Partial Differential Equations Iii

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 734 pages
File Size : 43,7 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9781441970497

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Partial Differential Equations III by Michael E. Taylor Pdf

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed 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

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 45,5 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.

Author : Michael Taylor
Publisher : Springer Science & Business Media
Page : 629 pages
File Size : 44,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475741902

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Partial Differential Equations III by Michael Taylor Pdf

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed 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. ^

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 54,6 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 634 pages
File Size : 54,7 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9781441970527

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Partial Differential Equations II by Michael E. Taylor Pdf

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.

Author : Michael E. Taylor
Publisher : Unknown
Page : 740 pages
File Size : 45,7 Mb
Release : 2010-11-04
Category : Electronic
ISBN : 1441970509

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Partial Differential Equations III by Michael E. Taylor Pdf

Author : Michael Eugene Taylor
Publisher : Springer Verlag
Page : 610 pages
File Size : 45,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780387946528

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Partial Differential Equations: Nonlinear equations by Michael Eugene Taylor Pdf

THIS TEXT PROVIDES AN INTRODUCTION TO THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS. IT INTRODUCES BASIC EXAMPLES OF PARTIAL DIFFERENTIAL EQUATIONS, ARISING IN CONTINUUM MECHANICS, ELECTROMAGNETISM, COMPLEX ANALYSIS AND OTHER Areas, AND DEVELOPS A NUMBER OF TOOLS FOR THEIR SOLUTION, INCLUDING PARTICULARLY FOURIER ANALYSIS, DISTRIBUTION THEORY, AND Sobolev SPACES.

Author : Michael Ruzhansky,Jens Wirth
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 45,7 Mb
Release : 2011-05-04
Category : Mathematics
ISBN : 9783034800693

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Modern Aspects of the Theory of Partial Differential Equations by Michael Ruzhansky,Jens Wirth Pdf

The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 537 pages
File Size : 41,8 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.

Author : Sandro Salsa
Publisher : Springer
Page : 701 pages
File Size : 50,9 Mb
Release : 2015-04-24
Category : Mathematics
ISBN : 9783319150932

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Partial Differential Equations in Action by Sandro Salsa Pdf

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Author : Alexander Komech,Andrew Komech
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 44,8 Mb
Release : 2009-10-05
Category : Mathematics
ISBN : 9781441910950

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Principles of Partial Differential Equations by Alexander Komech,Andrew Komech Pdf

This concise book covers the classical tools of Partial Differential Equations Theory in today’s science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.

Author : Misha Gromov
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 41,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662022672

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Partial Differential Relations by Misha Gromov Pdf

The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 43,9 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.

Author : Michael Renardy,Robert C. Rogers
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 53,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216874

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An Introduction to Partial Differential Equations by Michael Renardy,Robert C. Rogers Pdf

Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 47,9 Mb
Release : 2013-11-08
Category : Mathematics
ISBN : 9783319020990

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Introduction to Partial Differential Equations by Peter J. Olver Pdf

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.