The Analysis Of Linear Partial Differential Operators

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The Analysis of Linear Partial Differential Operators I

Author : Lars Hörmander
Publisher : Springer
Page : 460 pages
File Size : 55,8 Mb
Release : 1990-08-10
Category : Mathematics
ISBN : 354052343X

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The Analysis of Linear Partial Differential Operators I by Lars Hörmander Pdf

The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

The Analysis of Linear Partial Differential Operators III

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 537 pages
File Size : 51,5 Mb
Release : 2007-03-15
Category : Mathematics
ISBN : 9783540499374

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The Analysis of Linear Partial Differential Operators III by Lars Hörmander Pdf

From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987. "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.

The Analysis of Linear Partial Differential Operators IV

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 52,9 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783642001369

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The Analysis of Linear Partial Differential Operators IV by Lars Hörmander Pdf

From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987 "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987 Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006

Lectures on Linear Partial Differential Equations

Author : Grigoriĭ Ilʹich Eskin
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 53,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852842

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Lectures on Linear Partial Differential Equations by Grigoriĭ Ilʹich Eskin Pdf

This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.

The Analysis of Linear Partial Differential Operators I

Author : Lars Hörmander
Publisher : Springer
Page : 454 pages
File Size : 47,9 Mb
Release : 2015-03-30
Category : Mathematics
ISBN : 9783642614972

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The Analysis of Linear Partial Differential Operators I by Lars Hörmander Pdf

The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

The Analysis of Linear Partial Differential Operators II

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 42,7 Mb
Release : 2004-11-17
Category : Mathematics
ISBN : 3540225161

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The Analysis of Linear Partial Differential Operators II by Lars Hörmander Pdf

Author received the 1962 Fields Medal Author received the 1988 Wolf Prize (honoring achievemnets of a lifetime) Author is leading expert in partial differential equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 55,7 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

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.

Fundamental Solutions of Linear Partial Differential Operators

Author : Norbert Ortner,Peter Wagner
Publisher : Springer
Page : 398 pages
File Size : 43,9 Mb
Release : 2015-08-05
Category : Mathematics
ISBN : 9783319201405

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Fundamental Solutions of Linear Partial Differential Operators by Norbert Ortner,Peter Wagner Pdf

This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell’s system and others. The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.

Semigroups of Linear Operators and Applications to Partial Differential Equations

Author : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461255611

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Semigroups of Linear Operators and Applications to Partial Differential Equations by Amnon Pazy Pdf

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Lecture Notes on Functional Analysis

Author : Alberto Bressan
Publisher : American Mathematical Soc.
Page : 265 pages
File Size : 42,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821887714

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Lecture Notes on Functional Analysis by Alberto Bressan Pdf

This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.

Fundamental Solutions for Differential Operators and Applications

Author : Prem Kythe
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 49,6 Mb
Release : 1996-07-30
Category : Mathematics
ISBN : 0817638695

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Fundamental Solutions for Differential Operators and Applications by Prem Kythe Pdf

A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.

Linear Partial Differential Equations and Fourier Theory

Author : Marcus Pivato
Publisher : Cambridge University Press
Page : 631 pages
File Size : 40,8 Mb
Release : 2010-01-07
Category : Mathematics
ISBN : 9780521199704

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Linear Partial Differential Equations and Fourier Theory by Marcus Pivato Pdf

This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.

Beyond Partial Differential Equations

Author : Horst Reinhard Beyer
Publisher : Springer
Page : 291 pages
File Size : 51,7 Mb
Release : 2007-04-10
Category : Mathematics
ISBN : 9783540711292

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Beyond Partial Differential Equations by Horst Reinhard Beyer Pdf

This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

Linear Differential Operators

Author : Cornelius Lanczos
Publisher : SIAM
Page : 581 pages
File Size : 46,9 Mb
Release : 1997-12-01
Category : Mathematics
ISBN : 1611971187

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Linear Differential Operators by Cornelius Lanczos Pdf

Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."

Partial Differential Equations I

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 54,9 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9781441970558

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Partial Differential Equations I by Michael E. Taylor Pdf

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.