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Author | : Svetlin G. Georgiev |
Publisher | : Springer |
Total Pages | : 217 |
Release | : 2015-07-13 |
Genre | : Mathematics |
ISBN | : 3319195271 |
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This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
Author | : F. G. Friedlander |
Publisher | : Cambridge University Press |
Total Pages | : 192 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780521649711 |
Download Introduction to the Theory of Distributions Book in PDF, ePub and Kindle
The second edition of a classic graduate text on the theory of distributions.
Author | : J. Ian Richards |
Publisher | : CUP Archive |
Total Pages | : 172 |
Release | : 1995-09-29 |
Genre | : Mathematics |
ISBN | : 9780521558907 |
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A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Author | : J.J. Duistermaat |
Publisher | : Springer Science & Business Media |
Total Pages | : 455 |
Release | : 2010-08-09 |
Genre | : Mathematics |
ISBN | : 0817646752 |
Download Distributions Book in PDF, ePub and Kindle
This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Author | : J. Lützen |
Publisher | : Springer Science & Business Media |
Total Pages | : 241 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461394724 |
Download The Prehistory of the Theory of Distributions Book in PDF, ePub and Kindle
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
Author | : M.A. Al-Gwaiz |
Publisher | : CRC Press |
Total Pages | : 276 |
Release | : 1992-04-24 |
Genre | : Mathematics |
ISBN | : 0849306698 |
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A textbook for a graduate course in the theory of distributions and related topics, for students of applied mathematics or theoretical physics. Introduces the theory, explicates mathematical structures and the Hilbert-space aspects, and presents applications to typical boundary problems. Annotation
Author | : Gerd Grubb |
Publisher | : Springer Science & Business Media |
Total Pages | : 464 |
Release | : 2008-10-14 |
Genre | : Mathematics |
ISBN | : 0387848940 |
Download Distributions and Operators Book in PDF, ePub and Kindle
This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.
Author | : Jean F. Colombeau |
Publisher | : Springer |
Total Pages | : 193 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540475109 |
Download Multiplication of Distributions Book in PDF, ePub and Kindle
This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).
Author | : Israel Halperin |
Publisher | : |
Total Pages | : 0 |
Release | : 1952 |
Genre | : Education |
ISBN | : 9781487591328 |
Download Introduction to the Theory of Distributions Book in PDF, ePub and Kindle
This pamphlet, based on lectures given by Laurent Schwartz at the Canadian Mathematical Congress in 1951, gives a detailed introduction to the theory of distributions, in terms of classical analysis, for applied mathematicians and physicists. Mathematical Congress Lecture Series, No. 1
Author | : Gerrit Dijk |
Publisher | : Walter de Gruyter |
Total Pages | : 120 |
Release | : 2013-03-22 |
Genre | : Mathematics |
ISBN | : 3110298511 |
Download Distribution Theory Book in PDF, ePub and Kindle
The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added. It is suitable for a one-semester course at the advanced undergraduate or beginning graduate level or for self-study.