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Author: J.J. Duistermaat
Publisher: Springer Science & Business Media
ISBN: 0817646752
Category : Mathematics
Languages : en
Pages : 455
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Book Description
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.J. Duistermaat
Publisher: Springer Science & Business Media
ISBN: 0817646752
Category : Mathematics
Languages : en
Pages : 455
Get Book Here
Book Description
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: James C. Fu
Publisher: World Scientific
ISBN: 9810245874
Category : Mathematics
Languages : en
Pages : 174
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Book Description
A rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics.
Author: A.H. Zemanian
Publisher: Courier Corporation
ISBN: 0486151948
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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: Petre Teodorescu
Publisher: John Wiley & Sons
ISBN: 3527653635
Category : Science
Languages : en
Pages : 379
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Book Description
In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.
Author: R. S. Pathak
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842650202
Category : Mathematics
Languages : en
Pages : 162
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Book Description
Provides basic ideas and results of distribution theory and its applications to Fourier analysis and partial differential equations. Examples are provided to illustrate the concepts; exercises of various level of difficulty are given. Important topics covered like basic properties of distributions, convolution, Fourier transforms, Sobolev spaces, weak solutions, distributions on locally convex spaces and on differentiable manifolds.
Author: K. Balakrishnan
Publisher: Routledge
ISBN: 1351449117
Category : Mathematics
Languages : en
Pages : 668
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Book Description
The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon
Author: George Livadiotis
Publisher: Elsevier
ISBN: 0128046392
Category : Science
Languages : en
Pages : 740
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Book Description
Kappa Distributions: Theory and Applications in Plasmas presents the theoretical developments of kappa distributions, their applications in plasmas, and how they affect the underpinnings of our understanding of space and plasma physics, astrophysics, and statistical mechanics/thermodynamics. Separated into three major parts, the book covers theoretical methods, analytical methods in plasmas, and applications in space plasmas. The first part of the book focuses on basic aspects of the statistical theory of kappa distributions, beginning with their connection to the solid backgrounds of non-extensive statistical mechanics. The book then moves on to plasma physics, and is devoted to analytical methods related to kappa distributions on various basic plasma topics, spanning linear/nonlinear plasma waves, solitons, shockwaves, and dusty plasmas. The final part of the book deals with applications in space plasmas, focusing on applications of theoretical and analytical developments in space plasmas from the heliosphere and beyond, in other astrophysical plasmas. Kappa Distributions is ideal for space, plasma, and statistical physicists; geophysicists, especially of the upper atmosphere; Earth and planetary scientists; and astrophysicists. - Answers important questions, such as how plasma waves are affected by kappa distributions and how solar wind, magnetospheres, and other geophysical, space, and astrophysical plasmas can be modeled using kappa distributions - Presents the features of kappa distributions in the context of plasmas, including how kappa indices, temperatures, and densities vary among the species populations in different plasmas - Provides readers with the information they need to decide which specific formula of kappa distribution should be used for a certain occasion and system (toolbox)
Author: Gerrit Dijk
Publisher: Walter de Gruyter
ISBN: 3110298511
Category : Mathematics
Languages : en
Pages : 120
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Book Description
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.
Author: F. G. Friedlander
Publisher: Cambridge University Press
ISBN: 9780521649711
Category : Mathematics
Languages : en
Pages : 192
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Book Description
The second edition of a classic graduate text on the theory of distributions.
Author: Thu Pham-gia
Publisher: World Scientific
ISBN: 9811235309
Category : Business & Economics
Languages : en
Pages : 494
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Book Description
This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.
