgold
Publisher: John Wiley & Sons
ISBN: 0470906529
Format: PDF, Mobi
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Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.

Partial Differential Equations of Applied Mathematics

Author: Erich Zauderer
Publisher: John Wiley & Sons
ISBN: 1118031407
Format: PDF, Docs
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This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.

Books in Print

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Boundary Value Problems and Singular Pseudo Differential Operators

Author: Bert-Wolfgang Schulze
Publisher: Wiley
ISBN: 9780471975571
Format: PDF, Kindle
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This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. It features a self-contained presentation of the cone pseudo-differential calculus; a general method for pseudo-differential analysis on manifolds with edges for arbitrary model cones in spaces with discrete and continuous asymptotics; the presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory; and a new exposition of the pseudo-differential calculus with operator-valued symbols, based on twisted homogeneity as well as on parameter-dependent theories and reductions of orders.

Numerical Solution of Ordinary Differential Equations

Author: Kendall Atkinson
Publisher: John Wiley & Sons
ISBN: 047004294X
Format: PDF, Docs
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This is a complete and concise introduction to classical topics in the numerical solution of ordinary differential equations (ODEs). The text contains many up-to-date references to both analytical and numerical ODE literature while offering new unifying views on different problem classes.

Fourier Analysis

Author: Eric Stade
Publisher: John Wiley & Sons
ISBN: 1118165519
Format: PDF, Mobi
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A reader-friendly, systematic introduction to Fourieranalysis Rich in both theory and application, Fourier Analysispresents a unique and thorough approach to a key topic in advancedcalculus. This pioneering resource tells the full story of Fourieranalysis, including its history and its impact on the developmentof modern mathematical analysis, and also discusses essentialconcepts and today's applications. Written at a rigorous level, yet in an engaging style that doesnot dilute the material, Fourier Analysis brings twoprofound aspects of the discipline to the forefront: the wealth ofapplications of Fourier analysis in the natural sciences and theenormous impact Fourier analysis has had on the development ofmathematics as a whole. Systematic and comprehensive, the book: Presents material using a cause-and-effect approach,illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces,and related concepts Conveys information in a lucid, readable style, inspiringfurther reading and research on the subject Provides exercises at the end of each section, as well asillustrations and worked examples throughout the text Based upon the principle that theory and practice arefundamentally linked, Fourier Analysis is the ideal text andreference for students in mathematics, engineering, and physics, aswell as scientists and technicians in a broad range of disciplineswho use Fourier analysis in real-world situations.

Applied Functional Analysis

Author: Jean-Pierre Aubin
Publisher: John Wiley & Sons
ISBN: 9780471179764
Format: PDF, Kindle
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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.