Generalized Functions And Partial Differential Equations PDF Download
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Author | : Avner Friedman |
Publisher | : Courier Corporation |
Total Pages | : 22 |
Release | : 2011-11-30 |
Genre | : Mathematics |
ISBN | : 048615291X |
Download Generalized Functions and Partial Differential Equations Book in PDF, ePub and Kindle
This self-contained text details developments in the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. 1963 edition.
Author | : Georgij Evgen'evǐc Shilov |
Publisher | : |
Total Pages | : 345 |
Release | : 1968 |
Genre | : |
ISBN | : |
Download Generalized Functions and Partial Differential Equations Book in PDF, ePub and Kindle
Author | : Ram P. Kanwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 474 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468400355 |
Download Generalized Functions Theory and Technique Book in PDF, ePub and Kindle
This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.
Author | : J.F. Colombeau |
Publisher | : Elsevier |
Total Pages | : 297 |
Release | : 2011-08-18 |
Genre | : Mathematics |
ISBN | : 0080872247 |
Download Elementary Introduction to New Generalized Functions Book in PDF, ePub and Kindle
The author's previous book `New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced `new generalized functions' in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions. The aim here is to present these functions in a more direct and elementary way. In Part I, the reader is assumed to be familiar only with the concepts of open and compact subsets of R&eegr;, of C∞ functions of several real variables and with some rudiments of integration theory. Part II defines tempered generalized functions, i.e. generalized functions which are, in some sense, increasing at infinity no faster than a polynomial (as well as all their partial derivatives). Part III shows that, in this setting, the partial differential equations have new solutions. The results obtained show that this setting is perfectly adapted to the study of nonlinear partial differential equations, and indicate some new perspectives in this field.
Author | : Ram P. Kanwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 478 |
Release | : 1998-01-01 |
Genre | : Mathematics |
ISBN | : 9780817640064 |
Download Generalized Functions Theory and Technique Book in PDF, ePub and Kindle
This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.
Author | : Georgiĭ Evgenʹevich Shilov |
Publisher | : |
Total Pages | : 368 |
Release | : 1968 |
Genre | : Mathematics |
ISBN | : |
Download Generalized Functions and Partial Differential Equations Book in PDF, ePub and Kindle
Author | : Georgij Evgen'evič Šilov |
Publisher | : |
Total Pages | : 345 |
Release | : 1968 |
Genre | : Differential equations, Partial |
ISBN | : |
Download Generalized Functions and Partial Differential Equations Book in PDF, ePub and Kindle
Author | : Ram P. Kanwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 490 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681744 |
Download Generalized Functions Book in PDF, ePub and Kindle
Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
Author | : Michael Oberguggenberger |
Publisher | : Routledge |
Total Pages | : 400 |
Release | : 2022-02-28 |
Genre | : Mathematics |
ISBN | : 1351428039 |
Download Nonlinear Theory of Generalized Functions Book in PDF, ePub and Kindle
Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.
Author | : Michael Oberguggenberger |
Publisher | : Birkhäuser |
Total Pages | : 280 |
Release | : 2017-05-06 |
Genre | : Mathematics |
ISBN | : 3319519115 |
Download Generalized Functions and Fourier Analysis Book in PDF, ePub and Kindle
This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.