Full Read and Download Reference eBook
Introduction To The Theory Of Distributions Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Introduction To The Theory Of Distributions book. This book definitely worth reading, it is an incredibly well-written.
Author : F. G. Friedlander
Publisher : Cambridge University Press
Page : 192 pages
File Size : 27,13 MB
Release : 1998
Category : Mathematics
ISBN : 9780521649711
The second edition of a classic graduate text on the theory of distributions.
Author : J. Ian Richards
Publisher : CUP Archive
Page : 172 pages
File Size : 10,52 MB
Release : 1995-09-29
Category : Mathematics
ISBN : 9780521558907
A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Author : Svetlin G. Georgiev
Publisher : Springer
Page : 217 pages
File Size : 31,19 MB
Release : 2015-07-13
Category : Mathematics
ISBN : 3319195271
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 : A.H. Zemanian
Publisher : Courier Corporation
Page : 404 pages
File Size : 42,8 MB
Release : 2011-11-30
Category : Mathematics
ISBN : 0486151948
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Author : J.J. Duistermaat
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 36,97 MB
Release : 2010-08-09
Category : Mathematics
ISBN : 0817646752
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 : Israel Halperin
Publisher :
Page : 0 pages
File Size : 17,78 MB
Release : 1952
Category : Education
ISBN : 9781487591328
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 : Robert S. Strichartz
Publisher : World Scientific
Page : 238 pages
File Size : 41,83 MB
Release : 2003
Category : Mathematics
ISBN : 9789812384300
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Author : Thomas A. Severini
Publisher : Cambridge University Press
Page : 3 pages
File Size : 13,11 MB
Release : 2005-08-08
Category : Mathematics
ISBN : 1139446118
This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.
Author : Gerd Grubb
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 29,56 MB
Release : 2008-10-14
Category : Mathematics
ISBN : 0387848940
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 : Ricardo Estrada
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 28,43 MB
Release : 2012-09-08
Category : Mathematics
ISBN : 0817681302
"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic